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Qi, Jiang, and Chang-de Gong. "A single parameter scaling theory in a disordered layered system." Physics Letters A 127, no. 2 (1988): 105–8. http://dx.doi.org/10.1016/0375-9601(88)90393-3.
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Chakraverty, Snehashish, and Subrat Kumar Jena. "Free Vibration of Single Walled Carbon Nanotube Resting on Exponentially Varying Elastic Foundation." Curved and Layered Structures 5, no. 1 (2018): 260–72. http://dx.doi.org/10.1515/cls-2018-0019.
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Abstract In this article, free vibration of SingleWalled Carbon Nanotube (SWCNT) resting on exponentially varying Winkler elastic foundation is investigated by using Differential Quadrature Method (DQM). Euler-Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of edge conditions. Obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are illustrated to show the effects of nonuniform parameter, nonlocal parameter, aspect ratio,Winkler modulus parameter and edge conditions on the frequency parameters.
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Supponen, Outi, Danail Obreschkow, Marc Tinguely, Philippe Kobel, Nicolas Dorsaz, and Mohamed Farhat. "Scaling laws for jets of single cavitation bubbles." Journal of Fluid Mechanics 802 (August 3, 2016): 263–93. http://dx.doi.org/10.1017/jfm.2016.463.
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Fast liquid jets, called micro-jets, are produced within cavitation bubbles experiencing an aspherical collapse. Here we review micro-jets of different origins, scales and appearances, and propose a unified framework to describe their dynamics by using an anisotropy parameter $\unicode[STIX]{x1D701}\geqslant 0$, representing a dimensionless measure of the liquid momentum at the collapse point (Kelvin impulse). This parameter is rigorously defined for various jet drivers, including gravity and nearby boundaries. Combining theoretical considerations with hundreds of high-speed visualisations of bubbles collapsing near a rigid surface, near a free surface or in variable gravity, we classify the jets into three distinct regimes: weak, intermediate and strong. Weak jets ($\unicode[STIX]{x1D701}<10^{-3}$) hardly pierce the bubble, but remain within it throughout the collapse and rebound. Intermediate jets ($10^{-3}<\unicode[STIX]{x1D701}<0.1$) pierce the opposite bubble wall close to the last collapse phase and clearly emerge during the rebound. Strong jets ($\unicode[STIX]{x1D701}>0.1$) pierce the bubble early during the collapse. The dynamics of the jets is analysed through key observables, such as the jet impact time, jet speed, bubble displacement, bubble volume at jet impact and vapour-jet volume. We find that, upon normalising these observables to dimensionless jet parameters, they all reduce to straightforward functions of $\unicode[STIX]{x1D701}$, which we can reproduce numerically using potential flow theory. An interesting consequence of this result is that a measurement of a single observable, such as the bubble displacement, suffices to estimate any other parameter, such as the jet speed. Remarkably, the dimensionless parameters of intermediate and weak jets ($\unicode[STIX]{x1D701}<0.1$) depend only on $\unicode[STIX]{x1D701}$, not on the jet driver (i.e. gravity or boundaries). In the same regime, the jet parameters are found to be well approximated by power laws of $\unicode[STIX]{x1D701}$, which we explain through analytical arguments.
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Kalsi, Tara, Alessandro Romito, and Henning Schomerus. "Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling." Quantum 9 (February 26, 2025): 1651. https://doi.org/10.22331/q-2025-02-26-1651.
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A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single-parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that the scaling predictions are matched by a privileged stochastic process and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all time scales.
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Arapov, Yu G., S. V. Gudina, A. S. Klepikova, et al. "The temperature dependence of the conductivity peak values in the single and the double quantum well nanostructures n-InGaAs/GaAs after IR-illumination." Физика и техника полупроводников 51, no. 2 (2017): 281. http://dx.doi.org/10.21883/ftp.2017.02.44119.8302.
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The dependences of the longitudinal and Hall resistances on a magnetic field in n-InGaAs/GaAs heterostructures with a single and double quantum wells after infrared illumination are measured in the range of magnetic fields B=0-16 T and temperatures T=0.05-4.2 K. Analysis of the experimental results was carried out on a base of two-parameter scaling hypothesis for the integer quantum Hall effect. The value of the second (irrelevant) critical exponent of the theory of two-parameter scaling was estimated. DOI: 10.21883/FTP.2017.02.44119.8302
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Yu, Nan, Guy Delrieu, Brice Boudevillain, Pieter Hazenberg, and Remko Uijlenhoet. "Unified Formulation of Single- and Multimoment Normalizations of the Raindrop Size Distribution Based on the Gamma Probability Density Function." Journal of Applied Meteorology and Climatology 53, no. 1 (2014): 166–79. http://dx.doi.org/10.1175/jamc-d-12-0244.1.
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AbstractThis study offers a unified formulation of single- and multimoment normalizations of the raindrop size distribution (DSD), which have been proposed in the framework of scaling analyses in the literature. The key point is to consider a well-defined “general distribution” g(x) as the probability density function (pdf) of the raindrop diameter scaled by a characteristic diameter Dc. The two-parameter gamma pdf is used to model the g(x) function. This theory is illustrated with a 3-yr DSD time series collected in the Cévennes region, France. It is shown that three DSD moments (M2, M3, and M4) make it possible to satisfactorily model the DSDs, both for individual spectra and for time series of spectra. The formulation is then extended to the one- and two-moment normalization by introducing single and dual power-law models. As compared with previous scaling formulations, this approach explicitly accounts for the prefactors of the power-law models to yield a unique and dimensionless g(x), whatever the scaling moment(s) considered. A parameter estimation procedure, based on the analysis of power-law regressions and the self-consistency relationships, is proposed for those normalizations. The implementation of this method with different scaling DSD moments (rain rate and/or radar reflectivity) yields g(x) functions similar to the one obtained with the three-moment normalization. For a particular rain event, highly consistent g(x) functions can be obtained during homogeneous rain phases, whatever the scaling moments used. However, the g(x) functions may present contrasting shapes from one phase to another. This supports the idea that the g(x) function is process dependent and not “unique” as hypothesized in the scaling theory.
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BIETENHOLZ, W., and T. STRUCKMANN. "PERFECT LATTICE PERTURBATION THEORY: A STUDY OF THE ANHARMONIC OSCILLATOR." International Journal of Modern Physics C 10, no. 04 (1999): 531–53. http://dx.doi.org/10.1142/s0129183199000413.
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As an application of perfect lattice perturbation theory, we construct an O(λ) perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space, we obtain a set of 2-spin and 4-spin couplings ∝λ, which we evaluate for various masses. These couplings never involve variables separated by more than two lattice spacings. The O(λ) perfect action is simulated and compared to the standard action. We discuss the improvement for the first two energy gaps ΔE1, ΔE2 and for the scaling quantity ΔE2/ΔE1 in different regimes of the interaction parameter, and of the correlation length. For the quartic oscillator — which corresponds to an asymptotically free theory — we also discuss a classically perfect action. The single gaps perform very well, which corresponds to a clearly improved asymptotic scaling. On the other hand, it turns out to be difficult to demonstrate an improvement for the scaling ratio.
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OKABE, YUTAKA, and MACOTO KIKUCHI. "UNIVERSAL FINITE-SIZE-SCALING FUNCTIONS." International Journal of Modern Physics C 07, no. 03 (1996): 287–94. http://dx.doi.org/10.1142/s0129183196000223.
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The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions.
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Sivakumar, Adhithiya, and Jeffrey B. Weiss. "Volume Transport by a 3D Quasigeostrophic Heton." Fluids 7, no. 3 (2022): 92. http://dx.doi.org/10.3390/fluids7030092.
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Oceanic flows self-organize into coherent vortices, which strongly influence their transport and mixing properties. Counter-rotating vortex pairs can travel long distances and carry trapped fluid as they move. These structures are often modeled as hetons, viz. counter-rotating quasigeostrophic point vortex pairs with equal circulations. Here, we investigate the structure of the transport induced by a single three-dimensional heton. The transport is determined by the Hamiltonian structure of the velocity field induced by the heton’s component vortices. The dynamics display a sequence of bifurcations as one moves through the heton-induced velocity field in height. These bifurcations create and destroy unstable fixed points whose associated invariant manifolds bound the trapped volume. Heton configurations fall into three categories. Vertically aligned hetons, which are parallel to the vertical axis and have zero horizontal separation, do not move and do not transport fluid. Horizontally aligned hetons, which lie on the horizontal plane and have zero vertical separation, have a single parameter, the horizontal vortex half-separation Y, and simple scaling shows the dimensional trapped volume scales as Y3. Tilted hetons are described by two parameters, Y and the vertical vortex half-separation Z, rendering the scaling analysis more complex. A scaling theory is developed for the trapped volume of tilted hetons, showing that it scales as Z4/Y for large Z. Numerical calculations illustrate the structure of the trapped volume and verify the scaling theory.
