Relevant bibliographies by topics / Oscillatory universe

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Oscillatory universe'

Author: Grafiati
Published: 5 June 2025
Last updated: 15 July 2025

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Journal articles on the topic "Oscillatory universe"

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VENKATARATNAM, K. K. "BEHAVIOR OF NON-CLASSICAL INFLATON IN THE FRW UNIVERSE." Modern Physics Letters A 28, no. 37 (2013): 1350168. http://dx.doi.org/10.1142/s021773231350168x.

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We study the semiclassical Einstein equation and inflaton in the oscillatory region of the FRW Universe. We study the relative deviation of particle production in coherent and squeezed vacuum states for a minimally coupled scalar field in the oscillatory region of flat FRW Universe. We also study the behavior of inflaton field in non-oscillatory region. We examine whether the solution obtained in slow-roll approximation satisfies Klein–Gordon equation and commutation relation as well.
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Ghosh, Partha Pratim, Saibal Ray, A. A. Usmani, and Utpal Mukhopadhyay. "Oscillatory Universe, dark energy and general relativity." Astrophysics and Space Science 345, no. 2 (2013): 367–71. http://dx.doi.org/10.1007/s10509-013-1390-9.

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VENKATARATNAM, K. K., and P. K. SURESH. "OSCILLATORY PHASE OF NONCLASSICAL THERMAL INFLATON IN FRW UNIVERSE." International Journal of Modern Physics D 19, no. 07 (2010): 1147–95. http://dx.doi.org/10.1142/s0218271810017184.

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A minimally coupled nonclassical homogeneous scalar field is examined in the flat FRW universe in the semiclassical theory of gravity. Particle production in thermal coherent and squeezed states is studied for the flat FRW universe, in the oscillatory phase of the inflaton. Solutions for the semiclassical Friedmann equations are obtained in the thermal nonclassical states. Validity of the semiclassical theory is examined in the thermal coherent and squeezed states in the oscillatory phase of inflaton. Particle creation can be enhanced due to thermal and quantum effects. Quantum fluctuations of the inflaton in thermal coherent and squeezed state formalisms are also studied. Classical gravity differ from semiclassical gravity in the thermal coherent state only by an amplitude factor.
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Belinski, Vladimir A. "On the cosmological singularity." International Journal of Modern Physics D 23, no. 07 (2014): 1430016. http://dx.doi.org/10.1142/s021827181430016x.

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Gershtein, S. S., A. A. Logunov, M. A. Mestvirishvili, and N. P. Tkachenko. "Graviton mass, quintessence, and oscillatory character of Universe evolution." Physics of Atomic Nuclei 67, no. 8 (2004): 1596–604. http://dx.doi.org/10.1134/1.1788049.

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LEHNERS, JEAN-LUC, PAUL J. STEINHARDT, and NEIL TUROK. "THE RETURN OF THE PHOENIX UNIVERSE." International Journal of Modern Physics D 18, no. 14 (2009): 2231–35. http://dx.doi.org/10.1142/s0218271809015977.

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Georges Lemaitre introduced the term "phoenix universe" to describe an oscillatory cosmology with alternating periods of gravitational collapse and expansion. This model is ruled out observationally, because it requires a supercritical mass density and cannot accommodate dark energy. However, a new cyclic theory of the universe has been proposed that evades these problems. In a recent elaboration of this picture, almost the entire universe observed today is fated to become entrapped inside black holes, but a tiny region will emerge from these ashes like a phoenix to form an even larger smooth, flat universe filled with galaxies, stars, planets, and, presumably, life. Survival depends crucially on dark energy and suggests a reason why its density is small and positive today.
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Witkowski, Lukas T., Guillem Domènech, Jacopo Fumagalli, and Sébastien Renaux-Petel. "Expansion history-dependent oscillations in the scalar-induced gravitational wave background." Journal of Cosmology and Astroparticle Physics 2022, no. 05 (2022): 028. http://dx.doi.org/10.1088/1475-7516/2022/05/028.

