Free Energy Function Research Articles

Optimal Control of Dielectric Elastomer Actuated Multibody Dynamical Systems.

In this work, a simulation model for the optimal control of dielectric elastomer actuated flexible multibody dynamics systems is presented. The dielectric elastomer actuator (DEA) behaves like a flexible artificial muscle in soft robotics. It is modeled as an electromechanically coupled geometrically exact beam, where the electric charges serve as control variables. The DEA-beam is integrated as an actuator into multibody systems consisting of rigid and flexible components. The model also represents contact interaction via unilateral constraints between the beam actuator and, for example, a rigid body during the grasping process of a soft robot. With a mathematically concise and physically representative formulation, a reduced free energy function is developed for the electromechanically coupled beam. In the optimal control problem, an objective function is minimized while the electromechanically coupled dynamic balance equations for the multibody system have to be fulfilled together with the complementarity conditions for the contact and boundary conditions. The optimal control problem is solved via a direct transcription method, transforming it into a constrained nonlinear optimization problem. The electromechanically coupled geometrically exact beam is firstly semidiscretized with one-dimensional finite elements and then the multibody dynamics is temporally discretized with a variational integrator leading to the discrete Euler-Lagrange equations, which are further reduced with the null space projection. The discrete Euler-Lagrange equations and the boundary conditions serve as equality constraints, whereas the contact constraints are treated as inequality constraints in the optimization of the discretized objective. The constrained optimization problem is solved using the Interior Point Optimizer solver. The effectiveness of the developed model is demonstrated by three numerical examples, including a cantilever beam, a soft robotic worm, and a soft robotic grasper.

Thermomechanical response of nonlinear viscoelastic materials

In this article, the thermomechanical properties of the classical and nonclassical viscoelastic materials with particular emphasis on the entropy are studied in the framework of continuum thermodynamics. Specifically, considering the Clausius integral as “Part I” of the second law of thermodynamics in the classical formulation of continuum thermodynamics, the entropy function for various classes of nonclassical thermo-viscoelastic materials is shown to exist. This is achieved by employing the first law of thermodynamics and a scalar potential known as the Helmholtz free energy function. In addition, another function known as the internal rate of production of entropy defined for the classical and nonclassical thermo-viscoelastic materials is adopted to obtain a balance law for the entropy. Finally, upon linearizing the theory, a coupled system of differential equations is obtained for the nonclassical thermo-viscoelastic materials, which under some special circumstances, permits propagation of damped harmonic waves in the viscoelastic medium.

EPISOL: A software package with expanded functions to perform 3D-RISM calculations for the solvation of chemical and biological molecules.

Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.

Computing the Gromov-Wasserstein Distance between Two Surface Meshes Using Optimal Transport

The Gromov-Wasserstein (GW) formalism can be seen as a generalization of the optimal transport (OT) formalism for comparing two distributions associated with different metric spaces. It is a quadratic optimization problem and solving it usually has computational costs that can rise sharply if the problem size exceeds a few hundred points. Recently fast techniques based on entropy regularization have being developed to solve an approximation of the GW problem quickly. There are issues, however, with the numerical convergence of those regularized approximations to the true GW solution. To circumvent those issues, we introduce a novel strategy to solve the discrete GW problem using methods taken from statistical physics. We build a temperature-dependent free energy function that reflects the GW problem’s constraints. To account for possible differences of scales between the two metric spaces, we introduce a scaling factor s in the definition of the energy. From the extremum of the free energy, we derive a mapping between the two probability measures that are being compared, as well as a distance between those measures. This distance is equal to the GW distance when the temperature goes to zero. The optimal scaling factor itself is obtained by minimizing the free energy with respect to s. We illustrate our approach on the problem of comparing shapes defined by unstructured triangulations of their surfaces. We use several synthetic and “real life” datasets. We demonstrate the accuracy and automaticity of our approach in non-rigid registration of shapes. We provide numerical evidence that there is a strong correlation between the GW distances computed from low-resolution, surface-based representations of proteins and the analogous distances computed from atomistic models of the same proteins.