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YU, J., Y. NAMBA, and M. SHIOKAWA. "FRACTAL ROUGHNESS CHARACTERIZATION OF SUPER-GROUND Mn-Zn FERRITE SINGLE CRYSTALS." Fractals 04, no. 02 (1996): 205–11. http://dx.doi.org/10.1142/s0218348x96000285.
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The surface of superground Mn-Zn ferrite single crystal may be identified as a self-affine fractal in the stochastic sense. The rms roughness increased as a power of the scale from 102 nm to 106 nm with the roughness exponent α=0.17±0.04, and 0.11±0.06, for grinding feed rate of 15 and 10 μm/rev, respectively. The scaling behavior coincided with the theory prediction well used for growing self-affine surfaces in the interested region for magnetic heads performance. The rms roughnesses increased with increase in the feed rate, implying that the feed rate is a crucial grinding parameter affecting the supersmooth surface roughness in the machining process.
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Zhang, Shu, Bing Wei, Qun Wei, Renxian Li, Shiguo Chen, and Ningning Song. "Optical Force of Bessel Pincer Light-Sheets Beam on a Dielectric Sphere of Arbitrary Size." Nanomaterials 12, no. 21 (2022): 3723. http://dx.doi.org/10.3390/nano12213723.
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In the framework of Generalized Lorenz–Mie theory (GLMT), based on the expansion results of electromagnetic field radiation components of Bessel pincer light sheets beam acting on dielectric particles of arbitrary size, the expression of radiation force components in a Cartesian coordinate system is obtained by using the Maxwell stress tensor method. On the one hand, the effects of the refractive index and the equivalent radius of spherical particles on the distribution of radiation force are discussed; On the other hand, the influence of beam scaling parameter and beam order of Bessel pincer light sheets beam on the distribution of radiation force are investigated. The results indicate that the changes of particle’s refractive index and effective radius only affect the distribution of radiation force. However, the beam scaling parameter and beam order of Bessel pincer light sheets beam have a very sharp impact on the convergence position, distribution range and bending degree far away from the wave source of the radiation force. Single-beam optical tweezers using the self-focusing and self-bending Bessel pincer light-sheets beam are crucial for applications such as single molecule biophysics, optical manipulation and particle separation/clearing.
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Freedman, R., and J. P. Vogiatzis. "Theory of induced‐polarization logging in a borehole." GEOPHYSICS 51, no. 9 (1986): 1830–49. http://dx.doi.org/10.1190/1.1442229.
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Currently, there is interest by the petroleum well‐logging industry in the potential use of induced polarization (IP) measurements to improve formation evaluation in shaly sands. Shell Development Company has constructed an experimental four‐electrode IP and resistivity logging tool to obtain downhole measurements in shaly sands. This study contributes to the theoretical understanding and interpretation of the dynamic (i.e., time‐dependent) response of this type of downhole IP logging device. A low‐frequency (e.g., 32 Hz or less) electric current oscillating at a single fixed frequency is applied between a pair of current electrodes in a borehole. The resulting voltages induced between pairs of potential measuring electrodes in the borehole are calculated by solving the time‐dependent Maxwell’s equations. Inductive electromagnetic (EM) coupling contributions to apparent (e.g., measured) IP phase angles are automatically taken into account. The model is applied to the study of normal logging arrays for which the voltage measuring electrodes are interior to the current electrodes. The model responses are calculated for normal arrays in both infinitely thick noninvaded formations and infinitely thick invaded formations. EM coupling contributions to apparent IP phase angles have an approximately universal dependence on a scaling parameter defined here. The scaling relationship permits the quantitative estimate of EM coupling effects for specific tool parameters (i.e., electrode spacings and frequencies) and formation characteristics (i.e., apparent conductivities). Therefore, scaling relationships of this type should be useful in the design of IP tools. An inverse method, developed for determining true formation IP phase angles and resistivities from apparent values measured by an IP tool, utilizes data from multiple pairs of voltage‐measuring electrodes and exploits the fact that, for the systems of interest, the inverse resistivity and IP problems can be “decoupled.” The assumption that IP phase angles have a logarithmic dependence on frequency over a decade frequency interval leads to a nonlinear relationship between percent frequency effect (PFE) and IP phase angle. This nonlinear relationship agrees well with experimental data.
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Tóth, László Z., Emil Bronstein, Lajos Daróczi, Doron Shilo, and Dezső L. Beke. "Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni2MnGa." Materials 16, no. 5 (2023): 2089. http://dx.doi.org/10.3390/ma16052089.
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Temporal average shapes of crackling noise avalanches, U(t) (U is the detected parameter proportional to the interface velocity), have self-similar behavior, and it is expected that by appropriate normalization, they can be scaled together according to a universal scaling function. There are also universal scaling relations between the avalanche parameters (amplitude, A, energy, E, size (area), S, and duration, T), which in the mean field theory (MFT) have the form E∝A3, S∝A2, S∝T2. Recently, it turned out that normalizing the theoretically predicted average U(t) function at a fixed size, U(t)=atexp−bt2 (a and b are non-universal, material-dependent constants) by A and the rising time, R, a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation R~A1−φ too, where φ is a mechanism-dependent constant. It was shown that φ also appears in the scaling relations E~A3−φ and S~A2−φ, in accordance with the enigma for AE, that the above exponents are close to 2 and 1, respectively (in the MFT limit, i.e., with φ= 0, they are 3 and 2, respectively). In this paper, we analyze these properties for acoustic emission measurements carried out during the jerky motion of a single twin boundary in a Ni50Mn28.5Ga21.5 single crystal during slow compression. We show that calculating from the above-mentioned relations and normalizing the time axis of the average avalanche shapes with A1−φ, and the voltage axis with A, the averaged avalanche shapes for the fixed area are well scaled together for different size ranges. These have similar universal shapes as those obtained for the intermittent motion of austenite/martensite interfaces in two different shape memory alloys. The averaged shapes for a fixed duration, although they could be acceptably scaled together, showed a strong positive asymmetry (the avalanches decelerate much slower than they accelerate) and thus did not show a shape reminiscent of an inverted parabola, predicted by the MFT. For comparison, the above scaling exponents were also calculated from simultaneously measured magnetic emission data. It was obtained that the φ values are in accordance with theoretical predictions going beyond the MFT, but the AE results for φ are characteristically different from these, supporting that the well-known enigma for AE is related to this deviation.
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Chen, X. S., та V. Dohm. "Lattice φ4 Theory of Finite-Size Effects Above the Upper Critical Dimension". International Journal of Modern Physics C 09, № 07 (1998): 1073–105. http://dx.doi.org/10.1142/s012918319800100x.
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We present a perturbative calculation of finite-size effects near Tc of the φ4 lattice model in a d-dimensional cubic geometry of size L with periodic boundary conditions for d>4. The structural differences between the φ4 lattice theory and the φ4 field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters. One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite ξ/L where ξ is the bulk correlation length. At Tc, the large-L behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to Tc of the lattice model, such as T max (L) of the maximum of the susceptibility χ, are found to scale asymptotically as Tc-T max (L) ~L-d/2, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict χ max ~Ld/2 asymptotically. On a quantitative level, the asymptotic amplitudes of this large-L behavior close to Tc have not been observed in previous MC simulations at d=5 because of nonnegligible finite-size terms ~L(4-d)/2 caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the L(4-d)/2 and L4-d terms predicted by our theory.
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LIU, DONGZI, and S. DAS SARMA. "UNIVERSALITY IN TWO–DIMENSIONAL LANDAU LEVEL LOCALIZATION." Modern Physics Letters B 07, no. 07 (1993): 449–57. http://dx.doi.org/10.1142/s0217984993000448.
