Journal articles: 'Gibbs potential'

1

Lee, M. Howard. "Chemical potential: Gibbs-Duhem approach." Physical Review E 53, no. 5 (May 1, 1996): 5488–90. http://dx.doi.org/10.1103/physreve.53.5488.

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Chen, Long-Qing. "Chemical potential and Gibbs free energy." MRS Bulletin 44, no. 7 (July 2019): 520–23. http://dx.doi.org/10.1557/mrs.2019.162.

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Castillo, Enrique, Juan Ferrándiz, and Pilar Sanmartı́n. "Potential approach in marginalizing Gibbs models." International Journal of Approximate Reasoning 21, no. 3 (August 1999): 257–90. http://dx.doi.org/10.1016/s0888-613x(99)00026-2.

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SHINOHARA, TADATOMI, MARTIN V. SMALLEY, and IKUO S. SOGAMI. "GIBBS FREE ENERGY OF A SYSTEM OF TWO HIGHLY CHARGED PLATES IMMERSED IN AN ELECTROLYTE." International Journal of Modern Physics B 19, no. 20 (August 10, 2005): 3217–41. http://dx.doi.org/10.1142/s0217979205032061.

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The Gibbs free energy of two highly charged plates immersed in an electrolyte solution in a finite container is investigated using mean field theory. Adiabatic potential of the charged plates, which is derived from the Gibbs free energy, has a long-range weak attractive part and medium range strong repulsive part under the Dirichlet boundary condition. From comparison with the Helmholtz adiabatic potential, it is proved that the two adiabatic potentials have qualitatively the same structure of a repulsive component and an attractive component and that the Gibbs adiabatic potential shows the stronger attractive effect.

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Feistel, Rainer, and Eberhard Hagen. "On the GIBBS thermodynamic potential of seawater." Progress in Oceanography 36, no. 4 (January 1995): 249–327. http://dx.doi.org/10.1016/0079-6611(96)00001-8.

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Feistel, Rainer, and Eberhard Hagen. "A Gibbs thermodynamic potential of sea ice." Cold Regions Science and Technology 28, no. 2 (October 1998): 83–142. http://dx.doi.org/10.1016/s0165-232x(98)00014-7.

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HARIYA, YUU, and HIROFUMI OSADA. "DIFFUSION PROCESSES ON PATH SPACES WITH INTERACTIONS." Reviews in Mathematical Physics 13, no. 02 (February 2001): 199–220. http://dx.doi.org/10.1142/s0129055x01000661.

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We construct dynamics on path spaces C (ℝ; ℝ) and C([-r, r];ℝ) whose equilibrium states are Gibbs measures with free potential φ and interaction potential ψ. We do this by using the Dirichlet form theory under very mild conditions on the regularity of potentials. We take the carré du champ similar to the one of the Ornstein–Uhlenbeck process on C([0, ∞);ℝ). Our dynamics are non-Gaussian because we take Gibbs measures as reference measures. Typical examples of free potentials are double-well potentials and interaction potentials are convex functions. In this case the associated infinite-volume Gibbs measures are singular to any Gaussian measures on C(ℝ;ℝ).

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Yang, Qiang, Chaoyi Li, and Yaoru Liu. "Time-Independent Plasticity Formulated by Inelastic Differential of Free Energy Function." Journal of Non-Equilibrium Thermodynamics 46, no. 3 (March 19, 2021): 221–34. http://dx.doi.org/10.1515/jnet-2020-0076.

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Abstract The authors presented a time-independent plasticity approach, where a typical plastic-loading process is viewed as an infinitesimal state change of two neighboring equilibrium states, and the yield and consistency conditions are formulated based on the conjugate forces of the internal variables. In this paper, a stability condition is proposed, and the yield, consistency, and stability conditions are reformatted by the inelastic differential form of the Gibbs free energy. The Gibbs equation in thermodynamics with internal variables is a representation to the differential form of the Gibbs free energy by a single Gibbs free energy function. In this paper, we propose the so-called extended Gibbs equation, where the differential form may be represented by multiple potential functions. Various associated and nonassociated plasticity with a single or multiple yield functions can be derived from various representations based on the reformulated approach, where yield and plastic potential functions are in the form of inelastic differentials of the potential functions. The generalized Drucker inequality can only be derived from the one-potential representation as a stability condition. For a multiple-potential representation, the stability condition can be ensured if the multiple potentials are concave functions and possess the same stationary point.