A comparative study on DNA and protein binding properties of thymol and thymoquinone

Two phytochemicals, thymol and thymoquinone obtained from thymes (Thymus vulgaris L., Lamiaceae etc.) and Nagila Sativa seed, respectively. Both the phytochemicals show several biochemical activities like anticancer, antimicrobial etc. In this paper, we studied the affinities of thymol and thymoquinone towards calf thymus DNA (CT-DNA) and protein (bovine serum albumin). Spectroscopic and molecular modelling studies revealed that both compounds have a high affinity toward both the receptors; DNA and protein. Both phytochemicals binds to the minor grooves of DNA and suitable pockets of protein. Several free energy function and hydrogen bonding play significant role during the binding phenomenon. Communicated by Ramaswamy H. Sarma

Oxygen diffusion in glassy propylene carbonate: Energetics and spatial correlation of jump rates

Quenching of phenanthrene phosphorescence by molecular oxygen was used as a tool to determine the distribution function of the activation free energy of oxygen jumps in glassy propylene carbonate. The distribution width is shown to increase linearly with temperature within the range from 135 to 156 K. The dispersion of the activation free energy is caused by the spatial fluctuations of the activation entropy of oxygen jumps but not the energy barriers; the spatial dispersion of energy barriers is found to be zero. A characteristic length of the spatial correlation of the activation entropy is about 1.3 nm. The apparent activation energy linearly correlates with the macroscopic high-frequency shear modulus. The jump rates of oxygen molecules lie in the range of Johari-Goldstein relaxation rates. We suggest that an oxygen molecule overcomes the barrier between two neighboring interstitial sites due to low-frequency localized vibrational excitations of string-like groups of host molecules which draw the oxygen molecule in the motion.

Elastoplastic dynamic constitutive model of concrete with combined effects of temperature and strain rate

This short communication proposed a dynamic constitutive model, which investigated the combined effects of temperatures and strain rates to characterize the mechanical performance of concrete exposed to fire and blast simultaneously. Compared with the existing constitutive models, the proposed constitutive model is relatively simple with uniform series of parameters, and can be more easily applied to the numerical simulation of the dynamic behaviors of concrete. The elastic strain increment expression for concrete was derived from the elastic free energy function, and the plastic strain increment expression was based on the classical plastic theory. Based on Drucker-Prager yield criterion, the yield equation considering the strengthening effect of strain rate was established. The damage criterion was established to characterize the damage caused by various temperatures and strain rates. The stress–strain diagrams of concrete materials with different temperatures (200 °C, 400 °C, 600 °C, and 800 °C) and strain rates (50 s−1-185 s−1) were calculated under the condition of uniaxial dynamic compress and temperature loading. By comparing with the previous test results, it can be concluded that the current constitutive model accurately simulates the mechanical performance of concrete with various temperatures and various strain rates. It provided a theoretical basis for the safety evaluation of concrete engineering structures.

Thermodynamically consistent phase-field modelling of activated solute transport in binary solvent fluids

Active diffusion of substances in binary immiscible and incompressible fluids with different densities occurs universally in nature and industry, but relevant mathematical models and numerical simulation have been studied scarcely so far. In this paper, a thermodynamically consistent phase-field model is established to describe the activated solute transport in binary fluids with different densities. A mixed free-energy function for multiple solutes is proposed, which leads to different solute chemical potentials in binary solvent fluids, thus it has the ability to characterize the solubility difference of the solutes in two solvents. The two-phase flow is governed by a general hydrodynamic phase-field model that can account for general average velocity and different densities. The proposed model is derived rigorously using the second law of thermodynamics. Moreover, a general multi-component solute diffusion model is established using the Maxwell–Stefan approach, which involves the crossing influences between different solutes. To solve the model effectively, an efficient, linearized and decoupled numerical method is proposed for the model as well. The proposed numerical method can preserve the thermodynamical consistency, i.e. obeying an energy dissipation law at the discrete level, as well as guarantee the mass conservation law for the solutes and solvent fluids. Numerical experiments are carried out to show that the proposed model and numerical method can simulate various processes of the solute active diffusion in two-phase solvent fluids.