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Abstract Oscillations in the frequency profile of the scalar-induced contribution to the stochastic gravitational wave background are a characteristic signal for small-scale features during inflation. We investigate how this oscillatory frequency profile is affected by the expansion history of the post-inflationary universe. Our results are applicable as long as the equation of state of the universe can be taken as constant during the period in which the gravitational waves are produced, and we compute the spectrum of gravitational waves induced by both sharp and resonant features, associated with oscillations in k and log(k), respectively. For resonant features, the frequencies of the oscillatory contributions to the gravitational wave spectrum are unaffected by the equation of state, but not their relative amplitudes, allowing one to extract information about both inflationary physics and the post-inflationary expansion history from the oscillatory pattern. For sharp features we find that the gravitational wave spectrum only exhibits prominent modulations as long as the propagation speed of density fluctuations is cs < 1, with a frequency larger by a factor cs -1 than that of the scalar power spectrum. We find that the stiffer the equation of state, the larger the relative amplitude of the oscillations. In particular, a relative amplitude significantly higher than 20 % is not achievable for the `standard' case of radiation domination, and would be a smoking-gun signal of both nontrivial inflationary dynamics on small scales, and a post-inflationary universe not dominated by radiation.
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VENKATARATNAM, K. K., and P. K. SURESH. "DENSITY FLUCTUATIONS IN THE OSCILLATORY PHASE OF A NONCLASSICAL INFLATON IN THE FRW UNIVERSE." International Journal of Modern Physics D 17, no. 11 (2008): 1991–2005. http://dx.doi.org/10.1142/s0218271808013662.

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The use of the coherent and squeezed state formalisms of quantum optics for a minimally coupled nonclassical inflaton in the FRW metric is studied, in the semiclassical theory of gravity. The leading order solutions to the semiclassical Einstein equations in the coherent, squeezed and squeezed vacuum states are obtained perturbatively and exhibit power law expansion behavior. The validity of the semiclassical theory is examined in the squeezed vacuum state in the oscillatory phase of the inflaton. The semiclassical theory in the oscillatory phase of the nonclassical inflaton holds only if the associated squeezing parameter is much smaller than unity. Quantum fluctuations of the inflaton are also examined in the coherent and squeezed state formalisms.
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V. Etkin. "Local cycles of the universe." International Journal of Frontiers in Engineering and Technology Research 5, no. 1 (2023): 069–79. http://dx.doi.org/10.53294/ijfetr.2023.5.1.0019.

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The concept of the "dynamic Universe" is presented, in which the circulation of the continuum and corpuscular phases of matter with their inherent forms of energy. This process includes evolutionary and involutionary stages, the first of which begins with wave formation in the “hidden” (unstructured) part of the matter of the Universe and the transition of its “gravistatic” (potential) energy into “gravidynamic” (oscillatory) with the formation of a structured (baryonic) matter, its further compaction and complication, the formation of small and large celestial bodies, the occurrence of thermonuclear reactions in the latter, and an increase in pressure. The second stage includes their "explosion" of supernovae because of the violation of their stability, the later "big gap" and the return of matter to its original state. This circuit, occurring spontaneously in various regions of the infinite Universe, allows it to function in time and space indefinitely, bypassing the state of equilibrium. The data of astronomical observations are presented, confirming the proposed alternative to the "Standard Model" concept.
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Etkin, VA. "Perpetual movement of the universe." Aeronautics and Aerospace Open Access Journal 6, no. 2 (2022): 29–36. http://dx.doi.org/10.15406/aaoaj.2022.06.00139.

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The article substantiates the concept of the dynamic Universe, according to which the circulation of the field (continuum) and corpuscular phases of matter with their inherent forms of energy is carried out in it. This process includes evolutionary and involutionary stages, the first of which begins with wave formation in the hidden (unstructured) part of the matter of the Universe and the transition of its "gravistatic" energy into "gravidynamic" (oscillatory) with the formation of baryonic (structured) matter in the process of nucleosynthesis, the appearance in its thermonuclear reactions and its permanent compaction up to the singularity in separate regions of the Universe. The second stage includes the "explosion" of supernovae, their "big gap" and the return of matter to its original state. In this circuit, gravity plays the role of a "perpetual motion machine" that allows the Universe to function in time and space indefinitely, bypassing the state of equilibrium. The data of astronomical observations confirming the proposed concept are presented.
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Dissertations / Theses on the topic "Oscillatory universe"

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Anandan, Princia. "Two phase microfluidics: new trend in model identification." Doctoral thesis, Università di Catania, 2013. http://hdl.handle.net/10761/1303.

