scholarly journals Studying thermodynamics of metastable states

2005 ◽  
Vol 3 (2) ◽  
pp. 115-128
Author(s):  
Yuri Kornyushin

Simple classical thermodynamic approach to the general description of metastable states is presented. It makes it possible to calculate the explicit dependence of the Gibbs free energy on temperature, to calculate the heat capacity, the thermodynamic barrier, dividing metastable and more stable states, and the thermal expansion coefficient. Thermodynamic stability under mechanical loading is considered. The influence of the heating (cooling) rate on the measured dynamic heat capacity is investigated. A phase shift of the temperature oscillations of an ac heated sample is shown to be determined by the relaxation time of the relaxation of the metastable nonequilibrium state back to the metastable equilibrium one. This dependence allows one to calculate the relaxation time. A general description of the metastable phase equilibrium is proposed. Metastable states in AB3 alloys are considered. Reasons for the change from the diffusional mechanism of the supercritical nucleus growth to the martensitic one as the heating rate increases are discussed. The Ostwald stage rule is derived.

2021 ◽  
Author(s):  
Ilan N. Rubin ◽  
Iaroslav Ispolatov ◽  
Michael Doebeli

AbstractOne of the oldest and most persistent questions in ecology and evolution is whether natural communities tend to evolve toward saturation and maximal diversity. Robert MacArthur’s classical theory of niche packing and the theory of adaptive radiations both imply that populations will diversify and fully partition any available niche space. However, the saturation of natural populations is still very much an open area of debate and investigation. Additionally, recent evolutionary theory suggests the existence of alternative evolutionary stable states (ESSs), which implies that some stable communities may not be fully saturated. Using models with classical Lokta-Volterra ecological dynamics and three formulations of evolutionary dynamics (a model using adaptive dynamics, an individual-based model, and a partial differential equation model), we show that following an adaptive radiation, communities can often get stuck in low diversity states when limited by mutations of small phenotypic effect. These low diversity metastable states can also be maintained by limited resources and finite population sizes. When small mutations and finite populations are considered together, it is clear that despite the presence of higher-diversity stable states, natural populations are likely not fully saturating their environment and leaving potential niche space unfilled. Additionally, within-species variation can further reduce community diversity from levels predicted by models that assume species-level homogeneity.Author summaryUnderstanding if and when communities evolve to saturate their local environments is imperative to our understanding of natural populations. Using computer simulations of classical evolutionary models, we study whether adaptive radiations tend to lead toward saturated communities in which no new species can invade or remain trapped in alternative, lower diversity stable states. We show that with asymmetric competition and small effect mutations, evolutionary Red Queen dynamics can trap communities in low diversity metastable states. Moreover, limited resources not only reduces community population sizes, but also reduces community diversity, denying the formation of saturated communities and stabilizing low diversity, non-stationary evolutionary dynamics. Our results are directly relevant to the longstanding questions important to both ecological empiricists and theoreticians on the species packing and saturation of natural environments. Also, by showing the ease evolution can trap communities in low diversity metastable stats, we demonstrate the potential harm in relying solely on ESSs to answer questions of biodiversity.


2018 ◽  
Author(s):  
Simon Olsson ◽  
Frank Noé

AbstractMost current molecular dynamics simulation and analysis methods rely on the idea that the molecular system can be characterized by a single global state, e.g., a Markov State in a Markov State Model (MSM). In this approach, molecules can be extensively sampled and analyzed when they only possess a few metastable states, such as small to medium-sized proteins. However this approach breaks down in frustrated systems and in large protein assemblies, where the number of global meta-stable states may grow exponentially with the system size. Here, we introduce Dynamic Graphical Models (DGMs), which build upon the idea of Ising models, and describe molecules as assemblies of coupled subsystems. The switching of each sub-system state is only governed by the states of itself and its neighbors. DGMs need many fewer parameters than MSMs or other global-state models, in particular we do not need to observe all global system configurations to estimate them. Therefore, DGMs can predict new, previously unobserved, molecular configurations. Here, we demonstrate that DGMs can faithfully describe molecular thermodynamics and kinetics and predict previously unobserved metastable states for Ising models and protein simulations.


1992 ◽  
Vol 06 (03) ◽  
pp. 127-138 ◽  
Author(s):  
E. MA ◽  
M. ATZMON

Alloy phase formation in binary metallic systems by mechanical alloying (MA) of elemental powders is briefly reviewed. Our recent results indicate the inadequacy of the current understanding of the MA process, which has been depicted as an isothermal solid-state interdiffusion reaction under interfacial, metastable, equilibrium in layered composites. A structural and thermodynamic analysis of the supersaturation followed by amorphization in the Zr-Al system demonstrates that a system can be constrained to be a single phase without reaching two-phase (metastable) equilibrium during MA. Alloying, resulting in a single metastable phase, has also been achieved in immiscible systems with positive heat of mixing, such as Fe-Cu. In both cases, the interfacial free energy associated with a repeatedly deformed, fine-structured, two-phase alloy appears to pose polymorphous constraints. In addition, equilibrium phases can be formed during MA in an exothermic, self-sustained fashion, as observed for the formation of AlNi. Al-Ni phases formed under different milling conditions suggest that self-sustained reactions may occur, undetected, on a grain-by-grain basis.