A mechanistically motivated constitutive model of biopolymer hydrogels with structural evolution

Understanding the deformation behavior of biopolymer hydrogels would aid in the design of artificial hydrogels and nanoparticle-based drug delivery systems, which have been extensively used in the fields of biomedicine. Here, we develop a mechanistically motivated constitutive model to elucidate the structural evolution of biopolymer hydrogels. A free energy function includingconfigurational entropy of biopolymer nanofibers, potential energy of physical crosslinks, and mixing energy of water molecules is formulated. Both the micro/nanostructures and dynamic features of nanofibrous network under stretching are captured investigating the evolution of physical crosslinks and water hydration. In addition, a quantitative relationship correlating the pore size in the nanofibrous network with mechanical stretching is proposed. Different from chemically crosslinked hydrogels, the pore size of physically crosslinked hydrogels could continuously increase under stretching, which is attributed to the straightening and bundling of biopolymer nanofibers. We further find that a low strain rate or a high swelling ratio promotes the structural evolution of biopolymer hydrogels and increases the pore size of the network. The model predictions are in good agreement with the experimental results. This work could shed light on the deformation mechanisms of physically crosslinked biopolymer hydrogels, thus providing guidelines for the design of drug delivery systems translocating within biopolymer hydrogels.

Constitutive modeling for the training process of two-way shape memory effect under thermal cyclic loading

Shape memory alloys (SMAs)—if trained properly—can induce two-way shape memory effect which is applicable in actuator design using SMAs. In this study, a three-dimensional phenomenological model is proposed for SMAs within the framework of irreversible thermodynamics in order to predict the training process under cyclic loading and the induced two-way shape memory effect. In this regard, transformation and permanent strains are considered as internal variables and Helmholtz free energy function is introduced using several material parameters accounting for elastic, transformation and permanent deformation mechanisms. In order to demonstrate the capabilities of the proposed model, we first compare the model results with several experimental results and prove that the current model fits well with various experiments under cyclic loading as well as two-way shape memory effect. In addition, the capabilities of the present model in predicting the two-way shape memory effect, degradation effects, evolution rate, stabilization of permanent strain as well as multiaxial loading have been carefully examined through parametric studies. It is concluded that the present model is able to predict the training process from the initial cycles to stabilization and two-way effect for different materials and conditions.

Improved reweighting protocols for variationally enhanced sampling simulations with multiple walkers.

In molecular dynamics simulations utilizing enhanced-sampling techniques, reweighting is a central component for recovering the targeted ensemble averages of the "unbiased" system by calculating and applying a bias-correction function c(t). We present enhanced reweighting protocols for variationally enhanced sampling (VES) simulations by exploiting a recent reweighting method, originally introduced in the metadynamics framework [Giberti et al. J. Chem. Theory Comput., 2020, 16, 100-107], which was modified and extended to multiple-walker simulations: these may be implemented either as "independent" walkers (associated with one unique correction function per walker) or "cooperative" ones that all share one correction function, which is the hitherto only explored option. When each case is combined with the two possibilities of determining c(t) by time integration up to either t or over the entire simulation period , altogether four reweighting options result. Their relative merits were assessed by well-tempered VES simulations of two model problems: locating the free-energy difference between two metastable molecular conformations of the N-acetyl-L-alanine methylamide dipeptide, and the recovery of an a priori known distribution when one water molecule in the liquid phase is perturbed by a periodic free-energy function. The most rapid convergence occurred for large cooperative walkers, regardless of the upper integration limit, but integrating up to t proved advantageous for small walker ensembles. That novel reweighting method compared favorably to the standard VES reweighting, as well as to current state-of-the-art reweighting options introduced for metadynamics simulations that estimate c(t) by integration over the collective variables. For further gains in computational speed and accuracy, we also introduce analytical solutions for c(t), as well as offering further insight into its features by approximative analytical expressions in the "high-temperature" regime.

