Focus equilibrium state

Most traditional models focus on looking for equilibrium solutions among some set of (pre-defined) aggregate variables. The LEs are effectively mean-field equations, in which certain variables (i.e. attrition rate) are assumed to represent an entire force, the equilibrium state is explicitly solved for and declared the battle outcome. In contrast, ABMs focus on understanding the kinds of emergent patterns that might arise while the overall system is out of (or far from) equilibrium. 

Let us first summarize the principal features of the thermodynamic equilibrium states that are the principal focus of a thermodynamic description. According to the definitions of Section 2.10, such states are ... 

The central focus of Gibbs theory is the equilibrium state S, a quiescent limiting condition of a sufficiently large ( macroscopic ) physical system that exhibits characteristically simple responses to attempted changes of the control variables that specify the state. 

The phase coexistence observed around the first-order transition in NIPA gels cannot be interpreted by the Flory-Rehner theory because this theory tacitly assumes that the equilibrium state of a gel is always a homogeneous one. Heterogeneous structures such as two-phase coexistence are ruled out from the outset in this theory. Of course, if the observed phase coexistence is a transient phenomenon, it is beyond the thermodynamical theory. However, as will be described below, the result of the detailed experiment strongly indicates that the coexistence of phases is not a transient but rather a stable or metastable equilibrium phenomenon. At any rate, we will focus our attention in this article only on static equilibrium phenomena. 

In this chapter, we discuss the application of simulation techniques to the study of fluctuational escape and related phenomena in nonlinear optical systems that is, situations where a large deviation of the system from an equilibrium state occurs under the influence of relatively weak noise present in the system. We will be interested primarily in the analysis of situations where large deviations lead to new nontrivial behaviour or to a transition to a different state. The topics to be discussed have been selected mainly for their own intrinsic scientific interest, but also in order to provide an indication of the power and utility of the simulation approach as a means of focusing on, and... 

In examining a crystalline structure as revealed by diffraction experiments it is all too easy to view the crystal as a static entity and focus on what may be broadly termed attractive intermolecular interactions (dipole-dipole, hydrogen bonds, van der Waals etc., as detailed in Section 1.8) and neglect the actual mechanism by which a crystal is formed, i.e. the mechanism by which these interactions act to assemble the crystal from a non-equilibrium state in a super-saturated solution. However, it is very often nucleation phenomena that are ultimately responsible for the observed crystal structure and hence we were careful to draw a distinction between solution self-assembly and crystallisation at the beginning of this chapter. For example paracetamol, when crystallised from acetone solution gives the stable monoclinic crystal form I, but crystallisation from a molten sample in the absence of solvent... 

The fifth question focuses on a particular fixed volume element in the reactor and whether it changes as a function of time. If it does not, then the reactor is said to operate at a stationary state. If there are time variations, then the reactor is operating under transient conditions. A nontrivial example of the transient situation is designed on purpose to observe how a chemically reactive system at equilibrium relaxes back to the equilibrium state after a small perturbation. This type of relaxation experiment can often yield informative kinetic behavior. 

The essence of a nonhydrostatic stress is that different planes through a point are subject to different normal compressive stresses compressive stress is ct,- then we put forward the assertion that an equilibrium state that can be associated with plane i is a hydrostatic state whose pressure has the same magnitude as O . For illustration, see Figure 9.1. 

Another important characteristic of the gas bubble is its response to a periodic oscillation of the ambient pressure / ,. For large-amplitude oscillations of the pressure, or for an initial condition that is not near a stable equilibrium state for the bubble, the response can be very complicated, including the possibility of chaotic variations in the bubble radius.22 However, such features are outside the realm of simple, analytical solutions of the governing equations, and we focus our attention here on the bubble response to asymptotically small oscillations of the ambient pressure, namely,... 

The important aspect of adsorption processes at a liquid interface is lateral mobility which can lead to lateral excess transport of adsorbed molecules. Lateral transport disturbs the equilibrium state of an adsorption layer. In many important systems, such as emulsions, foams, and bubbly liquids, the properties of a non-equilibrium adsorption layer can be essential. This has been demonstrated in the systematic work of the Russian and Bulgarian schools summarised in monographs like "Thin Liquid Films" by Ivanov, "Coagulation and Dynamics of Thin Films" by Dukhin, Rulyov and Dimitrov, and "Foams and Foam Films" by Krugljakov and Exerowa. These books pay most attention to thick film drainage and stabilisation/destabilisation of thin liquid films. This book is focused on other dynamic processes at liquid interfaces in general or connected with phenomena of emulsions and foams. 

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