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9

Lee, M. Howard. "Chemical potential, Gibbs–Duhem equation and quantum gases." International Journal of Modern Physics B 31, no. 13 (March 2017): 1750104. http://dx.doi.org/10.1142/s0217979217501041.

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Thermodynamic relations like the Gibbs–Duhem are valid from the lowest to the highest temperatures. But they cannot by themselves provide any specific temperature behavior of thermodynamic functions like the chemical potential. In this work, we show that if some general conditions are attached to the Gibbs–Duhem equation, it is possible to obtain the low temperature form of the chemical potential for the ideal Fermi and Bose gases very directly.

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Feistel, Rainer. "A new extended Gibbs thermodynamic potential of seawater." Progress in Oceanography 58, no. 1 (July 2003): 43–114. http://dx.doi.org/10.1016/s0079-6611(03)00088-0.

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Lee, Sangyong, Prasad Yedlapalli, and Jae W. Lee. "Excess Gibbs Potential Model for Multicomponent Hydrogen Clathrates." Journal of Physical Chemistry B 110, no. 51 (December 2006): 26122–28. http://dx.doi.org/10.1021/jp063431y.

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12

Rastegar, Reza, Alexander Roitershtein, Vadim Roytershteyn, and Jiyeon Suh. "Discrete-Time Langevin Motion in a Gibbs Potential." Applied Mathematics 03, no. 12 (2012): 2032–37. http://dx.doi.org/10.4236/am.2012.312a280.

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13

Feistel, R., W. Wagner, V. Tchijov, and C. Guder. "Numerical implementation and oceanographic application of the Gibbs potential of ice." Ocean Science 1, no. 1 (May 31, 2005): 29–38. http://dx.doi.org/10.5194/os-1-29-2005.

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Abstract. The 2004 Gibbs thermodynamic potential function of naturally abundant water ice is based on much more experimental data than its predecessors, is therefore significantly more accurate and reliable, and for the first time describes the entire temperature and pressure range of existence of this ice phase. It is expressed in the ITS-90 temperature scale and is consistent with the current scientific pure water standard, IAPWS-95, and the 2003 Gibbs potential of seawater. The combination of these formulations provides sublimation pressures, freezing points, and sea ice properties covering the parameter ranges of oceanographic interest. This paper provides source code examples in Visual Basic, Fortran and C++ for the computation of the Gibbs function of ice and its partial derivatives. It reports the most important related thermodynamic equations for ice and sea ice properties.

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Feistel, R., W. Wagner, V. Tchijov, and C. Guder. "Numerical implementation and oceanographic application of the Gibbs potential of ice." Ocean Science Discussions 2, no. 1 (February 3, 2005): 37–61. http://dx.doi.org/10.5194/osd-2-37-2005.

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Abstract. The 2004 Gibbs thermodynamic potential function of naturally abundant water ice is based on much more experimental data than its predecessors, is therefore significantly more accurate and reliable, and for the first time describes the entire temperature and pressure range of existence of this ice phase. It is expressed in the ITS-90 temperature scale and is consistent with the current scientific pure water standard, IAPWS-95, and the 2003 Gibbs potential of seawater. The combination of these formulations provides sublimation pressures, freezing points, and sea ice properties covering the parameter ranges of oceanographic interest. This paper provides source code examples in Visual Basic, Fortran and C++ for the computation of the Gibbs function of ice and its partial derivatives. It reports the most important related thermodynamic equations for ice and sea ice properties.

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Vaninsky, K. L. "Gibbs' States for Moser-Calogero Potentials." International Journal of Modern Physics B 11, no. 01n02 (January 20, 1997): 203–11. http://dx.doi.org/10.1142/s0217979297000277.

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We present two independent approaches for computing the thermodynamics for classical particles interacting via the Moser-Calogero potential Combining the results we conjecture the form of equation of state or, what is equivalent, the asymptotics of the Jacobian between volume elements corresponding to two symplectic structures on the phase space.

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Feistel, R. "Numerical implementation and oceanographic application of the Gibbs thermodynamic potential of seawater." Ocean Science Discussions 1, no. 1 (November 17, 2004): 1–19. http://dx.doi.org/10.5194/osd-1-1-2004.

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Abstract. The 2003 Gibbs thermodynamic potential function represents a very accurate, compact, consistent and comprehensive formulation of equilibrium properties of seawater. It is expressed in the International Temperature Scale ITS-90 and is fully consistent with the current scientific pure water standard, IAPWS-95. Source code examples in FORTRAN, C++ and Visual Basic are presented for the numerical implementation of the potential function and its partial derivatives, as well as for potential temperature. A collection of thermodynamic formulas and relations is given for possible applications in oceanography, from density and chemical potential over entropy and potential density to mixing heat and entropy production. For colligative properties like vapour pressure, freezing points, and for a Gibbs potential of sea ice, the equations relating the Gibbs function of seawater to those of vapour and ice are presented.

