Phenomenological Coefficients Research Articles

Weak (non)conservation and stochastic dynamics of angular momentum

Angular momentum conservation influences equilibrium statistical mechanics, leading to a generalized microcanonical density for an isolated system and a generalized Gibbs density for a weakly coupled system. We study the stochastic decay of angular momentum due to the weakly imperfect rotational symmetry of the external potential that confines the isolated many-particle system. We present a mesoscopic description of the system, deriving Langevin and Fokker–Planck equations, which are consistent with equilibrium statistical mechanics when rotational symmetry is maintained. When the symmetry is weakly violated, we formulate a coarse-grained stochastic differential equation governing the decay of total angular momentum over time. To validate our analytical predictions, we conduct numerical simulations of the microcanonical ensemble, an isolated system undergoing thermalization due to weak two-body interactions. Our coarse-grained Langevin equation accurately characterizes both the decay of the angular momentum and its fluctuations in a steady state. Furthermore, we estimate the parameters of our mesoscopic model directly from simulations, providing insights into the dissipative phenomenological coefficients, such as friction. More generally, this study contributes to a deeper understanding of the behavior of the integrals of motion when the corresponding symmetry is weakly violated.

Thermodynamic analysis of energy coupling by determination of the Onsager phenomenological coefficients for a 3×3 system of coupled chemical reactions and transport in ATP synthesis and its mechanistic implications

The nonequilibrium coupled processes of oxidation and ATP synthesis in the fundamental process of oxidative phosphorylation (OXPHOS) are of vital importance in biosystems. These coupled chemical reaction and transport bioenergetic processes using the OXPHOS pathway meet >90% of the ATP demand in aerobic systems. On the basis of experimentally determined thermodynamic OXPHOS flux-force relationships and biochemical data for the ternary system of oxidation, ion transport, and ATP synthesis, the Onsager phenomenological coefficients have been computed, including an estimate of error. A new biothermokinetic theory of energy coupling has been formulated and on its basis the thermodynamic parameters, such as the overall degree of coupling, q and the phenomenological stoichiometry, Z of the coupled system have been evaluated. The amount of ATP produced per oxygen consumed, i.e. the actual, operating P/O ratio in the biosystem, the thermodynamic efficiency of the coupled reactions, η, and the Gibbs free energy dissipation, Φ have been calculated and shown to be in agreement with experimental data. At the concentration gradients of ADP and ATP prevailing under state 3 physiological conditions of OXPHOS that yield Vmax rates of ATP synthesis, a maximum in Φ of ∼0.5J(hmgprotein)−1, corresponding to a thermodynamic efficiency of ∼60% for oxidation on succinate, has been obtained. Novel mechanistic insights arising from the above have been discussed. This is the first report of a 3 × 3 system of coupled chemical reactions with transport in a biological context in which the phenomenological coefficients have been evaluated from experimental data.

Hydrodynamic fluctuations, diffusion and correlation functions in systems of particles adsorbed on solid surfaces

We present the detailed derivation of the equations describing the evolution of the hydrodynamic fluctuations of the coverage of particles adsorbed on homogeneous lattices. Using the method of the non-equilibrium statistical operator, we reduce the balance equation governing the behavior of the individual particles to the diffusion equation. On a macroscopic level, this equation describes the approach to equilibrium of the hydrodynamic coverage fluctuations. We obtain the analytical expressions for the Fickian diffusivity and Onsager phenomenological coefficient. These expressions are derived with account of the lateral interaction between the particles. They are simple functions of the thermodynamic quantities — derivatives of the thermodynamic potential over its arguments. The transport coefficients accurately describe the development of fluctuations in the entire coverage region and in the wide range of lateral interactions. We presented an elementary introduction to the theory of fluctuations in the lattice gas systems. For calculations of the correlation function and spectral density of fluctuations, we use the Langevin approach and the method of moments. The exact coincidence of the analytical expressions for the diffusion coefficients obtained by the two independent calculations is the direct proof of the accuracy of the approach developed in Chumak and Tarasenko (1980).