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We show, based on a direct numerical calculation of the Lyapunov exponents of the system and a finite-size single parameter scaling analysis, that the strong-field Landau level localization in a disordered two-dimensional electron gas is non-universal for short-range delta function random scatterers in the sense that the critical exponents in the two lowest Landau levels are substantially different. Inclusion of Landau level coupling and/or consideration of finite range of the random scattering potential in the theory restore the universality and make the computed critical exponents approximately equal.
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Lee, GyuWon, Viswanathan Bringi, and Merhala Thurai. "The Retrieval of Drop Size Distribution Parameters Using a Dual-Polarimetric Radar." Remote Sensing 15, no. 4 (2023): 1063. http://dx.doi.org/10.3390/rs15041063.
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The raindrop size distribution (DSD) is vital for applications such as quantitative precipitation estimation, understanding microphysical processes, and validation/improvement of two-moment bulk microphysical schemes. We trace the history of the DSD representation and its linkage to polarimetric radar observables from functional forms (exponential, gamma, and generalized gamma models) and its normalization (un-normalized, single/double-moment scaling normalized). The four-parameter generalized gamma model is a good candidate for the optimal representation of the DSD variability. A radar-based disdrometer was found to describe the five archetypical shapes (from Montreal, Canada) consisting of drizzle, the larger precipitation drops and the ‘S’-shaped curvature that occurs frequently in between the drizzle and the larger-sized precipitation. Similar ‘S’-shaped DSDs were reproduced by combining the disdrometric measurements of small-sized drops from an optical array probe and large-sized drops from 2DVD. A unified theory based on the double-moment scaling normalization is described. The theory assumes the multiple power law among moments and DSDs are scaling normalized by the two characteristic parameters which are expressed as a combination of any two moments. The normalized DSDs are remarkably stable. Thus, the mean underlying shape is fitted to the generalized gamma model from which the ‘optimized’ two shape parameters are obtained. The other moments of the distribution are obtained as the product of power laws of the reference moments M3 and M6 along with the two shape parameters. These reference moments can be from dual-polarimetric measurements: M6 from the attenuation-corrected reflectivity and M3 from attenuation-corrected differential reflectivity and the specific differential propagation phase. Thus, all the moments of the distribution can be calculated, and the microphysical evolution of the DSD can be inferred. This is one of the major findings of this article.
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Wang, Xiaofeng, and Wenshuo Li. "Stability Analysis of Simple Root Seeker for Nonlinear Equation." Axioms 12, no. 2 (2023): 215. http://dx.doi.org/10.3390/axioms12020215.
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In this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of the iterative method was analyzed by fractals. We discuss the stability of all fixed points and the parameter spaces starting from the critical points with the Mathematica software. The dynamical planes of the elements with good and bad dynamical behavior are given, and the optimal parameter element with stable behavior was obtained. Finally, a numerical experiment and practical application were carried out to prove the conclusion.
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Hsiao, Pai-Yi. "Scaling Theory of a Polymer Ejecting from a Cavity into a Semi-Space." Polymers 12, no. 12 (2020): 3014. http://dx.doi.org/10.3390/polym12123014.
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A two-stage model is developed in order to understand the scaling behaviors of single polymers ejecting from a spherical cavity through a nanopore. The dynamics of ejection is derived by balancing the free energy change with the energy dissipation during a process. The ejection velocity is found to vary with the number of monomers in the cavity, m, as mz1/(Nx1D3z1) at the confined stage, and it turns to be m−z2 at the non-confined stage, where N is the chain length and D the cavity diameter. The exponents are shown to be z1=(3ν−1)−1, z2=2ν and x1=1/3, with ν being the Flory exponent. The profile of the velocity is carefully verified by performing Langevin dynamics simulations. The simulations further reveal that, at the starting point, the decreasing of m can be stalled for a good moment. It suggests the existence of a pre-stage that can be explained by using the concept of a classical nucleation theory. By trimming the pre-stage, the ejection time are properly studied by varying N, D, and ϕ0 (the initial volume fraction). The scaling properties of the nucleation time are also analyzed. The results fully support the predictions of the theory. The physical pictures are given for various ejection conditions that cover the entire parameter space.
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Brandão, Rodolfo, Jacob R. Holley, and Ory Schnitzer. "Boundary-layer effects on electromagnetic and acoustic extraordinary transmission through narrow slits." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2242 (2020): 20200444. http://dx.doi.org/10.1098/rspa.2020.0444.
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We study the problem of resonant extraordinary transmission of electromagnetic and acoustic waves through subwavelength slits in an infinite plate, whose thickness is close to a half-multiple of the wavelength. We build on the matched-asymptotics analysis of Holley & Schnitzer (2019 Wave Motion 91 , 102381 (doi:10.1016/j.wavemoti.2019.102381)), who considered a single-slit system assuming an idealized formulation where dissipation is neglected and the electromagnetic and acoustic problems are analogous. We here extend that theory to include thin dissipative boundary layers associated with finite conductivity of the plate in the electromagnetic problem and viscous and thermal effects in the acoustic problem, considering both single-slit and slit-array configurations. By considering a distinguished boundary-layer scaling where dissipative and diffractive effects are comparable, we develop accurate analytical approximations that are generally valid near resonance; the electromagnetic–acoustic analogy is preserved up to a single parameter that is provided explicitly for both scenarios. The theory is shown to be in excellent agreement with GHz-microwave and kHz-acoustic experiments in the literature.
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Selvamani, Rajendran, M. Mahaveer Sree Jayan, Rossana Dimitri, Francesco Tornabene, and Farzad Ebrahimi. "Nonlinear magneto-thermo-elastic vibration of mass sensor armchair carbon nanotube resting on an elastic substrate." Curved and Layered Structures 7, no. 1 (2020): 153–65. http://dx.doi.org/10.1515/cls-2020-0012.
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AbstractThe present paper aims at studying the nonlinear ultrasonic waves in a magneto-thermo-elastic armchair single-walled (SW) carbon nanotube (CNT) with mass sensors resting on a polymer substrate. The analytical formulation accounts for small scale effects based on the Eringen’s nonlocal elasticity theory. The mathematical model and its differential equations are solved theoretically in terms of dimensionless frequencies while assuming a nonlinear Winkler-Pasternak-type foundation. The solution is obtained by means of ultrasonic wave dispersion relations. A parametric work is carried out to check for the effect of the nonlocal scaling parameter, together with the magneto-mechanical loadings, the foundation parameters, the attached mass, boundary conditions and geometries, on the dimensionless frequency of nanotubes. The sensitivity of the mechanical response of nanotubes investigated herein, could be of great interest for design purposes in nano-engineering systems and devices.
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Murtazaev, A. K., A. B. Babaev, and G. Y. Ataeva. "Critical properties of 2d disordered 3-state antiferromagnetic potts model ON TRIANGULAR LATTICE." EPJ Web of Conferences 185 (2018): 11001. http://dx.doi.org/10.1051/epjconf/201818511001.
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By introducing a small amount of non-magnetic impurities into an antiferromagnetic (AF) two-dimensional (2D) Potts model on a triangular lattice it is that the impurities in spin systems described by this model result in the change of a first order to a second-order phase transition. The systems with linear sizes L × L = N, L = 9-144 are considered. Investigations are performed using the standard Metropolis algorithm along with Monte-Carlo single-cluster Wolff algorithm. On the basis of the theory of finite-size scaling, critical exponents (CE) are calculated: the heat capacity α, the susceptibility γ, the order parameter β, and the CE of the correlation radius ν.
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Chavas, Daniel R., and Kerry Emanuel. "Equilibrium Tropical Cyclone Size in an Idealized State of Axisymmetric Radiative–Convective Equilibrium*." Journal of the Atmospheric Sciences 71, no. 5 (2014): 1663–80. http://dx.doi.org/10.1175/jas-d-13-0155.1.
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Abstract Tropical cyclone size remains an unsolved problem in tropical meteorology, yet size plays a significant role in modulating damage. This work employs the Bryan cloud model (CM1) to systematically explore the sensitivity of the structure of an axisymmetric tropical cyclone at statistical equilibrium to the set of relevant model, initial, and environmental external parameters. The analysis is performed in a highly idealized state of radiative–convective equilibrium (RCE) governed by only four thermodynamic parameters, which are shown to modulate the storm structure primarily via modulation of the potential intensity. Using dimensional analysis, the authors find that the equilibrium radial wind profile is primarily a function of a single nondimensional parameter given by the ratio of the storm radial length scale to the parameterized eddy radial length scale. The former is found to be the ratio of the potential intensity to the Coriolis parameter, matching the prediction for the “natural” storm length scale embedded within prevailing axisymmetric tropical cyclone theory; the Rossby deformation radius is shown not to be fundamental. Beyond this primary scaling, a second nondimensional parameter representing the nondimensional Ekman suction velocity is found to modulate the far outer wind field. Implications of the primary nondimensional parameter are discussed, including the critical role of effective turbulence in modulating inner-core structure and new insight into empirical estimates of the radial mixing length.
