Phase transitions of some non-linear stochastic models

1995 ◽  
Vol 32 (01) ◽  
pp. 193-201
Author(s):  
Shui Feng
Keyword(s):  
Phase Transitions ◽  
Explicit Expression ◽  
Critical Points ◽  
Stochastic Models ◽  
Domain Of Attraction ◽  
Rates Of Convergence ◽  
Non Linear

A class of non-linear stochastic models is introduced. Phase transitions, critical points and the domain of attraction are discussed in detail for some concrete examples. For one of the examples the explicit expression for the domain of attraction and the rates of convergence are obtained.

Phase transitions of some non-linear stochastic models

1995 ◽  
Vol 32 (1) ◽  
pp. 193-201
Author(s):  
Shui Feng
Keyword(s):  
Phase Transitions ◽  
Explicit Expression ◽  
Critical Points ◽  
Stochastic Models ◽  
Domain Of Attraction ◽  
Rates Of Convergence ◽  
Non Linear

A class of non-linear stochastic models is introduced. Phase transitions, critical points and the domain of attraction are discussed in detail for some concrete examples. For one of the examples the explicit expression for the domain of attraction and the rates of convergence are obtained.

Some features of phase transitions in solutions with two critical points

1996 ◽  
Vol 166 (6) ◽  
pp. 683-685 ◽  
Author(s):  
K.V. Kovalenko ◽  
S.V. Krivokhizha ◽  
Immanuil L. Fabelinskii ◽  
L.L. Chaikov
Keyword(s):  
Phase Transitions ◽  
Critical Points

scholarly journals Milstein-type semi-implicit split-step numerical methods for nonlinear stochastic differential equations with locally Lipschitz drift terms

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 1-12 ◽  
Author(s):  
Burhaneddin Izgi ◽  
Coskun Cetin
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Solutions ◽  
Rates Of Convergence ◽  
Ginzburg Landau ◽  
Linear Growth Condition ◽  
Locally Lipschitz ◽  
Non Linear ◽  
Ginzburg Landau Equations

We develop Milstein-type versions of semi-implicit split-step methods for numerical solutions of non-linear stochastic differential equations with locally Lipschitz coefficients. Under a one-sided linear growth condition on the drift term, we obtain some moment estimates and discuss convergence properties of these numerical methods. We compare the performance of multiple methods, including the backward Milstein, tamed Milstein, and truncated Milstein procedures on non-linear stochastic differential equations including generalized stochastic Ginzburg-Landau equations. In particular, we discuss their empirical rates of convergence.

Implications of new phase transitions approach onto specific black holes

2020 ◽  
Vol 35 (39) ◽  
pp. 2050326
Author(s):  
Abdul Jawad ◽  
Shahid Chaudhary
Keyword(s):  
Black Holes ◽  
Phase Transitions ◽  
Critical Points ◽  
Theoretical Physics ◽  
Open Questions ◽  
Standard Relation ◽  
Classical Gravity ◽  
Quantum Interpretation ◽  
Thermodynamic Phase ◽  
New Phase

Among many open questions in theoretical physics, consistent quantum gravity theory is still a major issue to be solved. Recent major works in phase transitions of black holes (BH) can be helpful for quantum interpretation of classical gravity. We study the new effective method to discuss the thermodynamic phase transitions onto well renowned regular BHs. Ordinary approaches of phase transitions depend upon equation of state and it is impossible to obtain all critical points with ordinary approaches. This study is derived from the slope of temperature versus entropy and it provides the possibility of finding all the critical points analytically. This technique provides pressure, which is different from standard relation of pressure and independent of other thermodynamical relations. We discuss some issues in ordinary methods and provide an easy approach to investigate the critical behavior of thermodynamical quantities. We find out the phase transitions points and horizon radii of non-physical range for BHs. We also use the new thermodynamical relations to briefly study well-known Joule–Thomson (JT) effect on regular BH.

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (04) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

scholarly journals CUMULATIVE MEASURE OF CORRELATION FOR MULTIPARTITE QUANTUM STATES

2014 ◽  
Vol 28 (07) ◽  
pp. 1450050 ◽  
Author(s):  
ANDRÉ L. FONSECA DE OLIVEIRA ◽  
EFRAIN BUKSMAN ◽  
JESÚS GARCÍA LÓPEZ DE LACALLE
Keyword(s):  
Phase Transitions ◽  
State Space ◽  
Present Article ◽  
Critical Points ◽  
Quantum Phase Transitions ◽  
The State ◽  
Quantum States ◽  
Quantum Phase ◽  
Mixed States ◽  
Different Dimensions

The present article proposes a measure of correlation for multiqubit mixed states. The measure is defined recursively, accumulating the correlation of the subspaces, making it simple to calculate without the use of regression. Unlike usual measures, the proposed measure is continuous additive and reflects the dimensionality of the state space, allowing to compare states with different dimensions. Examples show that the measure can signal critical points (CPs) in the analysis of Quantum Phase Transitions (QPTs) in Heisenberg models.

QUANTUM PHASE TRANSITIONS IN MESOSCOPIC SYSTEMS

2006 ◽  
Vol 20 (19) ◽  
pp. 2687-2694 ◽  
Author(s):  
F. IACHELLO
Keyword(s):  
Phase Transitions ◽  
Critical Points ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Mesoscopic Systems ◽  
Spectral Signatures

Shape phase transitions in nuclei, an example of quantum phase transitions in mesoscopic systems, are briefly reviewed. Spectral signatures of critical points in finite quantal systems are discussed and experimental examples are shown.

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