Ferrimagnetic Characteristics and Spin Compensation Temperatures of a Mixed Spin-3 and Spin-5/2 Blume–Capel Model

We study the molecular mean-field theory (MMFT) based on the Gibbs–Bogolyubov free energy function of a ferrimagnetic with mixed spin-3 and spin-5/2 for various magnetic crystal fields in the Blume–Capel model. We have evaluated the free energy depending on the trial Hamiltonian operator. By minimizing the free energy of the present system, we have obtained the characteristic features of the longitudinal magnetizations, compensation temperatures, and re-entrant behaviors in the ranges of low temperatures. In particular, we study the effect of magnetic anisotropies on the critical phenomena for the proposed model. The sublattice magnetization dependence of the free energy function has been discussed as well. Our results predict the existence of multiple spin compensation points in the disordered Blume–Capel system for a square lattice.

Cumulative Millisecond-Long Sampling for a Comprehensive Energetic Evaluation of Aqueous Ionic Liquid Effects on Amino Acid Interactions

The interactions of amino acid side-chains confer diverse energetic contributions and physical properties to a protein's stability and function. Various computational tools estimate the effect of changing a given amino acid on the protein's stability based on parametrized (free) energy functions. When parametrized for the prediction of protein stability in water, such energy functions can lead to suboptimal results for other solvents, such as ionic liquids (IL), aqueous ionic liquids (aIL), or salt solutions. However, to our knowledge, no comprehensive data are available describing the energetic effects of aIL on intramolecular protein interactions. Here, we present the most comprehensive set of potential of mean force (PMF) profiles of pairwise protein-residue interactions to date, covering 50 relevant interactions in water, the two biotechnologically relevant aIL [BMIM/Cl] and [BMIM/TfO], and [Na/Cl]. These results are based on a cumulated simulation time of >1 ms. aIL and salt ions can weaken, but also strengthen, specific residue interactions by more than 3 kcal mol-1, depending on the residue pair, residue-residue configuration, participating ions, and concentration, necessitating considering such interactions specifically. These changes originate from a complex interplay of competitive or cooperative noncovalent ion-residue interactions, changes in solvent structural dynamics, or unspecific charge screening effects and occur at the contact distance but also at larger, solvent-separated distances. This data provide explanations at the atomistic and energetic levels for complex IL effects on protein stability and should help improve the prediction accuracies of computational tools that estimate protein stability based on (free) energy functions.

Phase field modelling of ductile fracture in the frameworks of non-conventional thermodynamics and continuum damage mechanics

In the present work, a phase field approach for ductile fracture and fatigue failure in the framework of non-conventional thermodynamics is proposed. In contrast to brittle fracture, the physical mechanisms for fracture are supposed to be initiation, growth and coalescence of voids, driven by plastic deformation. Thus, the aim of the paper is to demonstrate how well-established ingredients of plasticity, continuum damage mechanics and phase field theories can be fit in the adopted framework. The main features of the proposed theory are that damage evolution is coupled to the evolution of plastic strain, that the appropriate modelling of yield stress effects in the free energy function is of central importance and that fatigue failure can be captured without employing fatigue degradation functions. Various numerical examples and comparisons with experimental data demonstrate the capabilities of the model.