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Vukanic, Jovan, and Rodoljub Simovic. "Reflection of keV light ions from solids at oblique and grazing incidence." Nuclear Technology and Radiation Protection 24, no. 3 (2009): 188–94. http://dx.doi.org/10.2298/ntrp0903188v.
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The particle reflection coefficient of light keV ions backscattered from heavy targets has been determined by two different analytical approaches: by the single collision model in the case of nearly perpendicular incidence and by the small-angle multiple scattering theory in the case of glancing angles of incidence. The obtained analytical formulae are approximately universal functions of the scaled transport cross-section describing the reflection of all light ions from heavy targets. Going from perpendicular to grazing incidence, the transition from pure single to pure multiple scattering type of reflection is observed. For larger values of the scaling parameter the results of these theories cover the whole region of ion incident angles and the present estimates of the particle reflection coefficient are in good agreement with the results obtained from the empirical formula of Tabata et al.
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NARENDAR, S., and S. GOPALAKRISHNAN. "A NONLOCAL CONTINUUM MECHANICS MODEL TO ESTIMATE THE MATERIAL PROPERTY OF SINGLE-WALLED CARBON NANOTUBES." International Journal of Nanoscience 11, no. 01 (2012): 1250007. http://dx.doi.org/10.1142/s0219581x1250007x.
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A subject of current technological interest is that of nanotechnology. It would appear that nonlocal continuum mechanics could potentially play a useful role in analysis related to nanotechnology applications. The present work explores this potential in the context of a specific application. The length scales associated with nanotechnology are often sufficiently small to call the applicability of classical continuum models into question. Atomic and molecular models, while certainly conceptually valid for small length scales, are difficult to formulate accurately and are almost always computationally intensive. Nonlocal continuum models represent attempts to extend the continuum approach to smaller length scales while retaining most of its many advantages. Therefore, continuum models need to be extended to consider the scale effect in nanomaterial studies. This can be accomplished through proposing nonlocal continuum mechanics models, where the internal size scale could be simply considered in constitutive equations as a material parameter. Usually, the magnitude of the nonlocal parameter e0, determines the nonlocal effect in the analysis. The modeling and analyses of nanostructures based on flexural displacement, require an accurate estimate of nonlocal scaling parameter. Such an attempt is made in the present work. From the present analysis, the value of the scale coefficient (e0a, a is carbon-carbon bond length) is recommended to be about 0.11 nm for the application of the nonlocal theory in the analysis of carbon nanotubes.
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LUMB, S., S. K. MUTHU, and K. K. SINGH. "LATTICE EQUILIBRIUM THEORY AND SIZE EFFECTS FOR BOSONS IN A BOUNDED HARMONIC POTENTIAL." International Journal of Modern Physics B 20, no. 02 (2006): 151–79. http://dx.doi.org/10.1142/s0217979206033164.
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Effects of finite spatial size of boson assemblies in traps are studied in a self-consistent lattice theory by modeling the trap as a bounded harmonic potential of size R0. The thermodynamic quantities exhibit scaling and crossover from ideal gas behaviour at small (R0/a0) to that appropriate to an unbounded harmonic potential at large (R0/a0) with a crossover parameter [Formula: see text], a0 being the harmonic oscillator length, and τ denoting the dimensionless thermal energy. The numerical results obtained earlier by computing the energy levels of the bounded harmonic oscillator fit the general structure predicted by the theory very well. For a1>10, the spatial size effects are negligible but for a1<10 they become appreciable and experimentally measurable in suitably designed traps. At low temperatures the self consistent cell size is found to be about 2.5a0 implying that the condensate is essentially a single coherent state contained in the central cell.
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Anfodillo, Tommaso, Marco Carrer, Filippo Simini, Ionel Popa, Jayanth R. Banavar, and Amos Maritan. "An allometry-based approach for understanding forest structure, predicting tree-size distribution and assessing the degree of disturbance." Proceedings of the Royal Society B: Biological Sciences 280, no. 1751 (2013): 20122375. http://dx.doi.org/10.1098/rspb.2012.2375.
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Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, whereas the metabolic scaling theory suggests that the tree number scales universally as −2 power of diameter. Here, we propose a simple functional scaling model in which these two opposing results are reconciled. Basic principles related to crown shape, energy optimization and the finite-size scaling approach were used to define a set of relationships based on a single parameter that allows us to predict the slope of the tree-size distributions in a steady-state condition. We tested the model predictions on four temperate mountain forests. Plots (4 ha each, fully mapped) were selected with different degrees of human disturbance (semi-natural stands versus formerly managed). Results showed that the size distribution range successfully fitted by the model is related to the degree of forest disturbance: in semi-natural forests the range is wide, whereas in formerly managed forests, the agreement with the model is confined to a very restricted range. We argue that simple allometric relationships, at an individual level, shape the structure of the whole forest community.
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Dawson, Thomas H. "Scaling Adult Doses of Antifungal and Antibacterial Agents to Children." Antimicrobial Agents and Chemotherapy 56, no. 6 (2012): 2948–58. http://dx.doi.org/10.1128/aac.05307-11.
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ABSTRACTMy general pharmacokinetic scaling theory is discussed for the important matter of determining pediatric dosing for existing and new therapeutic drugs when optimal, or near-optimal, dosing for adults is known. The basis for the scaling is the requirement of a time-scaled likeness of the free-drug concentration time histories of children and adults. Broad categories of single and periodic dosing are considered. The former involves the scaling of dosage, and the latter involves both the dosage and schedule. The validity of the scaling relations is demonstrated by using measurements from previously reported clinical trials with adults and children (with ages generally 1 year or older) for the relatively new antifungal agent caspofungin and for the relatively new antibacterial agent linezolid. Standard pharmacodynamic effectiveness criteria are shown to be satisfied for the scaled dosage and schedule for children to the same extent that they are for the referenced adult. Consideration of scaling from adults to children is discussed for the case of new agents where no pediatric data are available and needed parameters are determined fromin vitromeasurements and preclinical animal data. A connection is also made between the allometric representation of clearance data and the dosing formulas. Limitations of the scaling results for infants because of growth and maturational matters are discussed. The general conclusion from this work is that the scaling theory does indeed have application to pediatric dosing for children, for both confirmation and refinement of present practice and guidance in pediatric treatment with new therapeutic agents.
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Neunaber, Ingrid, Joachim Peinke, and Martin Obligado. "Application of the Townsend–George theory for free shear flows to single and double wind turbine wakes – a wind tunnel study." Wind Energy Science 7, no. 1 (2022): 201–19. http://dx.doi.org/10.5194/wes-7-201-2022.
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Abstract. The evolution of the mean velocity and the turbulence downstream of wind turbine wakes within the atmospheric boundary layer has been studied over the past decades, but an analytical description is still missing. One possibility to improve the comprehension of this is to look into the modeling of turbulent bluff body wakes. There, by means of the streamwise scaling of the centerline mean velocity deficit, the nature of the turbulence inside a wake can be classified. In this paper, we introduce the analytical model of classical wake theory as introduced by Albert Alan Townsend and William Kenneth George. To test the theories, data were obtained from wind tunnel experiments using hot-wire anemometry in the wakes of a single model wind turbine and a model wind turbine operating in the wake of an upstream model wind turbine. First, we test whether the requirements under which the Townsend–George theory is valid are fulfilled in the wake of a wind turbine. Based on this verification we apply the Townsend–George theory. Further, this framework allows for distinguishing between two types of turbulence, namely equilibrium and non-equilibrium turbulence. We find that the turbulence at the centerline is equilibrium turbulence and that non-equilibrium turbulence may be present at outer parts of the wake. Finally, we apply the Townsend–George theory to characterize the wind turbine wake, and we compare the results to the Jensen and the Bastankhah–Porté-Agel models. We find that the recent developments from the classical bluff body wake formalism can be used to further improve the wind turbine wake models. Particularly, the classical bluff body wake models perform better than the wind turbine wake models due to the presence of a virtual origin in the scalings, and we demonstrate the possibility of improving the wind turbine wake models by implementing this parameter. We also see how the dissipation changes across the wake, which is important to model wakes within wind farms correctly.
