Potential and flux decomposition for dynamical systems and non-equilibrium thermodynamics: curvature, gauge field, and generalized fluctuation-dissipation theorem

The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance. The response due to a small perturbation can be expressed by a spontaneous fluctuation. For non-equilibrium systems, we derived a generalized FDT that the response function is composed of two parts: (1) a spontaneous correlation representing the relaxation which is present in the near equilibrium systems with detailed balance and (2) a correlation related to the persistence of the curl flux in steady state, which is also in part linked to a internal curvature of a gauge field. The generalized FDT is also related to the fluctuation theorem. In the equal time limit, the generalized FDT naturally leads to non-equilibrium thermodynamics where the entropy production rate can be decomposed into spontaneous relaxation driven by gradient force and house keeping contribution driven by the non-zero flux that sustains the non-equilibrium environment and breaks the detailed balance. On any particular path, the medium heat dissipation due to the non-zero curl flux is analogous to the Wilson lines of an Abelian gauge theory.     

The rheological similarity of the physical networks of different origin

It has been established that the Newtonian viscosity of solutions of styrene-acrylic acid (4 mol%) copolymers inionomeric form (0–50 mol%) in DMPh is proportional to exp n (n being the degree of neutralization). The principle of temperature-time-concentration superposition is applicable for the dependence of shear modulus on temperature (20–100°), frequency (10^?3–1.5 Hz), decree of neutralization (0–50 mol%) and concentration (15–45 g/dl). These facts can be explained in terms of the rheological similarity of physical networks connected with macromolecular chain entanglements and with salt group interactions. Some details of the model for concentrated polymer solutions are discussed.     

The non-equilibrium charge screening effects in diffusion-driven systems with pattern formation

The effects of non-equilibrium charge screening in mixtures of oppositely charged interacting molecules on surfaces are analyzed in a closed system. The dynamics of charge screening and the strong deviation from the standard Debye-Hückel theory are demonstrated via a new formalism based on computing radial distribution functions suited for analyzing both short-range and long-range spacial ordering effects. At long distances the inhomogeneous molecular distribution is limited by diffusion, whereas at short distances (of the order of several coordination spheres) by a balance of short-range (Lennard-Jones) and long-range (Coulomb) interactions. The non-equilibrium charge screening effects in transient pattern formation are further quantified. It is demonstrated that the use of screened potentials, in the spirit of the Debye-Hückel theory, leads to qualitatively incorrect results.     

On the origin of the dynamical threshold for collision-induced dissociation processes

Collision-induced dissociation from the ground vibration-rotation state of the reactant diatom is studied in the systems He + H₂, H + H₂, and He + H⁺₂ by quasiclassical trajectory calculations, using ab initio potential energy surfaces. The dependence of the dynamical threshold values on the shape of the potential energy surface is discussed.     

Evaluation of adsorbent materials for heat pump and thermal energy storage applications in open systems

The evaluation of solid adsorbents in open sorption systems for heating, cooling and thermal energy storage (TES) applications is crucial for the ecological and economical performance of these systems. An appropriate adsorbent has to reach the temperature limit given by the heating/cooling system of the consumer. It has to provide high energy efficiency and a high energy density for storage applications. A method for an easy evaluation of different adsorbents for a specific application has been developed. The method is based on the adsorption equilibrium of the adsorbent and water vapor. The crucial property for the discussed field of applications is the differential heat of adsorption. Criteria for the evaluation of the adsorbent are the breakthrough curves (responsible for the dynamics of the process), the possible temperature lift (or the dehumidification) of the air, the thermal COP and the storage capacity.     

Electron energy distribution functions and dissociation kinetics of HCl in non-equilibrium plasmas

Electron energy distribution functions (edf) have been calculated by numerically solving the Boltzmann equation coupled to a system of vibrational master equations which simulates both the vibrational relaxation due to e—V (electron—vibration), V—V (vibration—vibration) and V—T (vibration—translation) energy exchanges and the dissociation process. The calculated edf strongly depend on the vibrational nonequilibrium present in the gas phase, even though the atoms coming from the dissociation process tend to destroy the vibrational energy content of the molecules. Vibrationally excited molecules determine a joint vibro—electronic mechanism in the dissociation of HCl. This mechanism is the more efficient the smaller the gas temperature and pressure. Finally the contribution of a purely vibrational mechanism in the dissociation of HCl is presented and discussed.     

Generalized spectral decompositions of mixing dynamical systems

We introduce a method for the explicit computation of the eigenvalue problem of the evolution operator of mixing dynamical systems. The method is based on the subdynamics decomposition of the Brussels–Austin groups directed by Professor I. Prigogine. We apply the method to three different representatives of mixing systems, namely, the Renyi maps, baker's transformations, and the Friedrichs model. The obtained spectral decompositions acquire meaning in suitable rigged Hilbert spaces that we construct explicitly for the three models. The resulting spectral decompositions show explicitly the intrinsic irreversibility of baker's transformations and Friedrichs model and the intrinsically probabilistic characters of the Renyi maps and baker's transformations. The dynamical properties are reflected in the spectrum because the eigenvalues are the powers of the Lyapunov times for the Renyi and baker systems and include the lifetimes for the Friedrichs model. © 1993 John Wiley & Sons, Inc.     