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The aim of the research is to give a proper understanding of the physical aspects involved in two-phase microfluidic systems: from the theoretical point of view to the development of numerical solutions for the flow field by Computational Modeling (CM) issue studies devoted to standard droplet generator for separation and segmented flow, bubble and drop formation, breakup and coalescence and then with increasing complexity in large scale microfluidic processors, bubble logic i.e. bubble to bubble hydrodynamic interaction provides an on-chip process control mechanism integrating chemistry and computation. This concept has been implemented using COMSOL multiphysics 3.5a software. These show the non-linearity, gain, bistability and programmability required for scalable universal computation. Alongside experimental work, numerical tools, such as computational fluid dynamics (CFD), allow us to study and analyses the behavior of immiscible fluids within microchannels. Good understanding of these microfluidic flows provides us with leverage when utilized in chemical and biological applications. The study in the context of micro-optofluidics analysis have allowed to define in some detail the integrated system used to Thorlabs has provided for the experiments in micro-optofluidics. In particular, the characterization of the microfluidic detection devices has been used in the experimental studies of two-phase flow. In addition, the analysis carried out in the various micro-channels fixed unique features in terms of flow rates for each dimensions. The key issue is finally the study and designs of an embedded system optofluidics in micro-optics Lab-On-Chip (LOC), which allows achieving very narrow spaces in a microfluidic system, ensuring a degree of portability, which it integrates optical realizing therefore, the right balance between the two disciplines. Played as part of a global project in which design and manufacture of micro devices LOC, and experimental studies within micro-optofluidics could easily fit in a biochemical analysis of the microscopic scale of biological particles of various kinds. The dynamical model identification of the asymptotic Time signals belonging to a microfluidic Two-Phase Flow process is presented. The experimental time series are used to synchronize another system with known mathematical model but unknown parameters: the Chua s oscillator. This system has been chosen for its simple mathematical structure and for the Possibility, respect to other chaotic systems, of mapping various non-linear experimental phenomena. A genetic algorithm was exploited for parameters estimation in relation to an optimization index that takes into an account of synchronization of master (microfluidic system) and slave system (Chua s oscillator).
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Kus, Václav. "Analogový univerzální oscilátor s transadmitančními zesilovači." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-218853.

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The aim of this thesis is to design a universal analog oscillator using transconductance amplifiers. For studying behaviour of chaotic dynamical systems can be used systems Class C. Suitable way for the purpose modeling dynamic phenomena arising in these systems is an electronic circuit that exhibits the same behavior as modeled system. After familiarization with the basic principles of synthesis of integrators systems, and studying the involvement of frequently used functional blocks were designed the concept of universal chaotic oscillator using transconductance amplifiers. The functionality of this circuit has been verified by PSpice simulation program. A typical feature of chaotic oscillator is extremely sensitivity to initial conditions. Each small change on the initial parameters can lead to major change in the shape of the attractor. The result of this thesis is a functional sample of a universal chaotic oscillator, which was verified by the dynamic behavior of the given differential equations.
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Khatib, Nabhan. "Obvody pro analogové zpracování signálů na bázi nekonvenčních aktivních prvků." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-233586.

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Disertační práce se zabývá zaváděním nových struktur moderních aktivních prvků pracujících v napěťovém, proudovém a smíšeném režimu. Funkčnost a chování těchto prvků byly ověřeny prostřednictvím SPICE simulací. V této práci je zahrnuta řada simulací, které dokazují přesnost a dobré vlastnosti těchto prvků, přičemž velký důraz byl kladen na to, aby tyto prvky byly schopny pracovat při nízkém napájecím napětí, jelikož poptávka po přenosných elektronických zařízeních a implantabilních zdravotnických přístrojích stále roste. Tyto přístroje jsou napájeny bateriemi a k tomu, aby byla prodloužena jejich životnost, trend navrhování analogových obvodů směřuje k stále většímu snižování spotřeby a napájecího napětí. Hlavním přínosem této práce je návrh nových CMOS struktur: CCII (Current Conveyor Second Generation) na základě BD (Bulk Driven), FG (Floating Gate) a QFG (Quasi Floating Gate); DVCC (Differential Voltage Current Conveyor) na základě FG, transkonduktor na základě nové techniky BD_QFG (Bulk Driven_Quasi Floating Gate), CCCDBA (Current Controlled Current Differencing Buffered Amplifier) na základě GD (Gate Driven), VDBA (Voltage Differencing Buffered Amplifier) na základě GD a DBeTA (Differential_Input Buffered and External Transconductance Amplifier) na základě BD. Dále je uvedeno několik zajímavých aplikací užívajících výše jmenované prvky. Získané výsledky simulací odpovídají teoretickým předpokladům.
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Herencsár, Norbert. "Nové aktivní funkční bloky a jejich aplikace v kmitočtových filtrech a kvadraturních oscilátorech." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2010. http://www.nusl.cz/ntk/nusl-233510.