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Xia, Xi, Chengming He, and Peng Zhang. "Universality in the viscous-to-inertial coalescence of liquid droplets." Proceedings of the National Academy of Sciences 116, no. 47 (2019): 23467–72. http://dx.doi.org/10.1073/pnas.1910711116.
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We present a theory on the coalescence of 2 spherical liquid droplets that are initially stationary. The evolution of the radius of a liquid neck formed upon coalescence was formulated as an initial value problem and then solved to yield an exact solution without free parameters, with its 2 asymptotic approximations reproducing the well-known scaling relations in the inertially limited viscous and inertial regimes. The viscous-to-inertial crossover observed in previous research is also recovered by the theory, rendering the collapse of data of different viscosities onto a single curve.
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Jena, Subrat Kumar, and S. Chakraverty. "Free Vibration Analysis of Single Walled Carbon Nanotube with Exponentially Varying Stiffness." Curved and Layered Structures 5, no. 1 (2018): 201–12. http://dx.doi.org/10.1515/cls-2018-0015.
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Abstract In this paper, Differential Quadrature Method (DQM) is applied to investigate free vibration of Single Walled Carbon Nanotubes (SWCNTs) with exponentially varying stiffness based on non-local Euler-Bernoulli beam theory. Application of DQ method in the governing differential equation converts the problem to a generalized eigenvalue problem and its solution gives frequency parameters. Convergence of the results show that DQM solutions converge fast. In this article, a detailed investigation has been reported and MATLAB code has been developed to analyze the numerical results for different scaling parameters as well as for four types of boundary conditions. Present results are compared with other available results and are found to be in good agreement.
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WOSNIK, MARTIN, LUCIANO CASTILLO, and WILLIAM K. GEORGE. "A theory for turbulent pipe and channel flows." Journal of Fluid Mechanics 421 (October 25, 2000): 115–45. http://dx.doi.org/10.1017/s0022112000001385.
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A theory for fully developed turbulent pipe and channel flows is proposed which extends the classical analysis to include the effects of finite Reynolds number. The proper scaling for these flows at finite Reynolds number is developed from dimensional and physical considerations using the Reynolds-averaged Navier–Stokes equations. In the limit of infinite Reynolds number, these reduce to the familiar law of the wall and velocity deficit law respectively.The fact that both scaled profiles describe the entire flow for finite values of Reynolds number but reduce to inner and outer profiles is used to determine their functional forms in the ‘overlap’ region which both retain in the limit. This overlap region corresponds to the constant, Reynolds shear stress region (30 < y+ < 0.1R+ approximately, where R+ = u*R/v). The profiles in this overlap region are logarithmic, but in the variable y + a where a is an offset. Unlike the classical theory, the additive parameters, Bi, Bo, and log coefficient, 1/κ, depend on R+. They are asymptotically constant, however, and are linked by a constraint equation. The corresponding friction law is also logarithmic and entirely determined by the velocity profile parameters, or vice versa.It is also argued that there exists a mesolayer near the bottom of the overlap region approximately bounded by 30 < y+ < 300 where there is not the necessary scale separation between the energy and dissipation ranges for inertially dominated turbulence. As a consequence, the Reynolds stress and mean flow retain a Reynolds number dependence, even though the terms explicitly containing the viscosity are negligible in the single-point Reynolds-averaged equations. A simple turbulence model shows that the offset parameter a accounts for the mesolayer, and because of it a logarithmic behaviour in y applies only beyond y+ > 300, well outside where it has commonly been sought.The experimental data from the superpipe experiment and DNS of channel flow are carefully examined and shown to be in excellent agreement with the new theory over the entire range 1.8 × 102 < R+ < 5.3 × 105. The Reynolds number dependence of all the parameters and the friction law can be determined from the single empirical function, H = A/(ln R+)α for α > 0, just as for boundary layers. The Reynolds number dependence of the parameters diminishes very slowly with increasing Reynolds number, and the asymptotic behaviour is reached only when R+ [Gt ] 105.
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Cao, Kai, Xiangqi Bai, Yiguang Hong, and Lin Wan. "Unsupervised topological alignment for single-cell multi-omics integration." Bioinformatics 36, Supplement_1 (2020): i48—i56. http://dx.doi.org/10.1093/bioinformatics/btaa443.
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Abstract Motivation Single-cell multi-omics data provide a comprehensive molecular view of cells. However, single-cell multi-omics datasets consist of unpaired cells measured with distinct unmatched features across modalities, making data integration challenging. Results In this study, we present a novel algorithm, termed UnionCom, for the unsupervised topological alignment of single-cell multi-omics integration. UnionCom does not require any correspondence information, either among cells or among features. It first embeds the intrinsic low-dimensional structure of each single-cell dataset into a distance matrix of cells within the same dataset and then aligns the cells across single-cell multi-omics datasets by matching the distance matrices via a matrix optimization method. Finally, it projects the distinct unmatched features across single-cell datasets into a common embedding space for feature comparability of the aligned cells. To match the complex non-linear geometrical distorted low-dimensional structures across datasets, UnionCom proposes and adjusts a global scaling parameter on distance matrices for aligning similar topological structures. It does not require one-to-one correspondence among cells across datasets, and it can accommodate samples with dataset-specific cell types. UnionCom outperforms state-of-the-art methods on both simulated and real single-cell multi-omics datasets. UnionCom is robust to parameter choices, as well as subsampling of features. Availability and implementation UnionCom software is available at https://github.com/caokai1073/UnionCom. Supplementary information Supplementary data are available at Bioinformatics online.
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Zhou, Yuxing, Baicheng Mei, and Kenneth S. Schweizer. "Activated relaxation in supercooled monodisperse atomic and polymeric WCA fluids: Simulation and ECNLE theory." Journal of Chemical Physics 156, no. 11 (2022): 114901. http://dx.doi.org/10.1063/5.0079221.
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We combine simulation and Elastically Collective Nonlinear Langevin Equation (ECNLE) theory to study the activated relaxation in monodisperse atomic and polymeric Weeks–Chandler–Andersen (WCA) liquids over a wide range of temperatures and densities in the supercooled regime under isochoric conditions. By employing novel crystal-avoiding simulations, metastable equilibrium dynamics is probed in the absence of complications associated with size polydispersity. Based on a highly accurate structural input from integral equation theory, ECNLE theory is found to describe well the simulated density and temperature dependences of the alpha relaxation time of atomic fluids using a single system-specific parameter, ac, that reflects the nonuniversal relative importance of local cage and collective elastic barriers. For polymer fluids, the explicit dynamical effect of local chain connectivity is modeled at the fundamental dynamic free energy trajectory level based on a different parameter, Nc, that quantifies the degree of intramolecular correlation of bonded segment activated barrier hopping. For the flexible chain model studied, a physically intuitive value of Nc ≈ 2 results in good agreement between simulation and theory. A direct comparison between atomic and polymeric systems reveals that chain connectivity can speed up activated segmental relaxation due to weakening of equilibrium packing correlations but can slow down relaxation due to local bonding constraints. The empirical thermodynamic scaling idea for the alpha time is found to work well at high densities or temperatures but fails when both density and temperature are low. The rich and subtle behaviors revealed from simulation for atomic and polymeric WCA fluids are all well captured by ECNLE theory.
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Nino, Daniel F., Daniel Djayakarsana, and Joshua N. Milstein. "FOCAL3D: A 3-dimensional clustering package for single-molecule localization microscopy." PLOS Computational Biology 16, no. 12 (2020): e1008479. http://dx.doi.org/10.1371/journal.pcbi.1008479.