Introducing the concept of generalized thermal diffusivity to understand coupled heat–charge transport in ionic solutions

A theoretical framework addressing the coupled thermal and charge transport phenomena in ionic solutions is here developed. Starting from the microscopic definitions of thermal and charge currents from Onsager formulation of non-equilibrium thermodynamics, a unique, very general and compact form of the governing differential equation for the evolution of a temperature profile is derived. In particular, the concept of generalized thermal diffusivity is introduced to capture the overall effect of the coupling between heat and charge transport in a single phenomenological coefficient as well as to shed light on the non-equivalent situations of concurrent or discordant heat and charge currents. To validate our theoretical framework, an ionic salt solution of NaCl in water is investigated.

Numerical Equivalent Acoustic Material for Air-Filled Porous Absorption Simulations in Finite Different Time Domain Methods: Design and Comparison

Extracting the microscopic parameters of a porous material is a complex task, and attempts have been made to develop models that can simulate their characteristics, gathering the least amount of information possible. As a case in point, tests to evaluate macroscopic behaviors such as tortuosity, which depends directly on the microscopic fluid velocities, are highly susceptible to generate errors if the precision of the measurement devices is not correct, and the same goes for the other parameters. For this reason, in this paper, a sound propagation model in porous materials with a rigid frame is presented based on a local theory, which tries to simplify, even more, the way to obtain the basic characteristics of porous materials, such as their absorption coefficient at normal and random incidence, and their normal surface impedance. The proposed linearized equivalent fluid model presents four phenomenological coefficients, which characterize acoustic propagation trough the material. Their values are obtained from the material thickness and a measurement in an impedance tube following the ISO 10534 standard. Thus, what is only required is the measured absorption coefficient, either on one third or one octave bands, to fully represent the acoustic behavior in the finite different in time domain (FDTD) method. The model has been simulated with FDTD in porous and fibrous kernels, and the results show a strong agreement with the laboratory measurements and with the analytical results calculated with well-established semi-phenomenological models.

Design, Transport/Molecular Scale Electronics, Electric Properties, and a Conventional Quantum Study of a New Potential Molecular Switch for Nanoelectronic Devices.

In this study, we examined the influence of an external electric field applied in two directions: horizontal (X-axis) and vertical (Y-axis) on the electronic and vibrational properties of a field-effect molecular switch, denoted as M. We employed density functional theory and quantum theory of atoms in molecules for this analysis. The current-voltage (I-V) characteristic curve of molecular switch system M was computed by applying the Landauer formula. The results showed that the switching mechanism depends on the direction of the electric field. When the electric field is applied along the X-axis and its intensity is around 0.01 au, OFF/ON switching mechanisms occur. By utilizing electronic localization functions and localized-orbital locator topological analysis, we observed significant intramolecular electronic charge transfer "back and forth" in Au-M-Au systems when compared to the isolated system. The noncovalent interaction revealed that the Au-M-Au complex is also stabilized by electrostatic interactions. However, if the electric field is applied along the Y-axis, a switching mechanism (OFF/ON) occurs when the electric field intensity reaches 0.008 au. Additionally, the local electronic phenomenological coefficients (Lelec) of this field-effect molecular switch were determined by using the Onsager phenomenological approach. It can also be predicted that the molecular electrical conductance (G) increases as Lelec increases. Finally, the electronic and vibrational properties of the proposed models M and Au-M-Au exhibit a powerful switching mechanism that may potentially be employed in a new generation of electronic devices.

Progress in the Measurements of Coupled Transport Mechanisms in the Electrolyte of a PEM Based Thermogalvanic Cell