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Feistel, R. "Numerical implementation and oceanographic application of the Gibbs thermodynamic potential of seawater." Ocean Science 1, no. 1 (April 12, 2005): 9–16. http://dx.doi.org/10.5194/os-1-9-2005.

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Abstract. The 2003 Gibbs thermodynamic potential function represents a very accurate, compact, consistent and comprehensive formulation of equilibrium properties of seawater. It is expressed in the International Temperature Scale ITS-90 and is fully consistent with the current scientific pure water standard, IAPWS-95. Source code examples in FORTRAN, C++ and Visual Basic are presented for the numerical implementation of the potential function and its partial derivatives, as well as for potential temperature. A collection of thermodynamic formulas and relations is given for possible applications in oceanography, from density and chemical potential over entropy and potential density to mixing heat and entropy production. For colligative properties like vapour pressure, freezing points, and for a Gibbs potential of sea ice, the equations relating the Gibbs function of seawater to those of vapour and ice are presented.

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Bobrov, V. B., and S. A. Trigger. "Virial theorem and Gibbs thermodynamic potential for Coulomb systems." Physics of Plasmas 21, no. 10 (October 2014): 100703. http://dx.doi.org/10.1063/1.4897175.

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19

Smit, B., and D. Frenkel. "Calculation of the chemical potential in the Gibbs ensemble." Molecular Physics 68, no. 4 (November 1989): 951–58. http://dx.doi.org/10.1080/00268978900102651.

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20

YAYAMA, YUKI. "On factors of Gibbs measures for almost additive potentials." Ergodic Theory and Dynamical Systems 36, no. 1 (August 11, 2014): 276–309. http://dx.doi.org/10.1017/etds.2014.50.

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Let$(X,{\it\sigma}_{X}),(Y,{\it\sigma}_{Y})$be one-sided subshifts and${\it\pi}:X\rightarrow Y$a factor map. Suppose that$X$has the specification property. Let${\it\mu}$be a unique invariant Gibbs measure for a sequence of continuous functions${\mathcal{F}}=\{\log f_{n}\}_{n=1}^{\infty }$on$X$, which is an almost additive potential with bounded variation. We show that${\it\pi}{\it\mu}$is a unique invariant Gibbs measure for a sequence of continuous functions${\mathcal{G}}=\{\log g_{n}\}_{n=1}^{\infty }$on$Y$. When$(X,{\it\sigma}_{X})$is a full shift, we characterize${\mathcal{G}}$and${\it\mu}$by using relative pressure. This${\mathcal{G}}$is a generalization of a continuous function found by Pollicott and Kempton in their work on factors of Gibbs measures for continuous functions. We also consider the following question: given a unique invariant Gibbs measure${\it\nu}$for a sequence of continuous functions${\mathcal{F}}_{2}$on$Y$, can we find an invariant Gibbs measure${\it\mu}$for a sequence of continuous functions${\mathcal{F}}_{1}$on$X$such that${\it\pi}{\it\mu}={\it\nu}$? We show that such a measure exists under a certain condition. In particular, if$(X,{\it\sigma}_{X})$is a full shift and${\it\nu}$is a unique invariant Gibbs measure for a function in the Bowen class, then there exists a preimage${\it\mu}$of ${\it\nu}$which is a unique invariant Gibbs measure for a function in the Bowen class.

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Koukkari, Pertti, and Risto Pajarre. "A Gibbs energy minimization method for constrained and partial equilibria." Pure and Applied Chemistry 83, no. 6 (May 4, 2011): 1243–54. http://dx.doi.org/10.1351/pac-con-10-09-36.

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The conventional Gibbs energy minimization methods apply elemental amounts of system components as conservation constraints in the form of a stoichiometric conservation matrix. The linear constraints designate the limitations set on the components described by the system constituents. The equilibrium chemical potentials of the constituents are obtained as a linear combination of the component-specific contributions, which are solved with the Lagrange method of undetermined multipliers. When the Gibbs energy of a multiphase system is also affected by conditions due to immaterial properties, the constraints must be adjusted by the respective entities. The constrained free energy (CFE) minimization method includes such conditions and incorporates every immaterial constraint accompanied with its conjugate potential. The respective work or affinity-related condition is introduced to the Gibbs energy calculation as an additional Lagrange multiplier. Thus, the minimization procedure can include systemic or external potential variables with their conjugate coefficients as well as non-equilibrium affinities. Their implementation extends the scope of Gibbs energy calculations to a number of new fields, including surface and interface systems, multi-phase fiber suspensions with Donnan partitioning, kinetically controlled partial equilibria, and pathway analysis of reaction networks.