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Single-molecule localization microscopy (SMLM) is a powerful tool for studying intracellular structure and macromolecular organization at the nanoscale. The increasingly massive pointillistic data sets generated by SMLM require the development of new and highly efficient quantification tools. Here we present FOCAL3D, an accurate, flexible and exceedingly fast (scaling linearly with the number of localizations) density-based algorithm for quantifying spatial clustering in large 3D SMLM data sets. Unlike DBSCAN, which is perhaps the most commonly employed density-based clustering algorithm, an optimum set of parameters for FOCAL3D may be objectively determined. We initially validate the performance of FOCAL3D on simulated datasets at varying noise levels and for a range of cluster sizes. These simulated datasets are used to illustrate the parametric insensitivity of the algorithm, in contrast to DBSCAN, and clustering metrics such as the F1 and Silhouette score indicate that FOCAL3D is highly accurate, even in the presence of significant background noise and mixed populations of variable sized clusters, once optimized. We then apply FOCAL3D to 3D astigmatic dSTORM images of the nuclear pore complex (NPC) in human osteosaracoma cells, illustrating both the validity of the parameter optimization and the ability of the algorithm to accurately cluster complex, heterogeneous 3D clusters in a biological dataset. FOCAL3D is provided as an open source software package written in Python.
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Abreu, Rafael. "Micropolar Modeling of Shear Wave Dispersion in Marine Sediments and Deep Earth Materials: Deriving Scaling Laws." Geosciences 15, no. 4 (2025): 124. https://doi.org/10.3390/geosciences15040124.
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We draw connections between eight different theories used to describe microscopic (atomic) and macroscopic (seismological) scales. In particular, we show that all these different theories belong to a particular case of a single partial differential equation, allowing us to gain new physical insights and draw connection among them. With this general understanding, we apply the micropolar theory to the description of shear-wave dispersion in marine sediments, showing how we can reproduce observations by only using two micropolar parameters in contrast to the seventeen parameters required by modifications of Biot’s theory. We next establish direct connections between the micro (laboratory) and macro (seismological) scales, allowing us to predict (and confirm) the presence of post-perovskite in the lowermost mantle based on laboratory experiments and to predict the characteristic length Lc at which shear deformation becomes significant at seismological scales in the lowermost mantle.
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SAVVIDY, G. K., and K. G. SAVVIDY. "STRING FINE-TUNING." International Journal of Modern Physics A 08, no. 22 (1993): 3993–4011. http://dx.doi.org/10.1142/s0217751x93001624.
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We develop further a new geometrical model of a discretized string, proposed in Ref. 1, and establish its basic physical properties. The model can be considered as the natural extension of the usual Feynman amplitude of the random walks to random surfaces. Both amplitudes coincide in the case, when the surface degenerates into a single particle world line. We extend the model to open surfaces as well. The boundary contribution is proportional to the full length of the boundary, and the coefficient of proportionality can be treated as a hopping parameter of the quarks. In the limit when this parameter tends to infinity, the theory is essentially simplified. We prove that the contribution of a given triangulation to the partition function is finite and have found the explicit form for the upper bound. The question of the convergence of the full partition function remains open. In this model the string tension may vanish at the critical point, if the last one exists, and possesses a nontrivial scaling limit. The model contains hidden fermionic variables and can be considered as an independent model of hadrons.
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Wiryanto, Leo Hari, and Warsoma Djohan. "Fourth Order PDE: Model of Thin Film Flow Involving Surface Tension." Journal of the Indonesian Mathematical Society 31, no. 2 (2025): 1454. https://doi.org/10.22342/jims.v31i2.1454.
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Surface wave on thin film is considered by involving surface tension. The fluid flows on an inclined channel. The model is based on lubrication theory, and presented in a single equation of the thickness of the fluid as wave movement, and the equation is strongly nonlinear. In solving the model, scaling and linearized processes are applied. So that three physical parameters play an important role in the wave propagation: bottom inclination, length of the scaling and the surface tension. Each of those parameters is represented as a term in the equation. Then, the equation is solved numerically by an implicit finite difference method for the linearized equation, so that the solution can be used to observe the effect of those physical quantities. We found that the surface wave propagates with different speed and reducing the amplitude. When the surface tension is involved, the profile of the wave slightly changes, beside it also effect to the movement of the wave. This is simulated in this paper.
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Picard, Nicolas. "Asymmetric Competition Can Shape the Size Distribution of Trees in a Natural Tropical Forest." Forest Science 65, no. 5 (2019): 562–69. http://dx.doi.org/10.1093/forsci/fxz018.
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Abstract The architecture (here, the size distribution combined with the spatial pattern of individuals) of natural forest at demographic equilibrium can be used to infer the demographic processes that drive the forest dynamics. In particular, a constant growth rate and a constant mortality rate for all trees would generate an exponential distribution of their size, whereas the metabolic scaling theory predicts a power distribution. In an undisturbed tropical rainforest in French Guiana, the diameter distribution was significantly steeper than the best-fit exponential distribution and significantly flatter than the best-fit power distribution. A simple individual-based model of forest dynamics with asymmetric competition between trees, where the strength of competition was regulated by a single parameter, was able to predict the observed distribution. Competition drove the forest into a self-organized state with stronger inequalities of size among trees, a lower mean competition index, and a spatial pattern of trees that deviated from complete spatial randomness.
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FANG, JUN, JING SHI, XI-QUN CHEN, and ZHENG QIN. "A TWO-DIMENSIONAL CA TRAFFIC MODEL WITH DYNAMIC ROUTE CHOICES BETWEEN RESIDENCE AND WORKPLACE." International Journal of Modern Physics C 21, no. 02 (2010): 221–37. http://dx.doi.org/10.1142/s0129183110015075.
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The Biham, Middleton and Levine (BML) model is extended to describe dynamic route choices between the residence and workplace in cities. The traffic dynamic in the city with a single workplace is studied from the velocity diagram, arrival time probability distribution, destination arrival rate and convergence time. The city with double workplaces is also investigated to compare with a single workplace within the framework of four modes of urban growth. The transitional region is found in the velocity diagrams where the system undergoes a continuous transition from a moving phase to a completely jamming phase. We perform a finite-size scaling analysis of the critical density from a statistical point of view and the order parameter of this jamming transition is estimated. It is also found that statistical properties of urban traffic are greatly influenced by the urban area, workplace area and urban layout.
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Korup, Oliver, Lisa V. Luna, and Joaquin V. Ferrer. "Size scaling of large landslides from incomplete inventories." Natural Hazards and Earth System Sciences 24, no. 11 (2024): 3815–32. http://dx.doi.org/10.5194/nhess-24-3815-2024.
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Abstract. Landslide inventories have become cornerstones for estimating the relationship between the frequency and size of slope failures, thus informing appraisals of hillslope stability, erosion, and commensurate hazard. Numerous studies have reported how larger landslides are systematically rarer than smaller ones, drawing on probability distributions fitted to mapped landslide areas or volumes. In these models, much uncertainty concerns the larger landslides (defined here as affecting areas ≥ 0.1 km2) that are rarely sampled and often projected by extrapolating beyond the observed size range in a given study area. Relying instead on size-scaling estimates from other inventories is problematic because landslide detection and mapping, data quality, resolution, sample size, model choice, and fitting method can vary. To overcome these constraints, we use a Bayesian multi-level model with a generalised Pareto likelihood to provide a single, objective, and consistent comparison grounded in extreme value theory. We explore whether and how scaling parameters vary between 37 inventories that, although incomplete, bring together 8627 large landslides. Despite the broad range of mapping protocols and lengths of record, as well as differing topographic, geological, and climatic settings, the posterior power-law exponents remain indistinguishable between most inventories. Likewise, the size statistics fail to separate known earthquakes from rainfall triggers and event-based triggers from multi-temporal catalogues. Instead, our model identifies several inventories with outlier scaling statistics that reflect intentional censoring during mapping. Our results thus caution against a universal or solely mechanistic interpretation of the scaling parameters, at least in the context of large landslides.
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Ruiz, Alejandro. "Dynamic Balance: A Thermodynamic Principle for the Emergence of the Golden Ratio in Open Non-Equilibrium Steady States." Entropy 27, no. 7 (2025): 745. https://doi.org/10.3390/e27070745.
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We develop a symmetry-based variational theory that shows the coarse-grained balance of work inflow to heat outflow in a driven, dissipative system relaxed to the golden ratio. Two order-2 Möbius transformations—a self-dual flip and a self-similar shift—generate a discrete non-abelian subgroup of PGL(2,Q(5)). Requiring any smooth, strictly convex Lyapunov functional to be invariant under both maps enforces a single non-equilibrium fixed point: the golden mean. We confirm this result by (i) a gradient-flow partial-differential equation, (ii) a birth–death Markov chain whose continuum limit is Fokker–Planck, (iii) a Martin–Siggia–Rose field theory, and (iv) exact Ward identities that protect the fixed point against noise. Microscopic kinetics merely set the approach rate; three parameter-free invariants emerge: a 62%:38% split between entropy production and useful power, an RG-invariant diffusion coefficient linking relaxation time and correlation length Dα=ξz/τ, and a ϑ=45∘ eigen-angle that maps to the golden logarithmic spiral. The same dual symmetry underlies scaling laws in rotating turbulence, plant phyllotaxis, cortical avalanches, quantum critical metals, and even de-Sitter cosmology, providing a falsifiable, unifying principle for pattern formation far from equilibrium.