Chiral nonreciprocal elasticity and mechanical activity

There has been significant recent interest in creating, modeling, and exploiting the novel functionality afforded by odd elastic solids, which are a specific class of active matter whose behavior cannot be described by a free energy function. As a result, the mechanical behavior of such solids can be described by a non-symmetric elasticity tensor which means they can be mechanically active, and thus do work on their surroundings through quasistatic deformation cycles without energetic gain or loss terms explicitly appearing in the solid’s equation of state. However, previous incarnations of such solids have required the usage of active elements coupled with robotic machinery powered by independent external energy sources to operate. As such, it is unclear whether the non-symmetric elasticity of these solids can be developed using only passive elements that do not require the usage of energy sources, and furthermore how nonreciprocity in elastic media enables non-symmetric elasticity in elastic solids or mechanical activity. In this work, we propose the notion of chiral, nonreciprocal elasticity, which represents a generic route to enabling 2D, isotropic elastic solids exhibiting non-symmetric elasticity. Chiral, nonreciprocal elasticity describes elastic behaviors that result from coupling chirality with nonreciprocity—specifically, (1) the modulation of the elastic properties depending on the mode and direction of deformation and (2) the nonreciprocal coupling of different deformation fields, both of which enable the solid to exhibit a non-symmetric elasticity tensor. To motivate this, we introduce an isotropic 2D chiral metamaterial made of passive chiral elements that, by exploiting local geometric asymmetry, behaves in a chiral, nonreciprocal elastic fashion. We derive, based on the mechanics of a discrete model of this chiral element, the resulting continuum field equations and constitutive relationships that capture the chiral, nonreciprocal elastic behavior. Then, we establish a thermodynamic framework of energy balance and conservation of chiral, nonreciprocal elastic solids, based on which we demonstrate the ability of the proposed chiral metamaterial to act as a source of mechanical work when used in specific quasistatic deformation cycles, though no energy is dissipated by its passive elements. Finally, we demonstrate through numerical finite element simulations the practical implementation of the deformation cycles, while elucidating the specific conditions needed for the chiral metamaterial to exhibit linear, chiral nonreciprocal elastic behavior throughout the deformation cycle, and thus reveal mechanical activity.

Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals.

Dynamic density functional theory (DDFT) is a promising approach for predicting the structural evolution of a drying suspension containing one or more types of colloidal particles. The assumed free-energy functional is a key component of DDFT that dictates the thermodynamics of the model and, in turn, the density flux due to a concentration gradient. In this work, we compare several commonly used free-energy functionals for drying hard-sphere suspensions, including local-density approximations based on the ideal-gas, virial, and Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state as well as a weighted-density approximation based on fundamental measure theory (FMT). To determine the accuracy of each functional, we model one- and two-component hard-sphere suspensions in a drying film with varied initial heights and compositions, and we compare the DDFT-predicted volume fraction profiles to particle-based Brownian dynamics (BD) simulations. FMT accurately predicts the structure of the one-component suspensions even at high concentrations and when significant density gradients develop, but the virial and BMCSL equations of state provide reasonable approximations for smaller concentrations at a reduced computational cost. In the two-component suspensions, FMT and BMCSL are similar to each other but modestly overpredict the extent of stratification by size compared to BD simulations. This work provides helpful guidance for selecting thermodynamic models for soft materials in nonequilibrium processes, such as solvent drying, solvent freezing, and sedimentation.

Symmetry (Asymmetry) of the Molar Excess Gibbs Free Energy Function of the Binary Mixed Micelles of Bile Acid Anion and Classical Cationic Surfactant: Influence of Sterically Shielded and Sterically Unshielded Polar Groups of the Steroid Skeleton