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Kmitočtové filtry a sinusoidní oscilátory jsou lineární elektronické obvody, které jsou používány v široké oblasti elektroniky a jsou základními stavebními bloky v analogovém zpracování signálu. V poslední dekádě pro tento účel bylo prezentováno velké množství stavebních funkčních bloků. V letech 2000 a 2006 na Ústavu telekomunikací, VUT v Brně byly definovány univerzální proudový konvejor (UCC) a univerzální napět'ový konvejor (UVC) a vyrobeny ve spolupráci s firmou AMI Semiconductor Czech, Ltd. Ovšem, stále existuje požadavek na vývoj nových aktivních prvků, které nabízejí nové výhody. Hlavní přínos práce proto spočívá v definici dalších původních aktivních stavebních bloků jako jsou differential-input buffered and transconductance amplifier (DBTA), current follower transconductance amplifier (CFTA), z-copy current-controlled current inverting transconductance amplifier (ZC-CCCITA), generalized current follower differential input transconductance amplifier (GCFDITA), voltage gain-controlled modified current-feedback operational amplifier (VGC-MCFOA), a minus-type current-controlled third-generation voltage conveyor (CC-VCIII-). Pomocí navržených aktivních stavebních bloků byly prezentovány původní zapojení fázovacích článků prvního řádu, univerzální filtry druhého řádu, ekvivalenty obvodu typu KHN, inverzní filtry, aktivní simulátory uzemněného induktoru a kvadraturní sinusoidní oscilátory pracující v proudovém, napět'ovém a smíšeném módu. Chování navržených obvodů byla ověřena simulací v prostředí SPICE a ve vybraných případech experimentálním měřením.
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LAI, WEI-HAN, and 賴威翰. "Implementation and Application of Voltage-Mode Universal Biquadratic Filters and Quadrature Oscillator." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/27c4gw.

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碩士<br>明志科技大學<br>電子工程系碩士班<br>107<br>In this thesis, three voltage-mode biquadratic filters and a voltage-mode quadrature oscillator based on differential difference current conveyor transconductance amplifiers (DDCCTAs) are proposed. The first proposed circuit uses two DDCCTAs, two grounded capacitors, and two grounded resistors. The use of grounded resistors and capacitors makes the proposed circuit ideal for integrated circuit (IC) implementation. The circuit simultaneously provides low-pass (LP), band-pass (BP), high-pass (HP), and band-reject (BR) filtering responses, while the all-pass (AP) filtering response can be easily obtained by adding an input voltage signal. The circuit permits high-input impedance and offers orthogonal controllability of the quality factor (Q) and resonance angular frequency (ωo). Besides, a quadrature sinusoidal oscillator with independent control of the condition of oscillation and the oscillation frequency is second proposed by modifying the first proposed voltage-mode biquadratic filter. The second proposed oscillator provides two quadrature voltage outputs and one high-impedance amplitude-tunable current output. The oscillator can be used to provide an amplitude modulation (AM) or an amplitude shift keying signals, when the input bias current of first DDCCTA is used a modulating signal. The AM/ASK signals are widely used in communication systems. The third proposed circuit uses two DDCCTAs, two grounded capacitors, and three grounded resistors. The proposed circuit simultaneously provides voltage-mode LP, BP, HP, BR, and AP filtering responses at high-input impedance terminal, which enable easy cascadeability. No critical component-matching conditions are required, and the Q and the ωo of the circuit can be orthogonally tuned. The four proposed circuit uses a single DDCCTA combined with two grounded capacitors and three resistors that can simultaneously realize LP, BP, HP, BR, and AP filtering responses from the same configuration. The circuit also enjoys orthogonal controllable of Q and the ωo. Finally, this thesis conducted simulations for the proposed circuits using Hspice and Spectre for verifying their feasibility.
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Bruskiewich, Patrick. "The dressed oscillator approach and particle creation in two simple models of a Friedmann-Robertson-Walker Universe." Thesis, 2001. http://hdl.handle.net/2429/11466.