A method to estimate the Gibbs free energy of non-equilibrium alloys by thermal analysis

A method has been developed to estimate the Gibbs free energy $ \left( {G_{\text{S}}^{\text{NE}} } \right) $ of the non-equilibrium solid alloys with multicomponents based on differential scanning calorimetry (DSC) analysis. In this method, the DSC curves of the non-equilibrium and equilibrium alloys during heating up to fully melting and those of the alloys during solidifying were measured. Then the thermal effects of the solid phase transformations from non-equilibrium to equilibrium states and the equilibrium solidification could be calculated. By evolving the traditional equal-G curve principle to equal-G point, the Gibbs free energy of the equilibrium solid alloy with multicomponents could be obtained on condition that the free energy of the liquid alloy was known. Considering the thermal effects of the solid phase transformations from non-equilibrium to equilibrium states, the Gibbs free energy value of the non-equilibrium alloys with a given composition could be achieved although the phase constitution of the equilibrium solid alloys and the Gibbs free energy of each phase were not known, and the calculation errors could be reduced by dividing the alloys into many infinitesimal virtual pure metals. The Gibbs free energy of the non-equilibrium Al?CSi?CMn alloys was calculated by using this method, confirming the validity of this method.     

Structural and dynamical analysis of monodisperse and polydisperse colloidal systems

We present a semigrand ensemble Monte Carlo and Brownian dynamics simulation study of structural and dynamical properties of polydisperse soft spheres interacting via purely repulsive power-law potentials with a varying degree of "softness." Comparisons focus on crystal and amorphous phases at their coexistence points. It is shown through detailed structural analysis that as potential interactions soften, the "quality of crystallinity" of both monodisperse and polydisperse systems deteriorates. In general, polydisperse crystalline phases are characterized by a more ordered structure than the corresponding monodisperse ones (i.e., for the same potential softness). This counter-intuitive feature originates partly from the fact that particles of different sizes may be accommodated more flexibly in a crystal structure and from the reality that coexistence (osmotic) pressure is substantially higher for polydisperse systems. These trends diminish for softer potentials. Potential softness eventually produces substitutionally disordered crystals. However, substitutional order is apparent for the hard-spherelike interactions. Diffusionwise, crystals appear quite robust with a slight difference in the vibrational amplitudes of small and large particles. This difference, again, diminishes with potential softness. Overcrowding in amorphous polydisperse suspensions causes "delayed" diffusion at intermediate times.     

An effective continuum approach for modeling non-equilibrium structural evolution of protein nanofiber networks

We quantify the formation and evolution of protein nanofibers using a new phase field modeling framework and compare the results to transmission electron microscopy measurements (TEM) and time-dependent growth measurements given in the literature. The modeling framework employs a set of effective continuum equations combined with underlying nanoscale forces and chemical potential relations governing protein nanofiber formation in solution. Calculations based on the theoretical framework are implemented numerically using a nonlinear finite element phase field modeling approach that couples homogenized protein molecular structure via a vector order parameter with chemical potential relations that describe interactions between the nanofibers and the surrounding solution. Homogenized, anisotropic molecular and chemical flux relations are found to be critical in obtaining nanofiber growth from seed particles or a random monomer bath. In addition, the model predicts both sigmoidal and first-order growth kinetics for protein nanofibers for unseeded and seeded models, respectively. These simulations include quantitative predictions on time scales of typical protein self-assembly behavior which qualitatively match TEM measurements of the RADA16-I protein and growth rate measurements for amyloid nanofibers from the literature. For comparisons with experiments, the numerical model performs multiple nanofiber protein evolution simulations with a characteristic length scale of ～2.4 nm and characteristic time scale of ～9.1 h. These results provide a new modeling tool that couples underlying monomer structure with self-assembling nanofiber behavior that is compatible with various external loadings and chemical environments.     

强阳离子交换整体电渗泵流量影响因素研究

采用丙烯酸,2-丙烯酰胺-2-甲基丙磺酸为功能单体,N,N’-亚甲基双丙烯酰胺为交联剂,正十二醇、1,4-丁二醇及二甲基亚砜为致孔剂,偶氮二异丁腈为引发剂在原位聚合,制备出了以丙烯酰胺类强阳离子交换整体柱为核心的电渗泵.在乙腈-磷酸盐二元流动相体系下,考察了驱动电压,有机调节剂,盐浓度,pH对该泵流量的影响.流量与驱动...     