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Nagy, József, Sándor Nagy, and Kornél Sailer. "Time Scales of Slow-Roll Inflation in Asymptotically Safe Cosmology." Universe 11, no. 3 (2025): 77. https://doi.org/10.3390/universe11030077.
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Making use of the well-known renormalization group (RG) scale dependences of the gravitational couplings in the framework of the two-parameter Einstein–Hilbert (EH) theory of gravity, the single scalar field-driven cosmological inflation is discussed in a spatially homogeneous, isotropic, and flat model universe. The inflaton field is represented by a one-component real, non-self-interacting, massive scalar field minimally coupled to gravity. Cases without and with the incorporation of the RG scaling of the inflaton mass are compared with each other and with the corresponding classical case. It is shown that the quantum improvement drastically alters the timing of the slow-roll inflation with the desirable number N≈60 e-foldings, as compared with the classical case. Furthermore, accounting for the RG flow of the inflaton mass has an enormous effect on the timing of the desirable slow roll, too. Although providing the desirable slow-roll inflation, none of the versions of the investigated quantum-improved toy models provide a realistic value of the amplitude of the scalar perturbations.
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Lazarus, Eli D., Kirstin L. Davenport, and Ana Matias. "Dynamic allometry in coastal overwash morphology." Earth Surface Dynamics 8, no. 1 (2020): 37–50. http://dx.doi.org/10.5194/esurf-8-37-2020.
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Abstract. Allometry refers to a physical principle in which geometric (and/or metabolic) characteristics of an object or organism are correlated to its size. Allometric scaling relationships typically manifest as power laws. In geomorphic contexts, scaling relationships are a quantitative signature of organization, structure, or regularity in a landscape, even if the mechanistic processes responsible for creating such a pattern are unclear. Despite the ubiquity and variety of scaling relationships in physical landscapes, the emergence and development of these relationships tend to be difficult to observe – either because the spatial and/or temporal scales over which they evolve are so great or because the conditions that drive them are so dangerous (e.g. an extreme hazard event). Here, we use a physical experiment to examine dynamic allometry in overwash morphology along a model coastal barrier. We document the emergence of a canonical scaling law for length versus area in overwash deposits (washover). Comparing the experimental features, formed during a single forcing event, to 5 decades of change in real washover morphology from the Ria Formosa barrier system, in southern Portugal, we find differences between patterns of morphometric change at the event scale versus longer timescales. Our results may help inform and test process-based coastal morphodynamic models, which typically use statistical distributions and scaling laws to underpin empirical or semi-empirical parameters at fundamental levels of model architecture. More broadly, this work dovetails with theory for landscape evolution more commonly associated with fluvial and alluvial terrain, offering new evidence from a coastal setting that a landscape may reflect characteristics associated with an equilibrium or steady-state condition even when features within that landscape do not.
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Kormendy, John, and K. C. Freeman. "Scaling Laws for Dark Matter Halos in Late-Type and Dwarf Spheroidal Galaxies." Symposium - International Astronomical Union 220 (2004): 377–97. http://dx.doi.org/10.1017/s0074180900183706.
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Published mass models fitted to galaxy rotation curves are used to study the systematic properties of dark matter (DM) halos in late-type and dwarf spheroidal (dSph) galaxies. Halo parameters are derived by fitting non-singular isothermals to (V2 – V2vis)1/2, where V(r) is the observed rotation curve and Vvis is the rotation curve of the visible matter. the latter is calculated from the surface brightness assuming that the mass-to-light ratio M/L is constant with radius. “Maximum disk” values of M/L are adjusted to fit as much of the inner rotation curve as possible without making the halo have a hollow core. Rotation curve decomposition becomes impossible fainter than absolute magnitude Mb ≃ −14, where V becomes comparable to the velocity dispersion of the gas. To increase the luminosity range further, we include dSph galaxies, which are physically related to spiral and irregular galaxies. Combining the data, we find that DM halos satisfy well defined scaling laws analogous to the “fundamental plane” relations for elliptical galaxies. Halos in less luminous galaxies have smaller core radii rc, higher central densities ρ0, and smaller central velocity dispersions σ. Scaling laws provide new and detailed constraints on the nature of DM and on galaxy formation and evolution. Some simple implications include:1 – A single, continuous physical sequence of increasing mass extends from dSph galaxies with Mb ≃ −7.6 to Sc I galaxies with Mb ≃ −22.4.2 – the high DM densities in dSph galaxies are normal for such tiny galaxies. Since virialised density depends on collapse redshift zcoll, ρ0 ∝ (1 + zcoll)3, the smallest dwarfs formed at least Δzcoll ≃ 7 earlier than the biggest spirals.3 – the high DM densities of dSphs implies that they are real galaxies formed from primordial density fluctuations. They are not tidal fragments. Tidal dwarfs cannot retain even the low DM densities of their giant-galaxy progenitors. in contrast, dSphs have higher DM densities than do giant-galaxy progenitors.4 – the fact that, as luminosity decreases, dwarf galaxies become much more numerous and also more nearly dominated by DM raises the possibility that there exists a large population of objects that are completely dark. Such objects are a canonical prediction of cold DM theory. If they exist, “empty halos” are likely to be small and dense -that is, darker versions of Draco and UMi.5 – the slopes of the DM parameter correlations provide a measure on galactic mass scales of the slope n of the power spectrum |δk|2 ∝ kn of primordial density fluctuations. Our preliminary results, not yet corrected for baryonic compression of DM, give n ≃ –1.9 ± 0.2. This is consistent with cold DM theory.
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GUENDELMAN, E. I., and A. B. KAGANOVICH. "SSB OF SCALE SYMMETRY, FERMION FAMILIES AND QUINTESSENCE WITHOUT THE LONG-RANGE FORCE PROBLEM." International Journal of Modern Physics A 17, no. 03 (2002): 417–33. http://dx.doi.org/10.1142/s0217751x02005736.
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We study a scale-invariant two measures theory where a dilaton field ϕ has no explicit potentials. The scale transformations include the translation of a dilaton ϕ→ϕ+ const . The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame (CEF), after SSB of scale invariance, the theory develops the exponential potential and, in general, the nonlinear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. As examples, two different possibilities for the choice of the dimensionless parameters are presented where the theory permits to get interesting cosmological results. For the first choice, the theory has standard scaling solutions for ϕ usually used in the context of the quintessential scenario. For the second choice, the theory allows three different solutions, one of which is a scaling solution with equation of state pϕ=wρϕ where w is predicted to be restricted by -1<w<-0.82. The regime where the fermionic matter dominates (as compared to the dilatonic contribution) is analyzed. There it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles in CEF that appears to suggest a new approach to the family problem of particle physics. It is automatically achieved that for two of them, fermion masses are constants, the energy–momentum tensor is canonical and the "fifth force" is absent. For the third type of particles, a fermionic self-interaction appears as a result of SSB of scale invariance.
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Avsarkisov, Victor, Erich Becker, and Toralf Renkwitz. "Turbulent Parameters in the Middle Atmosphere: Theoretical Estimates Deduced from a Gravity Wave–Resolving General Circulation Model." Journal of the Atmospheric Sciences 79, no. 4 (2022): 933–52. http://dx.doi.org/10.1175/jas-d-21-0005.1.