A promising measure to increase the efficiency of energy conversion is the use of low temperature waste heat being readily available in a vast amount. Thermogalvanic cells (TGC) offer the possibility of electrical energy harvesting from such thermal energy. An externally applied heat source leads to a temperature gradient across the electrolyte inducing a gradient in the chemical potential and a difference in the electrical potential between the electrodes. Due to the aim of approaching a homogeneous equilibrium different coupled molecular transport mechanisms are taking place in the electrolyte impacting the performance of the TGC. In contrast to the common approach of using classical transport correlations such as Fourier’s, Ohm’s or Fick’s law to describe these coupled processes this work applies the theory of non-equilibrium thermodynamics (NET). The method considers all interactions of the driving forces and resulting fluxes occurring in the electrolyte and clearly separates the transport phenomena into their origin. The knowledge of these relations, which can be described by characteristic phenomenological coefficients, gives a better understanding of the TGCs internal processes and the opportunity to determine the entropy production aligned with local heat sources inside its electrolyte. In this work a TGC based on a polymer electrolyte membrane with two gaseous hydrogen electrodes of different temperatures was investigated experimentally. Due to the need of water in the electrolyte to ensure ionic transport the TGC was fed with a humidified hydrogen gas. The experimental setup gives the opportunity of precisely adjusting the temperature and composition of the species at both electrodes thus control the gradients in temperature, concentration i.e. chemical potential and electric potential between the electrodes. By suppressing all but one driving force across the electrolyte and measuring the open circuit voltage (OCV) different coupling coefficients as well as the occurring fluxes in the electrolyte were determined for a wide variety of working conditions. By implementing the measured phenomenological coefficients in an earlier published model of the TGC considered in this work a significantly lower deviation of the modeled and measured OCV values compared to the approach of using classical transport coefficients can be determined. This indicates the importance of applying the NET when considering transport phenomena while different gradients being present. We also show that by an aligned combination of the gradients in temperature and chemical potential of the water their impacts on the electrical potential can sum up leading to a higher OCV or even cause a pole reversal due to contrary effects on the electrical potential difference. Figure 1

H-theorem and boundary conditions for two-temperature model: Application to wave propagation and heat transfer in polyatomic gases.

Polyatomic gases find numerous applications across various scientific and technological fields, necessitating a quantitative understanding of their behavior in nonequilibrium conditions. In this study, we investigate the behavior of rarefied polyatomic gases, particularly focusing on heat transfer and sound propagation phenomena. By utilizing a two-temperature model, we establish constitutive equationsfor internal and translational heat fluxes based on the second law of thermodynamics. A novel reduced two-temperature model is proposed, which accurately describes the system's behavior while reducing computational complexity. Additionally, we develop phenomenological boundary conditions adhering to the second law, enabling the simulation of gas-surface interactions. The phenomenological coefficients in the constitutive equationsand boundary conditions are determined by comparison with relevant literature. Our computational analysis includes conductive heat transfer between parallel plates, examination of sound wave behavior, and exploration of spontaneous Rayleigh-Brillouin scattering. The results provide valuable insights into the dynamics of polyatomic gases, contributing to various technological applications involving heat transfer and sound propagation.

Relativistic hydrodynamics from the single-generator bracket formalism of nonequilibrium thermodynamics

Abstract We employ the generalized bracket formalism of nonequilibrium thermodynamics by Beris and Edwards to derive Lorentz-covariant time-evolution equations for an imperfect fluid with viscosity, dilatational viscosity, and thermal conductivity. Following closely the analysis presented by Öttinger (Physica A, 259, 1998, 24–42; Physica A, 254, 1998, 433–450) to the same problem but for the GENERIC formalism, we include in the set of hydrodynamic variables a covariant vector playing the role of a generalized thermal force and a covariant tensor closely related to the velocity gradient tensor. In our work here, we derive first the nonrelativistic equations and then we proceed to obtain the relativistic ones by elevating the thermal variable to a four-vector, the mechanical force variable to a four-by-four tensor, and by representing the Hamiltonian of the system with the time component of the energy-momentum tensor. For the Poisson and dissipation brackets we assume the same general structure as in the nonrelativistic case, but with the phenomenological coefficients in the dissipation bracket describing friction to heat and viscous effects being properly constrained for the resulting dynamic equations to be manifest Lorentz-covariant. The final relativistic equations are identical to those derived by Öttinger but the present approach seems to be more general in the sense that one could think of alternative forms of the phenomenological coefficients describing friction that could ensure Lorentz-covariance.