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Capitelli, M., and D. Giordano. "Demythicizing the Gibbs Potential for Determination of Chemical Equilibrium Conditions." Journal of Thermophysics and Heat Transfer 16, no. 2 (April 2002): 283–85. http://dx.doi.org/10.2514/2.6679.

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Iuliia, Mazur, Kosterin Sergiy, Veklich Tetyana, and Shkrabak Oleksandr. "Gibbs-Donnan Potential as a Tool for Membrane Vesicles Polarization." Journal of Biophysical Chemistry 05, no. 02 (2014): 78–89. http://dx.doi.org/10.4236/jbpc.2014.52009.

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Koralov, Leonid. "An inverse problem for Gibbs fields with hard core potential." Journal of Mathematical Physics 48, no. 5 (May 2007): 053301. http://dx.doi.org/10.1063/1.2719141.

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Misra, Anil, and Payam Poorsolhjouy. "Granular micromechanics model of anisotropic elasticity derived from Gibbs potential." Acta Mechanica 227, no. 5 (February 1, 2016): 1393–413. http://dx.doi.org/10.1007/s00707-016-1560-2.

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Buchholz, Simon. "Phase transitions for a class of gradient fields." Probability Theory and Related Fields 179, no. 3-4 (February 6, 2021): 969–1022. http://dx.doi.org/10.1007/s00440-020-01021-5.

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AbstractWe consider gradient fields on $${\mathbb {Z}}^d$$ Z d for potentials V that can be expressed as $$\begin{aligned} e^{-V(x)}=pe^{-\frac{qx^2}{2}}+(1-p)e^{-\frac{x^2}{2}}. \end{aligned}$$ e - V ( x ) = p e - q x 2 2 + ( 1 - p ) e - x 2 2 . This representation allows us to associate a random conductance type model to the gradient fields with zero tilt. We investigate this random conductance model and prove correlation inequalities, duality properties, and uniqueness of the Gibbs measure in certain regimes. We then show that there is a close relation between Gibbs measures of the random conductance model and gradient Gibbs measures with zero tilt for the potential V. Based on these results we can give a new proof for the non-uniqueness of ergodic zero-tilt gradient Gibbs measures in dimension 2. In contrast to the first proof of this result we rely on planar duality and do not use reflection positivity. Moreover, we show uniqueness of ergodic zero tilt gradient Gibbs measures for almost all values of p and q and, in dimension $$d\ge 4$$ d ≥ 4 , for q close to one or for $$p(1-p)$$ p ( 1 - p ) sufficiently small.

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Borsato, Luísa, and Sophie MacDonald. "Conformal measures and the Dobrušin-Lanford-Ruelle equations." Proceedings of the American Mathematical Society 149, no. 10 (July 27, 2021): 4355–69. http://dx.doi.org/10.1090/proc/15545.

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We demonstrate the equivalence of two definitions of a Gibbs measure on a subshift over a countable group. We formulate a more general version of the classical Dobrušin-Lanford-Ruelle equations with respect to a measurable cocycle, which reduce to the classical equations when the cocycle is induced by an interaction or a potential, and show that a measure satisfying these equations must have the conformal property. We also review methods of constructing an interaction from a potential and vice versa, such that the interaction and the potential have the same Gibbs and equilibrium measures.

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TARASOV, VASILY E. "CLASSICAL CANONICAL DISTRIBUTION FOR DISSIPATIVE SYSTEMS." Modern Physics Letters B 17, no. 23 (October 10, 2003): 1219–26. http://dx.doi.org/10.1142/s0217984903006268.

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We derive the canonical distribution as a stationary solution of the Liouville equation for the classical dissipative system. Dissipative classical systems can have stationary states that look like canonical Gibbs distributions. The condition for non-potential forces which leads to this stationary solution is very simple: the power of the non-potential forces must be directly proportional to the velocity of the Gibbs phase (phase entropy density) change. The example of the canonical distribution for a linear oscillator with friction is considered.

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Dong, W. "Thermodynamics of interfaces extended to nanoscales by introducing integral and differential surface tensions." Proceedings of the National Academy of Sciences 118, no. 3 (January 15, 2021): e2019873118. http://dx.doi.org/10.1073/pnas.2019873118.