Binary mixtures of surfactants build a binary mixed micelle in which the ratio of surfactants usually differs from the initial ratio of surfactants in their binary mixture. The thermodynamic stabilization of the binary mixed micellar pseudophase about the hypothetical ideal state (intermolecular interactions between the different particles and the conformational states of the particles are identical to those of monocomponent states) is described by the molar excess Gibbs free energy (gE). The dependence of gE on the molar fraction of surfactant i (xi) from the binary mixed micelle can be described by a symmetric function (symmetry is described to the line parallel to the y-axis and passes through xi = 0.5) or by an asymmetric function. Theoretical analysis (canonical partition function, conformational analysis) examines how the presence of different polar functional groups, some of which are sterically shielded from the steroid skeleton of bile salts (surfactant), affect the symmetry of the function gE of the binary mixed micelle of the cholic acid anion (bile salts) and classic cationic surfactant (hydrophobic tail and polar head). Suppose the steroid skeleton of the bile salt contains non-sterically shielded polar groups (or the temperature is relatively high). In that case, gE is a symmetric function. At the same time, if the steroid skeleton also contains sterically shielded polar groups, then the gE function is asymmetric.

Modeling of load responses and aging of high strength fibers considering UV-radiation

Long-term illumination can damage the mechanical properties of high strength fiber composites, resulting in the material aging and loss of mechanical properties. To reveal the mechanism of ultraviolet- (UV-) induced damage, in this paper, a nonlinear constitutive model is developed to describe the elastic and inelastic deformation behavior of high strength fibers under UV-radiation and mechanical loadings. Two internal variables are employed to measure the effects of damage caused by UV-radiation and by mechanical loadings, respectively. The Helmholtz free energy function and the evolution equations of these two internal variables are investigated elaborately and given explicitly for high strength fibers. The proposed theoretical model is then applied to analyze the mechanical degradation of high-performance high strength fibers under uniaxial tension. The modulus and strength of the material predicted by the theoretical model match the aging experimental results rather well, which verifies the rationality and accuracy of the present model. This model is expected to predict the evolution of mechanical properties of high-strength fibers under UV-radiation, which can also provide a theoretical basis for the development of anti-UV technology of fiber reinforced composites.

Riemannian geometry of optimal driving and thermodynamic length and its application to chemical reaction networks

It is known that the trajectory of an endoreversibly driven system with minimal dissipation is a geodesic on the equilibrium state space. Thereby, the state space is equipped with the Riemannian metric given by the Hessian of the free energy function, known as Fisher information metric. However, the derivations given until now require both the system and the driving reservoir to be in local equilibrium. In the present article, we rederive the framework for chemical reaction networks (CRN) and thereby enhance its scope of applicability to the nonequilibrium situation. Moreover, because our results are derived without restrictive assumptions, we are able to discuss phenomena that could not be seen previously. We introduce a suitable weighted Fisher information metric on the space of chemical concentrations and show that it characterizes the dissipation caused by diffusive driving, with arbitrary diffusion rate constants. This allows us to consider driving far from equilibrium. As the main result, we show that the isometric embedding of a steady-state manifold into the concentration space yields a lower bound for the dissipation when the system is driven along the manifold. We give an analytic expression for this bound and for the corresponding geodesic, and thereby are able to dissect the contributions from the driving kinetics and from thermodynamics. Finally, we discuss in detail the application to quasithermostatic steady states.

Accelerating equilibration in first-principles molecular dynamics with orbital-free density functional theory

We introduce a practical hybrid approach that combines orbital-free density functional theory (DFT) with Kohn-Sham DFT for speeding up first-principles molecular dynamics simulations. Equilibrated ionic configurations are generated using orbital-free DFT for subsequent Kohn-Sham DFT molecular dynamics. This leads to a massive reduction of the simulation time without any sacrifice in accuracy. We assess this finding across systems of different sizes and temperature, up to the warm dense matter regime. To that end, we use the cosine distance between the time series of radial distribution functions representing the ionic configurations. Likewise, we show that the equilibrated ionic configurations from this hybrid approach significantly enhance the accuracy of machine-learning models that replace Kohn-Sham DFT. Our hybrid scheme enables systematic first-principles simulations of warm dense matter that are otherwise hampered by the large numbers of atoms and the prevalent high temperatures. Moreover, our finding provides an additional motivation for developing kinetic and noninteracting free-energy functionals for orbital-free DFT.