Способ экспериментального нахождения коэффициента склоновой эрозии

The article deals with the theory of slope erosion, developed on the basis of the phenomenological law, according to which the intensity vector of soil erosion from the slope is proportional to the absolute value of its height gradient vector and inverse in direction. Since the erosion model includes a phenomenological coefficient of proportionality between the intensity of soil weathering and the elevation gradient, it is necessary to provide a way to find such a coefficient experimentally. Comparison of changes in elevation data obtained during field monitoring with the results of theoretical calculations enables identifying it

A new approach for evaluating photosynthetic bio-hydrogen production: The dissipation rate method

A dissipative rate model is established by using the non-equilibrium thermodynamics method to evaluate photosynthetic bio-hydrogen production process. The mass transfer dissipation rate, chemical reaction dissipation rate and total dissipation rate for the bio-hydrogen production processes with glucose and acetic acid are calculated and analyzed respectively by using the proposed dissipation rate model. When substrate concentration is taken as variable (15 g/L,20 g/L and25 g/L), the total dissipation rate and mass transfer phenomenological coefficient of hydrogen production process with 20 g/L are the lowest, and the maximum dissipation rate is 7.7288J/h. The phenomenological coefficient of chemical reaction is larger at high concentration. When the temperature is variable (298.15 K,303.15Kand308.15 K), the dissipation rate is lowest at 303.15 K and the chemical reaction coefficient is largest and the maximum dissipation rate is 6.0596J/h. In addition, the mass transfer phenomenological coefficient is larger at high temperature. With the initial pH as variable (6.5,7.0,7.5), the maximum dissipation rate of 11.2271J/h is obtained at pH 7.5. At high pH, the mass transfer phenomenological coefficient is large and the chemical reaction coefficient is exactly the opposite. This model can predict the energy dissipation law in the process of photosynthetic biohydrogen production, and provide a theoretical basis for the subsequent process optimization.

State-and-rate friction in contact-line dynamics.

In order to probe the dynamics of contact-line motion, we study the macroscopic properties of sessile drops deposited on and then aspirated from carefully prepared horizontal surfaces. By measuring the contact angle and drop width simultaneously during droplet removal, we determine the changes in the shape of the drop as it depins and recedes. Our data indicate that there is a force which opposes the motion of the contact line that depends both on the amount of time that the drop has been in contact with the surface and on the withdrawal rate. For water on silanized glass, we capture the experimentally observed behavior with an overdamped dynamical model of contact-line motion in which the phenomenological drag coefficient and the assumed equilibrium contact angle are the only inputs. In this case, the damping coefficient decreases with increasing velocity of the contact line. For other liquid-substrate pairs, the observed contact-line motion suggests that a maximum static friction force is important in addition to damping. The dependence on time of contact and withdrawal rate, reminiscent of rate-and-state friction between solid surfaces, is qualitatively consistent across three substrate-liquid pairs.

Sedimentation velocity FDS studies of antibodies in pooled human serum.

The biotech industry has great interest in investigating therapeutic proteins in high concentration environments like human serum. The fluorescence detection system (Aviv-FDS) allows the performance of analytical ultracentrifuge (AUC) sedimentation velocity (SV) experiments in tracer or BOLTS protocols. Here, we compare six pooled human serum samples by AUC SV techniques and demonstrate the potential of this technology for characterizing therapeutic antibodies in serum. Control FDS SV experiments on serum alone reveal a bilirubin-HSA complex whose sedimentation is slowed by solution nonideality and exhibits a Johnston-Ogston (JO) effect due to the presence of high concentrations of IgG. Absorbance SV experiments on diluted serum samples verify the HSA-IgG composition as well as a significant IgM pentamer boundary at 19s. Alexa-488 labeled Simponi (Golimumab) is used as a tracer to investigate the behavior of a therapeutic monoclonal antibody (mAb) in serum, and the sedimentation behavior of total IgG in serum. Serum dilution experiments allow extrapolation to zero concentration to extract so, while global direct boundary fitting with SEDANAL verifies the utility of a matrix of self- and cross-term phenomenological nonideality coefficients (ks and BM1) and the source of the JO effect. The best fits include weak reversible association (~ 4 × 103M-1) between Simponi and total human IgG. Secondary mAbs to human IgG and IgM verify the formation of a 10.2s 1:1 complex with human IgG and a 19s complex with human IgM pentamers. These results demonstrate that FDS AUC allows a range of approaches for investigating therapeutic antibodies in human serum.