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In the First part of this thesis I look at the Algebraic Method which is a very straightforward technique. The idea behind the Algebraic Method is to generate all the states of a quantum system beginning with a well defined base state, generally the lowest energy state, through successive application of a creation operator (also known as a raising operator) which modifies the lowest energy state in such a fashion as to then characterize the rest of the spectrum of the system. The lowest energy state is defined as the state that is annihilated by the annihilation operator (also known as the lowering operator). Several examples of the Algebraic technique are presented including Landau Levels. In the Second part of this thesis I look at several examples of Unitary Similarity Transformations and how they can be used to simplify Hamiltonians describing quantum systems. Examples of the Similarity Transformation Method discussed in this thesis include a method to determine the ground state eigen-function using a generating function, Electron-Spin Resonance, the Foldy and Wouthuysen Transformation and an approach first proposed by Wentzel and applied by Schwinger to describe the non-relativistic interaction of an electron with a field. Schwinger used this approach to solve for the Lamb shift of the electron in a central coulombic potential. In the Third Part of this thesis I look at the Bogoliubov Transformation which can be used for Diagonalizing a Quadratic Bosonic Hamiltonian. In the Fourth Part I describe the coupling between a non-relativistic system of oscillators coupled linearly to a scalar field in ordinary Euclidean 3-space. From a physical point of view we give a nonperturbative treatment to the oscillator radiation introducing some coordinates that permit us to divide the coupled system into two parts, the "dressed" oscillator and the field. I also look at how one can describe transitions due to a forcing function. The first four sections of this thesis build up the mathematical tools, namely the Algebraic Method, the Bogoliubov transformation and the "dressed" oscillator approach, for Part Five in which I look at uniform acceleration n Rindler space, particle creation in two simple models of a Friedmann-Robertson-Walker Universe, as well as a hypothesis that Gravity is an Induced Quantum Effect.
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Schittler, Neves Fabio. "Universal Computation and Memory by Neural Switching." Doctoral thesis, 2010. http://hdl.handle.net/11858/00-1735-0000-0006-B5D1-6.

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Books on the topic "Oscillatory universe"

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Andrieu, Arnaud. Once upon a Time the Universe: Anharmonic Oscillator. Lulu Press, Inc., 2022.

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Isett, Philip. Bounds for the Corrections. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0022.

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This chapter derives the bounds for the correction terms, starting with bounds for the velocity correction. Based on V of the form V = Δ‎ x W, it introduces a proposition for estimating the spatial derivatives of W. Since the number of Wsubscript I supported at any given region of ℝ x ³ is bounded by a universal constant, it suffices to estimate Wsubscript I uniformly in I. For an individual wave, it is easy to see that the estimate will hold. During repeated differentiation, the derivative hits either the oscillatory factor, the phase direction, or the amplitude wsubscript I or one of its derivatives. In any case, the largest cost happens when differentiating the phase function. The chapter also gives estimates for derivatives of the coarse scale material derivative of W and concludes with bounds for the pressure correction.
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Book chapters on the topic "Oscillatory universe"

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De Weger, John, Doug Binks, Jaap Molenaar, and Willem Van De Water. "Universal Bifurcations in Impact Oscillators." In Solid Mechanics and Its Applications. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5778-0_50.

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Dai, Liang, and Ramesh Harjani. "Universal Model for Ring Oscillator Phase Noise." In Design of High-Performance CMOS Voltage-Controlled Oscillators. Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-1145-8_5.

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Miao, Haixing. "Universal Entanglement Between an Oscillator and Continuous Fields." In Exploring Macroscopic Quantum Mechanics in Optomechanical Devices. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25640-0_8.

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Testa, James, José Perez, and Carson Jeffries. "Evidence for Universal Chaotic Behavior of a Driven Nonlinear Oscillator." In Universality in Chaos. CRC Press, 2017. http://dx.doi.org/10.1201/9780203734636-17.

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"OSCILLATORY MOTION." In The Mechanical Universe. Cambridge University Press, 1986. http://dx.doi.org/10.1017/cbo9780511818493.013.

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"2. Dynamics of universe models." In Oscillatory Models in General Relativity. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110515367-002.

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"3. Anisotropic and homogeneous universe models." In Oscillatory Models in General Relativity. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110515367-003.