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As a system shrinks down in size, more and more molecules are found in its surface region, so surface contribution becomes a large or even a dominant part of its thermodynamic potentials. Surface tension is a venerable scientific concept; Gibbs defined it as the excess of grand potential of an inhomogeneous system with respect to its bulk value per interface area [J. W. Gibbs, “The Collected Works” in Thermodynamics (1928), Vol. 1]. The mechanical definition expresses it in terms of pressure tensor. So far, it has been believed the two definitions always give the same result. We show that the equivalence can break down for fluids confined in narrow pores. New concepts of integral and differential surface tensions, along with integral and differential adsorptions, need to be introduced for extending Gibbs thermodynamics of interfaces. We derived two generalized Gibbs adsorption equations. These concepts are indispensable for an adequate description of nanoscale systems. We also find a relation between integral surface tension and Derjaguin’s disjoining pressure. This lays down the basis for measuring integral and differential surface tensions from disjoining pressure by using an atomic force microscope.

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CONRAD, FLORIAN, and TOBIAS KUNA. "A NOTE ON AN INTEGRATION BY PARTS FORMULA FOR THE GENERATORS OF UNIFORM TRANSLATIONS ON CONFIGURATION SPACE." Infinite Dimensional Analysis, Quantum Probability and Related Topics 15, no. 04 (December 2012): 1250028. http://dx.doi.org/10.1142/s0219025712500282.

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An integration by parts formula is derived for the first-order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on ℝd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

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Budjak, J. S. "Gibbs Grand Thermodynamic Potential in the Theory of Kinetic Crystal Properties." Фізика і хімія твердого тіла 18, no. 1 (March 15, 2017): 7–14. http://dx.doi.org/10.15330/pcss.18.1.7-14.

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In this paper, using Gibbs grand thermodynamic potential, kinetic tensors of electrical and thermal conductivity generalized equations known in non-equilibrium thermodynamics have been proven. These tensors determine calculation algorithms of the material tensors of conductor crystals and various galvanomagnetic and thermomagnetic effects coefficients. These algorithms are pragmatic formulas in calculation problems of crystals kinetic properties and in the problems for prediction of semiconductor crystals with preset properties. Their pragmatism is proven by the huge number of scientific papers dedicated to kinetic properties of semiconductor crystals study.

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Gao, G. T., Wenchuan Wang, and X. C. Zeng. "Gibbs ensemble simulation of HCFC/HFC mixtures by effective Stockmayer potential." Fluid Phase Equilibria 158-160 (June 1999): 69–78. http://dx.doi.org/10.1016/s0378-3812(99)00147-8.

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Surana, K. S., Y. Mendoza, and J. N. Reddy. "Constitutive theories for thermoelastic solids in Lagrangian description using Gibbs potential." Acta Mechanica 224, no. 5 (January 11, 2013): 1019–44. http://dx.doi.org/10.1007/s00707-012-0805-y.

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Sheikholeslami, R. "Scaling potential index (SPI) for CaCO3 based on Gibbs free energies." AIChE Journal 51, no. 6 (2005): 1782–89. http://dx.doi.org/10.1002/aic.10415.

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Dargahi Noubary, Kaveh, Michael Kellner, Johannes Hötzer, Marco Seiz, Hans J. Seifert, and Britta Nestler. "Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models." Journal of Materials Science 56, no. 20 (April 12, 2021): 11932–52. http://dx.doi.org/10.1007/s10853-021-06033-7.

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Abstract In order to approximate Gibbs energy functions, a semi-automated framework is introduced for binary and ternary material systems, using Calphad databases. To generate Gibbs energy formulations by means of second-order polynomials, the framework includes a precise approach. Furthermore, an optional extensional step enables the modeling of systems in which a direct generation leads to the unsatisfactory results in the representation of the thermodynamics. Furthermore, an optional extensional step enables the modeling of systems, in which a direct generation leads to the unsatisfactory results, when representing the thermodynamics. Within this extension, the commonly generated functions are modified to satisfy the equilibrium conditions in the observed material systems, leading to a better correlation with thermodynamic databases. The generated Gibbs energy formulations are verified by recalculating the equilibrium concentrations of the phases and rebuilding the phase diagrams in the considered concentration and temperature ranges, prior to the simulation studies. For all comparisons, a close match is achieved between the results and the Calphad databases. As practical examples of the method, phase-field simulation studies for the directional solidification of the binary – and the ternary – eutectic systems are performed. Good agreements between the simulation results and the reported theoretical and experimental studies from literature are found, which indicates the applicability of the presented approaches. Graphical Abstract

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Jacob, K. T., V. S. Saji, and Y. Waseda. "Standard Gibbs energy of formation of Pb2Ru2O6.5." Journal of Materials Research 22, no. 5 (May 2007): 1174–81. http://dx.doi.org/10.1557/jmr.2007.0171.