Unsaturated polyester resins cure: Kinetic,rheologic, and mechanical dynamical analysis. II. The glass transition in the mechanical dynamical spectrum of polyester networks

Unsaturated polyester networks with various structures built from an orthophtalic polyester, with methyl ethyl ketone peroxide as an initiator and cobalt octoate as a promoter, were studied with dynamic mechanical thermal analysis from −50 to 200 °C to characterize changes in the mechanical properties as a function of the temperature. From these measurements, the glass‐transition temperatures of the different networks were determined, their dependence on conversion being fitted to an equation related to the Couchman and DiBenedetto equations. Finally, the different transitions were analyzed as a function of the cure conditions. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 146–152, 2001     

The origin of energy functional in Roothaan open shell SCF theory

Different methods of averaging of energy over the states of electronic configurations γ^N (n_γ = 1, 2, 3 and N = 1, 2, …, 2n_γ ? 1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (VCC ) in energy functionals for various states as well as for average values of energy are presented. It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations t^N (N = 2–4) and e² there exist states for which VCC are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such “non-Roothaan” terms and peculiarities of its calculation by the restricted Hartree–Fock method are discussed.     

The automotive system — a complex coupling of matter and energy networks

Linear equations are shown with schematic diagrams which together describe the automotive dynamic model. However, the principal intent of the paper is not to study the dynamics of automotive operations. The schematic diagrams of each sub-system are presented to indicate the possible points of energy storage and dissipation and how they relate to the continuity of energy.From the sub-system diagrams it is now possible to generate energy and matter balances for the automotive system. The final energie matrix expression (eqn 49), which relates to all components of the system, is developed.     

Self-organization in nonlinear dynamical systems and its relation to the materials science

This review paper presents briefly the main concepts of nonlinear dynamics and their exemplary manifestations in selected systems, including those important from the point of view of materials science. It is an extended version of the conference presentation. The conditions of instabilities leading to spontaneous formation of dissipative structures are given. Principles of nonlinear dynamics are illustrated with several examples from the homogeneous and heterogeneous and physical and chemical systems: pattern formation in the convective motion of fluids subject to various kinds of driving forces, periodic precipitation phenomena, oscillations, and pattern formation in the Belousov–Zhabotinski (BZ) reaction and the catalytic oxidation of thiocyanate ions with hydrogen peroxide, as well as bistability and tristability in the electrochemical reduction of azide complexes of nickel(II). The application of nonlinear dynamics in materials science is first exemplified by its role in polymerization reactions. Such processes can either exhibit internal couplings leading to oscillations or can be coupled with the chemical oscillatory process through, e.g., the covalent bonding of its catalyst to the polymer network. Other selected examples of the application of nonlinear dynamics in materials science, referring to electrochemical processes, were briefly reviewed. Nonlinear dynamics appears to be useful for designing new materials, including those at the nanoscale.

The dynamical theory of energy partition. Loss of a hydrogen atom from the hydroxymethylene radical cation

The translational energy releases accompanying fromation of H^˙ and [CHO]⁺ from [CHOH]^+˙, H^˙ and [CDO]⁺ from [CDOH]^+˙, D^˙ and [CHO]⁺ from [CHOD]^+˙ and D^˙ and [CDO]⁺ from [CDOD]^+˙ have been calculated from the widths at half-height of the respective metastable peaks. The energy releases for [CHOD]^+˙ and [CDOD]^+˙ are similar to each other in magnitude, but are both significantly larger than those for [CHOH]^+˙ and [CDOH]^+˙. These differences are discussed in terms of the dynamical theory of energy partition. The larger energy releases for decompositions giving D^˙ are attributed to larger proportions of the kinetic energy being associated with the departing D^˙ in the transition states, as compared to H^˙ in the transition states for the decompositions yielding H^˙.     

Steric and electrostatic interactions in hexacyclic ring systems: The origin of the buttressing effect

Ring deformation in a number of 2-trichloromethyl-1,3-dioxanes could be traced in their ¹H NMR spectra from anomalies in coupling constants. No distortion occurs when the 2-substituent is a dichloromethyl or a tertiobutyl group, or when a 4-axial substituent is lacking. It was impossible to deduce the ring geometry from the vicinal coupling constants, but the nature of the ring deformation has been ascertained by NMR data (³J_exo, Δδ) and dipole moment calculations. Flexible conformations are not the origin of the observed anomalies. The rotomeric populations in 2-dichloromethyl-1,3-dioxanes has been evaluated and the origin of the buttressing effect, as caused by different substitution, has been disclosed.     

Thermal analysis and energy systems

Journal of Thermal Analysis and Calorimetry -     

Simulation of non-equilibrium energy distributions of current carriers in proton-conducting oxides with perovskite structure

A simulation method based on the integral equation for the sticking probability of ion in well was discussed for its application to study energy distributions of protons carried in simple and complex perovskite-like structures. In the terms of the Wiener—Hopf computational technique, a numerical algorithm was developed to detect deviations of the energy distribution function from the Boltzmann distribution near the potential barrier peak due to random interaction of ion with the nearest environment. Being considered as non-equilibrium in this sense, the derived distributions essentially deviated from the equilibrium distribution for a wide energy loss range of protons carried from one lattice position to another. The developed simulation algorithm may be of methodological interest in general practice for numerical solution of the Wiener—Hopf equations, because the known solution techniques for integral equations of this type are inapplicable to the studied problems of electrochemical kinetics due to their essentially different boundary conditions.