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"6. Time dependent constants in an oscillatory universe." In Oscillatory Models in General Relativity. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110515367-006.

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"4. Metric waves in a nonstationary universe and dissipative oscillator." In Oscillatory Models in General Relativity. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110515367-004.

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"5. Bosonic and fermionic models of a Friedman–Robertson–Walker universe." In Oscillatory Models in General Relativity. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110515367-005.

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Conference papers on the topic "Oscillatory universe"

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Lombardi, Michael A. "Determining the Uncertainty of Frequency Measurements Referenced to GPS Disciplined Oscillators." In NCSL International Workshop & Symposium. NCSL International, 2013. http://dx.doi.org/10.51843/wsproceedings.2013.34.

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GPS disciplined oscillators (GPSDOs) are commonly used as references for frequency calibrations. Over long intervals, a GPSDO is an inherently accurate source of frequency because it is continuously adjusted to agree with the Coordinated Universal Time (UTC) time scale maintained by the United States Naval Observatory (USNO). However, most frequency calibrations last for intervals of one day or less, and it can be difficult for metrologists to determine the uncertainty of a GPSDO during a short interval, and even more difficult to prove their uncertainty claims to skeptical laboratory assessors. This paper can serve as a guide to metrologists and laboratory assessors who work with GPSDOs as frequency standards. It describes the relationship between GPS time and Coordinated Universal Time (UTC) and explains why GPS time is traceable to the SI. It discusses how a GPSDO utilizes the GPS signals to control the frequency of its local oscillator. It explains how to estimate frequency stability, and how to apply estimates of frequency stability to determine the uncertainty of a GPSDO used as the reference for a frequency calibration.
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Klomkarn, Kitdakorn, and Pitikhate Sooraksa. "A Universal-Mode Chaotic Oscillator." In 2019 Joint International Conference on Digital Arts, Media and Technology with ECTI Northern Section Conference on Electrical, Electronics, Computer and Telecommunications Engineering (ECTI DAMT-NCON). IEEE, 2019. http://dx.doi.org/10.1109/ecti-ncon.2019.8692295.

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Kaplan, A. E. "Quantum Stairs and Multi-Rabi Chaos in a Driven Anharmonic Oscillator." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.oc510.

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A single magnetized electron driven by the EM wave in the vicinity of the cyclotron frequency can exhibit large hysteretic resonance caused by a tiny relativistic change of its mass [1]. Consistent with the theory [1] this effect has recently been observed in experiment [2]. The theory of this most fundamental multi-stable interaction of light with matter can be developed using a simple model of a quantum anharmonic oscillator driven by a periodic force. Making a common assumption that quantum transitions occur only between neighboring slightly-nonequidistant eigenstates of the oscillator, one can describe the dynamics of the system by infinite number of coupled kinetic equations for the density matrix elements at each eigenstate. We found that the reaction of the system (expressed in the terms of expectation energy of excitation) dramatically depends on the speed of sweeping frequency of the driving force near the cyclotron resonance. If the driving frequency is swept downward infinitesimally slow and no dissipation is present, the system’s response shows strongly pronounced train of "quantum stairs" at the raising slope of the function "energy vs. driving frequency" (Fig. 1) starting at the main (cyclotron) frequency Ωr which is a resonant frequency of the unperturbed (i.e. harmonic) oscillator. The height of each of these stairs is ħΩr and they are equidistantly spaced by ΔΩsp = Ωn−Ωn−1 such that ΔΩsp/Ωr = ħΩr/moc2 = krre/α, where kr = Ωr/c, re = e2/moc2 is a classical electron radius, and α = e2/ħc = 1/137 is a fine structure constant; e.g., at λr = 2mm, ΔΩsp = 180.76 Hz. The stair of each consequent order n can be interpreted as an adiabaticly slow Landau-Zenner transition between (n-1)th and n-th excited level respectively. However, when the frequency sweeping is sufficiently fast, these transitions become oscillatory with the oscillations at each one of them being due to a Rabi frequency pertinent to that individual transition. Since all of them are coupled and since due to the anharmonicity all the Rabi oscillations form an infinite set of incommensurate frequencies, these oscillations evolve into strongly chaotic motion (Fig. 2). These quantum effects are universal and should exist in any anharmonic oscillator as long as its anharmonicity is much stronger than dissipation, i.e. when ΔΩspτ ≫ 1, where τ is relaxation time of the system (for a single cyclotron electron with its energy dissipation attributed to the synchrotron radiation, ΔΩspτ = 3/2α = 205.5). This work is supported by AFOSR.
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4

Korotin, S., and K. Kiselev. "Grid of NLTE corrections for sulfur lines in the atmospheres of A–K stars." In Modern astronomy: from the Early Universe to exoplanets and black holes. Special Astrophysical Observatory of the Russian Academy of Sciences, 2024. https://doi.org/10.26119/vak2024.067.