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Lead ruthenate is used as a bifunctional electrocatalyst for both oxygen evolution and reduction and as a conducting component in thick-film resistors. It also has potential applications in supercapacitors and solid oxide fuel cells. However, thermodynamic properties of the compound have not been reported in the literature. The standard Gibbs energy of formation has now been determined in the temperature range from 873 to 1123 K using a solid-state cell incorporating yttria-stabilized zirconia (YSZ) as the electrolyte, a mixture of PbO + Pb2Ru2O6.5 + Ru as the measuring electrode, and Ru + RuO2 as the reference. The design of the measuring electrode is based on a study of phase relations in the ternary system Pb–Ru–O at 1123 K. For the reaction,the standard enthalpy of formation and standard entropy at 298.15 K are estimated from the high-temperature measurements. An oxygen potential diagram for the system Pb–Ru–O is composed based on data obtained in this study and auxiliary information from the literature

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Silva, Jojomar Lucena, and José Raimundo Novaes Chiappin. "A geometria como instrumento heurístico da reformulação da termodinâmica na representação de ciclos para a de potenciais." Principia: an international journal of epistemology 21, no. 3 (May 7, 2018): 291–315. http://dx.doi.org/10.5007/1808-1711.2017v21n3p291.

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History shows that up to 1870’s, the thermodynamic cycles, particularly Carnot’s cycle, were the most important heuristic instruments as much to formulate the general laws of physics as well to deduce the experimental laws. From this moment on, this instrument falls into disuse with surprising rapidity. At the end of this decade emerges a new thermodynamic formulation, proposed by Gibbs, the thermodynamics of the potentials. This sudden transition from thermodynamic of cycles to potentials was triggered by the difficult to approach the emergence of the phase transition phenomena with the diagrammatic method. The main objective of the article is, then, to analyze the consequences of the substitution, by Gibbs, of the diagrammatic by the geometric method, particularly, its heuristic potential related to the proposal of the formulation of the thermodynamic of potentials.

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Rhodes, Christopher J., Thuy T. Tran, Philip Denton, and Harry Morris. "Rationalisation of the activities of phenolic (vitamin E-type) antioxidants." Spectroscopy 17, no. 4 (2003): 753–62. http://dx.doi.org/10.1155/2003/607917.

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Using Transition-State Theory, experimental rate constants, determined over a range of temperatures, for reactions of vitamin E type antioxidants are analysed in terms of their enthalpies and entropies of activation. It is further shown that computational methods may be employed to calculate enthalpies and entropies, and hence Gibbs Free Energies, for the overall reactions. Within the Linear Free Energy Relationship (LFER) assumption, that the Gibbs Free Energy of activation is proportional to the overall Gibbs Free Energy change for the reaction, it is possible to rationalise, and even to predict, the relative contributions of enthalpy and entropy for reactions of interest, involving potential antioxidants.

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Budzhak, Y. S., and T. Wacławski. "The Important Thermal Characteristics of Matter and Their Computations with the Use of the Gibbs Potentials." Фізика і хімія твердого тіла 19, no. 2 (May 2, 2019): 134–38. http://dx.doi.org/10.15330/pcss.19.2.134-138.

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In this paper, the important thermal characteristics of matter (they describe thermodynamic systems in a state of thermodynamic equilibrium) were calculated. There are the following important thermodynamic functions: the system internal energy , the thermal function (or enthalpy) the free Helmholtz energy, the thermo-dynamic potential (or Gibbs free energy), the Gibbs grand thermodynamic potential , the entropy , the specific heat capacity . These functions are explicit functions of system’s parameters, they fulfil some mathe-matical relationships and posses some total differentials. These functions are calculated in this paper and their physical sense is given in the cited works.

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Budzhak, Ya S., and T. Wacławski. "On the Question of the Problems of Statistical Calculations of the Conducting Crystals Thermodynamic and Kinetic Properties." Фізика і хімія твердого тіла 20, no. 4 (December 15, 2019): 345–53. http://dx.doi.org/10.15330/pcss.20.4.345-353.