2011 ◽  
Vol 233-235 ◽  
pp. 1619-1622 ◽  
Author(s):  
Ying Zeng ◽  
Xu Dong Yu ◽  
Jing Qiang Zhang ◽  
Long Gang Li

The metastable phase equilibrium in the ternary system containing potassium, lithium and chloride ions was studied at 298.15 K using an isothermal evaporation method. The solubility, density and refractive index of the equilibrated solution were measured. The crystalloid forms of the solid phase were determined using a schreinermarks wet residue method. On the basis of the experimental data, the metastable equilibrium phase diagram and the physicochemical properties vs composition in the ternary system at 298.15 K were plotted. The experimental results show that this system is of a simple eutectic type system, no double salt or solid solution formed at 298.15 K. The phase diagram consists of one invariant point, two uninvariant curves, and two crystallization regions. The crystallization regions correspond to potassium chloride (KCl) and lithium chloride monohydrate (LiCl·H2O), respectively. Salt KCl has the largest crystallization field, whereas salt LiCl·H2O has the smallest crystallization field. Salt LiCl has strong salting-out effect on salt KCl.


2014 ◽  
Vol 369 (1653) ◽  
pp. 20130532 ◽  
Author(s):  
Leonardo L. Gollo ◽  
Michael Breakspear

Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, while adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems—resonance pairs—promote stable zero-lag synchrony among the small motifs in which they are embedded, and whose effects can propagate along connected chains. Second, frustrated closed-loop motifs disrupt synchronous dynamics, enabling metastable configurations of zero-lag synchrony to coexist. We document these two complementary influences in small motifs and illustrate how these effects underpin stable versus metastable phase-synchronization patterns in prototypical modular networks and in large-scale cortical networks of the macaque (CoCoMac). We find that the variability of synchronization patterns depends on the inter-node time delay, increases with the network size and is maximized for intermediate coupling strengths. We hypothesize that the dialectic influences of resonance versus frustration may form a dynamic substrate for flexible neuronal integration, an essential platform across diverse cognitive processes.


1984 ◽  
Vol 220 (1) ◽  
pp. 173-178 ◽  
Author(s):  
I E Woodrow ◽  
G A Manson

A general description of a system consisting of a hysteretic enzyme and a series of coupling enzymes is presented. The chloroplast enzyme sedoheptulose-1,7-bisphosphatase and a sequence of three coupling enzymes is used as an example. An analysis using first-order rate equations for the coupling enzymes shows that the observed relaxation time of the system is the sum of the relaxation times of the coupling enzymes and that of the hysteretic enzyme. The behaviour of a system with relatively low concentrations of coupling enzymes, where the first-order assumption is not valid, is analysed by computer stimulation. Several methods for the accurate determination of the relaxation time of the hysteretic enzyme are discussed.


1972 ◽  
Vol 11 (11) ◽  
pp. 1569-1573 ◽  
Author(s):  
W.D Seward ◽  
V Reddy ◽  
J.W Shaner

2013 ◽  
Vol 662 ◽  
pp. 468-472 ◽  
Author(s):  
Xiao Hua Ma ◽  
Sun Bai ◽  
Li Wu ◽  
Zhi Liang Jin

The isothermal solubility of the ternary system K+,Mg2+/B4O72-—H2O at 25°C has been studied and the phase diagram is determined. The results show that the system is of the simple eutonic type and can be in metastable equilibrium state within 8—16 hours. The phase diagram consists of two solubility branches corresponding to the crystallization areas of K2B4O7•4H2O and MgB4O7•9H2O. The composition of the eutonic point is MgB4O7,0.5279%(Wt%) and K2B4O7,13.9629%(Wt%) respectively. The replicate experiments proved that the phase transformation of hungtsaoite (MgB4O7•9H2O) occurs after a 20 hours epuilibrium.


1996 ◽  
Vol 10 (29) ◽  
pp. 1441-1446 ◽  
Author(s):  
M. LÓPEZ DE HARO ◽  
L. L. GONÇALVES ◽  
J. TAGÜEÑA-MARTÍNEZ

The relaxational heat capacity of an infinite linear polymer chain is computed. The result is derived within a kinetic Ising-like model previously introduced to provide for a dynamical generalization of the Gibbs-di Marzio lattice model. The questions of universality of the dynamic responses of the chain and of the existence of more than one relaxation time if one considers different probes are discussed.


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