Automated reaction kinetics and network exploration (Arkane): A statistical mechanics, thermodynamics, transition state theory, and master equation software

AbstractThe open‐source statistical mechanics software described here, Arkane–Automated Reaction Kinetics and Network Exploration–facilitates computations of thermodynamic properties of chemical species, high‐pressure limit reaction rate coefficients, and pressure‐dependent rate coefficient over multi‐well molecular potential energy surfaces (PES) including the effects of collisional energy transfer on phenomenological kinetics. Arkane can use estimates to fill in information for molecules or reactions where quantum chemistry information is missing. The software solves the internal energy master equation for complex unimolecular reaction systems. Inputs to the software include converged electronic structure computations performed by the user using a variety of supported software packages (Gaussian, Molpro, Orca, TeraChem, Q‐Chem, Psi4). The software outputs high‐pressure limit rate coefficients and pressure‐dependent phenomenological rate coefficients, as well as computed thermodynamic properties (enthalpy, entropy, and constant pressure heat capacity) with added energy corrections. Some of the key features of Arkane include treatment of 1D, 2D or ND hindered internal rotation modes, treatment of free internal rotation modes, quantum tunneling effect consideration, transition state theory (TST) and Rice‐Ramsperger‐Kassel‐Marcus (RRKM) rate coefficient computations, master equation solution with four implemented methods, inverse‐Laplace transform of high‐pressure limit rate coefficients into the energy domain, energy corrections based on bond‐additivity or isodesmic reactions, automated and efficient PES exploration, and PES sensitivity analysis. The present work describes the design of Arkane, how it should be used, and refers to the theory that it employs. Arkane is distributed via the RMG‐Py software suite (https://github.com/ReactionMechanismGenerator/RMG‐Py).

Six-Field Theory for a Polyatomic Gas Mixture: Extended Thermodynamics and Kinetic Models

Polyatomic gases may be characterized by internal molecular degrees of freedom. As a consequence, at a macroscopic level, dynamic pressure appears, which may be related to the bulk viscosity of the gas. Inspired by the models of a single polyatomic gas with six fields, developed within rational extended thermodynamics (RET) and the kinetic theory of gases, this paper presents a six-field theory for the mixture of polyatomic gases. First, the macroscopic mixture model is developed within the framework of RET. Second, the mixture of gases with six fields is analyzed in the context of the kinetic theory of gases, and corresponding moment equations are derived. Finally, complete closure of the RET model, i.e., computation of the phenomenological coefficients, is achieved by means of a combined macroscopic/kinetic closure procedure.

On non-Darcian flow behavior in a rough-walled fracture filled with a porous medium

Fluid flow through filled rock fractures is relevant to numerous engineering applications and geophysical processes. However, a proper understanding of the flow behaviors in filled fractures is still far from being completed. To investigate the fluid flow in a rough-walled fracture filled with a porous medium, we systematically compare the micro- and macroscopic flow behaviors within filled fractures and corresponding open fractures and porous media based on a series of pore-scale simulation results. We find that the filling medium has a dual role in altering the flow regime, as the filling particles can not only cut the flow domain into several pore channels and thus limit the generation of large-span eddies, but also force the fluid to flow around them and promote the generation of local eddies. Compared with porous media, the fluid flow within filled fractures is confined by fracture walls, which greatly alters the media permeability and the flow nonlinearity therein. By introducing the hydraulic radius and Darcy-Weisbach equation, we develop a new semi-empirical model to estimate the fluid flow through filled fractures using phenomenological coefficients of corresponding open fractures and porous media. The proposed model, satisfying dimensional consistency, shows high fidelity in predicting water flow through filled fractures. More importantly, this model can be successfully reduced to the typical form of the Forchheimer equation applied to open fractures and porous media. The results and findings are expected to be useful in predicting and evaluating the fluid flow in complex geological setting.