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This paper presents an elementary model of a crystal and its thermodynamic equilibrium state. It was shown that the thermodynamic characteristics of the crystal at this state are described by the Gibbs grand thermodynamic potential. If the crystal is removed away from the equilibrium state, then in this state it will be described by the set of kinetic properties, and these properties are statistically calculated with the use of the non-equilibrium Gibbs grand thermodynamic potential. Crystals’ thermodynamic and kinetic properties have analytical dependence on the current carriers dispersion law and chemical potential of these carriers. In this work, it was shown that the determination of the dispersion law and chemical potential – these are complicated problems of statistical and kinetic theories of crystals’ properties.

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Mazhar, Amina A. "Interfacial behaviour of isopropanol at the Hg electrode from solutions of H2O-isopropanol-HCl." Canadian Journal of Chemistry 67, no. 12 (December 1, 1989): 2102–7. http://dx.doi.org/10.1139/v89-327.

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The adsorption of isopropanol on mercury in aqueous solutions of HCl at constant chemical potential of the acid has been determined from capacity and electrocapillary measurements. The maximum adsorption occurs at a charge of −2.2 μC cm−2. The Frumkin isotherm is obeyed, the a factor in the isotherm changes from a positive value for mixtures rich in water to a negative value for mixtures rich in alcohol. The standard Gibbs energy of adsorption depends quadratically on the potential. The orientation of the alcohol molecule in the interface is discussed. Keywords: interface, medium effects, adsorption isotherm, aliphatic alcohol, Gibbs energy of adsorption.

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FRADON, MYRIAM, and SYLVIE ROELLY. "INFINITE SYSTEM OF BROWNIAN BALLS: EQUILIBRIUM MEASURES ARE CANONICAL GIBBS." Stochastics and Dynamics 06, no. 01 (March 2006): 97–122. http://dx.doi.org/10.1142/s0219493706001669.

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We consider a system of infinitely many hard balls in ℝd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.

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43

TROSCHEIT, SASCHA. "Hölder differentiability of self-conformal devil's staircases." Mathematical Proceedings of the Cambridge Philosophical Society 156, no. 2 (January 9, 2014): 295–311. http://dx.doi.org/10.1017/s0305004113000698.

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AbstractIn this paper we consider the probability distribution function of a Gibbs measure supported on a self-conformal set given by an iterated function system (devil's staircase) applied to a compact subset of ${\mathbb R}$. We use thermodynamic multifractal formalism to calculate the Hausdorff dimension of the sets Sα0, Sα∞ and Sα, the set of points at which this function has, respectively, Hölder derivative 0, ∞ or no derivative in the general sense. This extends recent work by Darst, Dekking, Falconer, Kesseböhmer and Stratmann, and Yao, Zhang and Li by considering arbitrary such Gibbs measures given by a potential function independent of the geometric potential.

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Shangguan Dan-Hua, Lyu Yan, and Bao Jing-Dong. "Lévy flights in a steep potential well displaying non-Gibbs-Boltzmann statistics." Acta Physica Sinica 59, no. 11 (2010): 7607. http://dx.doi.org/10.7498/aps.59.7607.

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Sahu, Manjulata, Sumanta Mukherjee, Geeta R. Patkare, Smruti Dash, and M. K. Saxena. "Prediction of formation probability of rare earth uranates inside nuclear reactor fuel from the determined oxygen potential using a solid oxide galvanic cell." New Journal of Chemistry 45, no. 21 (2021): 9636–46. http://dx.doi.org/10.1039/d1nj00855b.

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SYROS, C. "DERIVATION OF GIBBS STATES FORM QUANTUM FIELD THEORY." Modern Physics Letters B 04, no. 17 (September 20, 1990): 1089–98. http://dx.doi.org/10.1142/s0217984990001379.

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A Lorentz invariant and Hermitian statistical field theory is presented. Its derivation is based on the random field theory, the evolution operator and the path integration. It yields the density matrix, the Gibbs states and the temperatures for equilibrium, nonequilibrium and variable particles numbers states. The chemical potential follows from a spontaneous energy renormalization of the Hamiltonian in the evolution operator. The generalization to any field other than scalar fields is straightforward.

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47

Spooner, Jacob, Brandon Smith, and Noham Weinberg. "Effect of high pressure on the topography of potential energy surfaces." Canadian Journal of Chemistry 94, no. 12 (December 2016): 1057–64. http://dx.doi.org/10.1139/cjc-2016-0295.