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Abstract We present a scaling analysis for the stratified turbulent and small-scale turbulent regimes of atmospheric flow with emphasis on the mesosphere. We distinguish rotating-stratified macroturbulence turbulence (SMT), stratified turbulence (ST), and small-scale isotropic Kolmogorov turbulence (KT), and we specify the length and time scales and the characteristic velocities for these regimes. It is shown that the buoyancy scale (Lb) and the Ozmidov scale (Lo) are the main parameters that describe the transition from SMT to KT. We employ the buoyancy Reynolds number and horizontal Froude number to characterize ST and KT in the mesosphere. This theory is applied to simulation results from a high-resolution general circulation model with a Smagorinsky-type turbulent diffusion scheme for the subgrid-scale parameterization. The model allows us to derive the turbulent root-mean-square (rms) velocity in the KT regime. It is found that the turbulent RMS velocity has a single maximum in summer and a double maximum in winter months. The secondary maximum in the winter MLT we associate with a secondary gravity wave–breaking phenomenon. The turbulent rms velocity results from the model agree well with full correlation analyses based on MF-radar measurements. A new scaling for the mesoscale horizontal velocity based on the idea of direct energy cascade in mesoscales is proposed. The latter findings for mesoscale and small-scale characteristic velocities support the idea proposed in this research that mesoscale and small-scale dynamics in the mesosphere are governed by SMT, ST, and KT in the statistical average. Significance Statement Mesoscale dynamics in the middle atmosphere, which consists of atmospheric turbulence and gravity waves, remains a complex problem for atmospheric physics and climate studies. Due to its high nonlinearity, the mesoscale dynamics together with the small-scale turbulence is the primary source of uncertainties and biases in high-altitude general circulation models (GCM) in the middle atmosphere. We use the stratified turbulence theory and the gravity wave–resolving GCM to characterize different scaling regimes and to define various length, time, and velocity scales, that are relevant for the mesoscale and small-scale dynamical regimes. Our results highlight the importance of stratified turbulence in the mesosphere and lower-thermosphere region.
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Selvamani, Rajendran, M. Mahaveer Sree Jayan, and Farzad Ebrahimi. "Nonlinear ultrasonic waves in a magneto-flexo-thermally actuated single walled armchair carbon nanotube embedded on polymer matrix." World Journal of Engineering 18, no. 1 (2020): 1–13. http://dx.doi.org/10.1108/wje-02-2020-0066.
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Purpose The purpose of this paper is concerned with the study of nonlinear ultrasonic waves in a magneto-flexo-thermo (MFT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix. Design/methodology/approach A mathematical model is developed for the analytical study of nonlinear ultrasonic waves in a MFT elastic armchair single walled carbon nanotube rested on polymer matrix using Euler beam theory. The analytical formulation is developed based on Eringen’s nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analysed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations. Findings From the literature survey, it is evident that the analytical formulation of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix is not discussed by any researchers. So, in this paper the analytical solutions of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix are studied. Parametric studies is carried out to scrutinize the influence of the nonlocal scaling, magneto-electro-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter and tube geometrical parameters have significant effects on dimensionless frequency of nanotubes. Originality/value This paper contributes the analytical model to find the solution of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix. It is observed that the increase in the foundation constants raises the stiffness of the medium and the structure is able to attain higher frequency once the edge condition is C-C followed by S-S. Further, it is noticed that the natural frequency is arrived below 1% in both local and nonlocal boundary conditions in the presence of temperature coefficients. Also, it is found that the density and Poisson ratio variation affects the natural frequency with below 2%. The results presented in this study can provide mechanism for the study and design of the nano devices such as component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro--magneto-mechanical systems that make use of the wave propagation properties of ASWCNTs embedded on polymer matrix.
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Moore, Jonathan R., Arthur P. K. Argles, Kai Zhu, Chris Huntingford, and Peter M. Cox. "Validation of demographic equilibrium theory against tree-size distributions and biomass density in Amazonia." Biogeosciences 17, no. 4 (2020): 1013–32. http://dx.doi.org/10.5194/bg-17-1013-2020.
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Abstract. Predicting the response of forests to climate and land-use change depends on models that can simulate the time-varying distribution of different tree sizes within a forest – so-called forest demography models. A necessary condition for such models to be trustworthy is that they can reproduce the tree-size distributions that are observed within existing forests worldwide. In a previous study, we showed that demographic equilibrium theory (DET) is able to fit tree-diameter distributions for forests across North America, using a single site-specific fitting parameter (μ) which represents the ratio of the rate of mortality to growth for a tree of a reference size. We use a form of DET that assumes tree-size profiles are in a steady state resulting from the balance between a size-independent rate of tree mortality and tree growth rates that vary as a power law of tree size (as measured by either trunk diameter or biomass). In this study, we test DET against ForestPlots data for 124 sites across Amazonia, fitting, using maximum likelihood estimation, to both directly measured trunk diameter data and also biomass estimates derived from published allometric relationships. Again, we find that DET fits the observed tree-size distributions well, with best-fit values of the exponent relating growth rate to tree mass giving a mean of ϕ=0.71 (0.31 for trunk diameter). This finding is broadly consistent with exponents of ϕ=0.75 (ϕ=1/3 for trunk diameter) predicted by metabolic scaling theory (MST) allometry. The fitted ϕ and μ parameters also show a clear relationship that is suggestive of life-history trade-offs. When we fix to the MST value of ϕ=0.75, we find that best-fit values of μ cluster around 0.25 for trunk diameter, which is similar to the best-fit value we found for North America of 0.22. This suggests an as yet unexplained preferred ratio of mortality to growth across forests of very different types and locations.
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WEST, DAMIEN, and BRUCE J. WEST. "ON ALLOMETRY RELATIONS." International Journal of Modern Physics B 26, no. 18 (2012): 1230010. http://dx.doi.org/10.1142/s0217979212300101.
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There are a substantial number of empirical relations that began with the identification of a pattern in data; were shown to have a terse power-law description; were interpreted using existing theory; reached the level of "law" and given a name; only to be subsequently fade away when it proved impossible to connect the "law" with a larger body of theory and/or data. Various forms of allometry relations (ARs) have followed this path. The ARs in biology are nearly two hundred years old and those in ecology, geophysics, physiology and other areas of investigation are not that much younger. In general if X is a measure of the size of a complex host network and Y is a property of a complex subnetwork embedded within the host network a theoretical AR exists between the two when Y = aXb. We emphasize that the reductionistic models of AR interpret X and Y as dynamic variables, albeit the ARs themselves are explicitly time independent even though in some cases the parameter values change over time. On the other hand, the phenomenological models of AR are based on the statistical analysis of data and interpret X and Y as averages to yield the empirical AR: 〈Y〉 = a〈X〉b. Modern explanations of AR begin with the application of fractal geometry and fractal statistics to scaling phenomena. The detailed application of fractal geometry to the explanation of theoretical ARs in living networks is slightly more than a decade old and although well received it has not been universally accepted. An alternate perspective is given by the empirical AR that is derived using linear regression analysis of fluctuating data sets. We emphasize that the theoretical and empirical ARs are not the same and review theories "explaining" AR from both the reductionist and statistical fractal perspectives. The probability calculus is used to systematically incorporate both views into a single modeling strategy. We conclude that the empirical AR is entailed by the scaling behavior of the probability density, which is derived using the probability calculus.
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Li, Xiaoxia, Zhixin Feng, Qiyu Zhang, Xue Wang, and Guizhi Xu. "Scaling of Attractors of a Multiscroll Memristive Chaotic System and its Generalized Synchronization with Sliding Mode Control." International Journal of Bifurcation and Chaos 31, no. 01 (2021): 2150007. http://dx.doi.org/10.1142/s0218127421500073.
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Memristor can greatly enhance the complexity of a chaotic system because of its nonlinear characteristics. In this paper, three different memristor models are introduced to the Yang system. The chaotic attractors with single scroll and double scrolls can be obtained by adjusting the action intensities of three memristors and all the attractors inherit the scaling property of attractors of the Yang system. By employing the complex polynomials transformation method in the chaotic system to expand the number of scrolls of the system, the ring-shaped multiscroll attractors are generated, and the number of scrolls can be changed by adjusting the powers of complex polynomials, which show that the memristive system has flexible scalability. Next, a synchronization method for the multiscroll chaotic system is proposed. The generalized synchronization controller and parameter adaptive law are designed by employing sliding mode control. The sufficient conditions for synchronization are given by Lyapunov stability theory. This method can be applied to the synchronization of multiscroll systems generated by means of changing the state variables of the original system by function transformation and then adding the transformation matrix to the system. Compared with the existing synchronization method, this method has a wider scope of application, and it can synchronize two multiscroll chaotic systems with greater difference. In addition, the conditions to be satisfied in this method are simpler. Finally, the method proposed above is applied to the synchronization between a chaotic system with a ring-shaped eight-scroll attractor and a grid-shaped [Formula: see text]-scroll attractor chaotic system with interference signals. The numerical simulation results verify the effectiveness of the method.