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A correction grid is presented to take into account the influence of departures from local thermodynamic equilibrium on sulfur lines in the atmospheres of stars in the range of spectral classes from A to K. The correction grid was obtained using the atomic model of sulfur that takes into account the most modern atomic data on collision rates with electrons and hydrogen. The influence of NLTE effects on lines in both the optical and IR regions, including lines in the H-band, is considered. For some lines of neutral sulfur, which are practically not subject to NLTE effects, the wavelengths and oscillator strengths in the solar spectrum have been refined. The modified atomic model of sulfur, used to determine the sulfur abundance from the spectra of stars of different metallicities, has shown its reliability and adequacy. All sulfur lines are well described by similar element contents, regardless of their sensitivity to the influence of NLTE effects.
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Harte, Peter, Eoghan O'Riordan, Elena Blokhina, Orla Feely, and Dimitri Galayko. "Universal nonlinear phenomena in a class of electronic oscillators." In 2015 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2015. http://dx.doi.org/10.1109/iscas.2015.7168981.

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6

Wareechol, Eakluck, Montree Kumngern, and Usa Torteanchai. "Quadrature Oscillator/Universal Filter Using CCCII with Adjustable Gain." In 2018 22nd International Computer Science and Engineering Conference (ICSEC). IEEE, 2018. http://dx.doi.org/10.1109/icsec.2018.8712631.

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7

Pertz, Oliver, Bernd Roth, Dominique Schreurs, and Adalbert Beyer. "A Universal Circuit for Microwave and Millimeterwave Oscillator Applications." In 53rd ARFTG Conference Digest. IEEE, 1999. http://dx.doi.org/10.1109/arftg.1999.327354.

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8

Shen, Yongjun, and Shaopu Yang. "Main Resonance of a Nonlinear Oscillator Under Semi-Active Control." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84724.

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The main resonance of a nonlinear oscillator under semi-active control is investigated, where the bifurcation and singularity are also included. The Main resonance is obtained analytically at first, and then all the bifurcation diagrams are researched and classified in the space composed of the amplitude of excitation and the detuning parameter through singularity theory. It could be proved that the response is the universal unfolding of the winged cusp bifurcation, and all of the bifurcation diagrams of the system are verified through numerical method. It is shown that this analytical method could not only analyze the response of the semi-active control oscillator, but also research the global dynamic behavior.
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Prommee, Pipat, Montri Somdunyakanok, and Kobchai Dejhan. "Universal filter and its oscillator modification employing only active components." In 2008 International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS 2008). IEEE, 2009. http://dx.doi.org/10.1109/ispacs.2009.4806759.

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10

Balasubramanian, Sathish, and Richard A. Skop. "Modeling Vortex-Excited Vibrations of Uniform Cylinders in Uniform and Shear Flow." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0050.

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Abstract In recent years, nonlinear wake oscillator models have been shown to arise as a leading order approximation to the vortex shedding instability from a circular cylinder in a uniform flow (Alberéde and Monkewitz, 1992). Skop and Balasubramanian (1995) and Balasubramanian and Skop (1996) have extended the Van der Pol oscillator to model vortex shedding in non-uniform flow scenarios by introducing an axial diffusive coupling term in the equation. The results of their investigations have yielded a universal linear relationship between a turbulent kinematic viscosity that scales the diffusive coupling term and the shear parameter that quantifies the shear in the flow. In this paper, following Skop and Balasubramanian (1997), we use the diffusively coupled Van der Pol oscillator as the governing equation for one component of the fluctuating lift force on the cylinder. The second component of the lift force is represented by a stall term which is linearly proportional to the transverse velocity of the cylinder. The coupled fluid-structural equations are employed to numerically simulate the response of a uniform pivoted cylinder in uniform and shear flow. The numerically predicted response amplitudes and bounds of lock-in are compared to available experimental results.
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