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Properties and reactivity of chemical compounds change dramatically at elevated pressures. Since kinetics and mechanisms of condensed-phase reactions are described in terms of their potential energy (PESs) or Gibbs energy (GESs) surfaces, chemical effects of high pressure can be assessed through analysis of pressure-induced deformations of GESs of solvated reaction systems. We discuss general trends expected for such changes and use quantum mechanical calculations to construct PESs of compressed species for hydrogen and methyl transfer reactions.

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48

Hasan, Akhmad Endang Zainal, Laksmi Ambarsari, and Karichsa Hariana. "THE POTENTIAL INHIBITION OF XANTHINE OXIDASE BY PHENOLIC AND FLAVONOIDS DATE (Phoenix dactylifera) WITH MOLECULAR DOCKING METHOD." Indonesian Journal of Applied Research (IJAR) 2, no. 2 (August 25, 2021): 126–43. http://dx.doi.org/10.30997/ijar.v2i2.129.

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Dates is fruit of palm trees that mostly grow in the Middle East. Dates contain phenolic acids and flavonoids that have antioxidants and potentially inhibit the ability of xanthine oxidase. The purpose of this research to determine the molecular interactions of xanthine oxidase by ligand of phenolic acids and flavonoids to inhibiting the production of uric acid. This research was conducted by site directed docking method. The size of the center of retardation used in this research is x = 26.569, y = 9.985, and z = 113.088 and the retardation volume of x = 14, y = 14, and z = 16. Inhibition by flavonoid and phenolic acid compounds has produces good inhibition strength shown by Gibbs free energy which is negative. The compound with the highest Gibbs free energy value is the anthocyanins compound which is -7.3 kCal / mol, the value is higher than the comparator ligand, allopurinol. Based on the bond analysis that is formed, the best compound in inhibiting xanthine oxidase is syringic acid.

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Wang, Qianglong, Xiaoguang Gao, Kaifang Wan, Fei Li, and Zijian Hu. "A Novel Restricted Boltzmann Machine Training Algorithm with Fast Gibbs Sampling Policy." Mathematical Problems in Engineering 2020 (March 20, 2020): 1–19. http://dx.doi.org/10.1155/2020/4206457.

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The restricted Boltzmann machine (RBM) is one of the widely used basic models in the field of deep learning. Although many indexes are available for evaluating the advantages of RBM training algorithms, the classification accuracy is the most convincing index that can most effectively reflect its advantages. RBM training algorithms are sampling algorithms essentially based on Gibbs sampling. Studies focused on algorithmic improvements have mainly faced challenges in improving the classification accuracy of the RBM training algorithms. To address the above problem, in this paper, we propose a fast Gibbs sampling (FGS) algorithm to learn the RBM by adding accelerated weights and adjustment coefficient. An important link based on Gibbs sampling theory was established between the update of the network weights and mixing rate of Gibbs sampling chain. The proposed FGS method was used to accelerate the mixing rate of Gibbs sampling chain by adding accelerated weights and adjustment coefficients. To further validate the FGS method, numerous experiments were performed to facilitate comparisons with the classical RBM algorithm. The experiments involved learning the RBM based on standard data. The results showed that the proposed FGS method outperformed the CD, PCD, PT5, PT10, and DGS algorithms, particularly with respect to the handwriting database. The findings of our study suggest the potential applications of FGS to real-world problems and demonstrate that the proposed method can build an improved RBM for classification.

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Chu, Hong Chao, Si Rong Yu, Cui Xiang Wang, and Qi Lou. "Theoretical Thermodynamic Analysis and Phase Analysis of AZ91D/Flyash Composites." Materials Science Forum 788 (April 2014): 604–7. http://dx.doi.org/10.4028/www.scientific.net/msf.788.604.

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The thermodynamic calculation is valuable for judging the feasibility of a reaction. In the present paper, the enthalpy change (∆HR), entropy change (∆SR) and Gibbs free energy change (∆GR) among various components in AZ91D Mg alloy-Cenosphere composites (FAC/AZ91D) were calculated. Through the calculation, we obtained the relationships between the Gibbs free energy changes and temperatures. The difficulty degree of every potential reaction could be directly reflected by the correlation curve between the temperature and the Gibbs free energy change. The analysis result provided the theoretical basis for the reaction temperature and the solution treatment temperature of the FAC/AZ91D system. At the same time, the analysis based on the minimum principle of the reaction free energy revealed the final components (MgO, Mg2Si and MgAl2O4), which was partially similar to the result of XRD analysis (MgO, Mg2Si and Mg17Al12).

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Journal articles on the topic 'Gibbs potential'

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