Diffusion in a binary mixture of molecules adsorbed on a multisite two-dimensional lattice

The diffusion in a binary mixture of species coadsorbed on a multisite square lattice is investigated by a theoretical approach (Chumak and Tarasenko, 1980) based on the non-equilibrium statistical operator method proposed by Zubarev (1961). The investigated lattice gas system is rather complex. There is a mixture of two types of particles (atoms, and/or molecules) adsorbed on a multisite lattice which consists of the three types of adsorption sites. This lattice can be subdivided onto three homogeneous square sublattices composed of the sites of the same type. As the binding energies for the molecules of distinct types adsorbed on the nonidentical sublattices are different, there are six average occupancies (coverages) describing the molecule distribution over the sublattices. A system of the balance equations, which controls the exchange of the molecules between the sublattices on the atomistic level is reduced to the diffusion equations describing the evolution of small hydrodynamic fluctuations of these coverages on the macroscopic level. The diffusion equations are written in the Onsager representation, when the driving forces are gradients of the chemical potentials and in the Fickian representation, when the driving forces are the gradients of coverages. The derivation of these equations results in the analytical expressions for the Fickian diffusivities and Onsager phenomenological coefficients. Despite the complex process of derivation, the final results are simple. The kinetic coefficients, which describe the non-equilibrium state of the molecule system, are expressed via the thermodynamic quantities calculated in the equilibrium state of the system: the chemical potentials (or activities), pair correlation functions and the isothermal susceptibilities. These expressions are derived with account of the lateral interactions between the nearest neighbor molecules. The matrix of the Fickian diffusivities has the ordinary classical form. The diffusivity is a non-symmetric 2 × 2 matrix. The Onsager coefficients are represented by a diagonal 2 × 2 matrix, where the cross terms are absent.

Domain-wall dynamics driven by thermal and electrical spin-transfer torque

According to spin Seebeck effect, a thermal spin current will be produced when a temperature gradient is applied to the metallic ferromagnet. Similar to the electrical spin transfer torque (ESTT) induced by spin-polarized current, there is also a thermal spin transfer torque (TSTT) caused by the thermal spin current, which can be attributed to the s-d interaction between the conduction electrons and the local magnetization. In this paper, the generalized analytical expressions of thermal spin current and TSTT are derived based on the spinor Boltzmann equation (SBE) under the local equilibrium approximation. This generalized TSTT has different terms compared to the previous phenomenological form, and the phenomenological coefficients can be determined theoretically within our framework. Combined with the SBE under the applied electric field and temperature gradient, we solve the Landau-Lifshitz-Gilbert-Levy equation to study the domain wall (DW) motion driven by the ESTT and TSTT. We investigated the temperature-dependent DW motion, the total spin torque, and TSTT in permalloys. We found that the velocity of the DW can be promoted by increasing temperature and temperature gradient, which provide a path to effectively utilize the Joule heating in spintronics devices.

A technique for obtaining analytical heuristic solutions in problems of diffraction on two-dimensional semi-infinite objects with non-ideal boundary conditions

A technique for obtaining analytical heuristic solutions in two-dimensional problems of electromagnetic wave diffraction on semi-infinite objects with non-ideal boundary conditions is proposed. The essence of the technique is that the values of the phenomenological coefficients contained in the heuristic formulas are found numerically, minimizing the discrepancy between the heuristic solution and the verification one. For the case of diffraction on a half-plane with two-sided impedance boundary conditions, an additional analytical solution of the corresponding problem is obtained. It is based on the requirement that the reciprocity principle be satisfied. The coincidence of the phenomenological adjusting coefficients found numerically for the same problem with those that were previously found analytically proves the effectiveness of the proposed technique.

Semianalytical Solution for Thermal Consolidation of Viscoelastic Marine Clay with the Fractional Order Derivative

The deformation property of marine clay under a heat source has received considerable attention in the geotechnical literature. In this paper, a three-parameter fractional order derivative model is introduced into the thermo-hydro-mechanical coupling governing equations with thermal filtration and thermo-osmosis to simulate viscoelastic characteristics of marine clay. The excess pore pressure, temperature increment, and displacement of marine clay are derived by using the Laplace transform method, and the semianalytical solution for the one-dimensional thermal consolidation in the time domain is derived by using a numerical inversion of the inverse Laplace transform. The influence of the order of the fractional derivative, material parameters, and phenomenological coefficient on thermal consolidation is investigated based on the present solutions. It is shown that the influence of the fractional derivative parameter on the excess pore pressure and displacement of marine clay depends on the properties of soil mass, and the temperature increment has an obvious effect on the thermal filtration and thermo-osmosis process.