A mathematical theory of the critical point of ferromagnetic Ising systems [PDF]
Physics Reports, 2023 We develop a theory of the critical point of the ferromagnetic Ising model, whose basic objects are the ergodic (pure) states of the infinite system. It proves the existence of anomalous critical fluctuations, for dimension $ν=2$ and, under a standard assumption, for $ν=3$, for the model with nearest neighbor interaction, in a way which is consistent ...
Marchetti, Domingos H. U. +2 more
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Interval Mathematics Applied to Critical Point Transitions [PDF]
Revista de Matemática: Teoría y Aplicaciones, 2005 The determination of critical points of mixtures is important for both practical and theoretical reasons in the modeling of phase behavior, especially at high pressure. The equations that describe the behavior of complex mixtures near critical points are highly nonlinear and with multiplicity of solutions to the critical point equations.
Benito A. Stradi
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Quaternions, Fréchet differentiation, and some equations of mathematical physics 1. Critical point theory [PDF]
Journal of Mathematical Analysis and Applications, 1979 AbstractFollowing an introduction discussing some properties of maps Q → Q and Q × Q → Q, where Q denotes the ring of quaternions, it is shown that many equations of mathematical physics can be written in this formalism. A concept of Fréchet differentiation is given in this setting, in a manner analogous to the usual definition.
Vadím Komkov
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Mathematical modelling of color, texture kinetics and sensory attributes characterisation of ripening bananas for waste critical point determination [PDF]
Journal of Food Engineering, 2016 Abstract It is vital to correlate the instrumental and non-instrumental analyses of food products so as to determine the product waste critical point. Texture and color (instrumental) were determined by a universal testing machine (UTM) and colorimetry respectively to ascertain the kinetics of bananas during ripening. While deterministic, descriptive
Stella Nannyonga +4 more
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A MATHEMATICAL DESCRIPTION OF THE CRITICAL POINT IN PHASE TRANSITIONS
International Journal of Modern Physics C, 2013 Let y(x) be a smooth sigmoidal curve, y(n) be its nth derivative and {xm,i} and {xa,i}, i = 1,2,…, be the set of points where respectively the derivatives of odd and even order reach their extreme values. We argue that if the sigmoidal curve y(x) represents a phase transition, then the sequences {xm,i} and {xa,i} are both convergent and they have a ...
Bilge, Ayse Humeyra, Pekcan, Onder
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Mathematical description of the phase transition curve near the critical point [PDF]
Applicationes Mathematicae, 2007 Tomasz Sułkowski
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MATHEMATICAL MODELING OF THE ASYMPTOTIC NEAR THE CRITICAL POINT
Scientific and Technical Volga region Bulletin, 2016 S.V. Rykov +3 more
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2023 Topological Data Analysis and Visualization (TopoInVis), 2023 11 pages, 8 figures, to appear in an IEEE VGTC sponsored ...
Vietinghoff, Dominik +3 more
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First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Critical Points in Coupled Nonlinear Systems. I: Mathematical Framework [PDF]
Fluids, 2021 This work presents the novel first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP), which enables the exact and efficient computation of the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) of coupled nonlinear models of physical systems characterized by ...
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A Morse complex for infinite dimensional manifolds - Part I [PDF]
, 2003 In this paper and in the forthcoming Part II we introduce a Morse complex for a class of functions f defined on an infinite dimensional Hilbert manifold M, possibly having critical points of infinite Morse index and coindex.
Abbondandolo +47 more
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