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This presentation provides information on stability analysis and selection principles, formalizing organization, and nonequilibrium statistical mechanics of organization.
In polymer nanoparticle composites (PNCs) with attractive interactions between nanoparticles (NPs) and polymers, a bound layer of the polymer forms on the NP surface, with significant effects on the macroscopic properties of the PNCs. The adsorption and wetting behaviors of polymer solutions in the presence of a solid surface are critical to the fabrication process of PNCs. In this study, we use both classical density functional theory (cDFT) and molecular dynamics (MD) simulations to study dilute and semi-dilute solutions of short polymer chains near a solid surface. Using cDFT, we calculate the equilibrium properties of polymer solutions near a flat surface while varying the solvent quality, surface–fluid interactions, and the polymer chain lengths to investigate their effects on the polymer adsorption and wetting transitions. Using MD simulations, we simulate polymer solutions near solid surfaces with three different curvatures (a flat surface and NPs with two radii) to study the static conformation of the polymer bound layer near the surface and the dynamic chain adsorption process. Additionally, we find that the bulk polymer concentration at which the wetting transition in the poor solvent system occurs is not affected by the difference in surface–fluid interactions; however, a threshold value of surface–fluid interaction is needed to observe the wetting transition. We also find that with good solvent, increasing the chain length or the difference in the surface–polymer interaction relative to the surface–solvent interaction increases the surface coverage of polymer segments and independent chains for all surface curvatures. Finally, we demonstrate that the polymer segmental adsorption times are heavily influenced only by the surface–fluid interactions, although polymers desorb more quickly from highly curved surfaces.
We present results from x-ray imaging of high-aspect-ratio magnetic reconnection experiments driven at the National Ignition Facility. Two parallel, self-magnetized, elongated laser-driven plumes are produced by tiling 40 laser beams. A magnetic reconnection layer is formed by the collision of the plumes. A gated x-ray framing pinhole camera with micro-channel plate detector produces multiple images through various filters of the formation and evolution of both the plumes and current sheet. As the diagnostic integrates plasma self-emission along the line of sight, two-dimensional electron temperature maps ⟨Te⟩Y are constructed by taking the ratio of intensity of these images obtained with different filters. The plumes have a characteristic temperature ⟨Te⟩Y=240 ± 20 eV at 2 ns after the initial laser irradiation and exhibit a slow cooling up to 4 ns. The reconnection layer forms at 3 ns with a temperature ⟨Te⟩Y=280 ± 50 eV as the result of the collision of the plumes. The error bars of the plumes and current sheet temperatures separate at 4 ns, showing the heating of the current sheet from colder inflows. Using a semi-analytical model, we survey various heating mechanisms in the current sheet. We find that reconnection energy conversion would dominate at low density (ne≲7×1018 cm−3) and electron-ion collisional drag at high-density (≳1019 cm−3).
We demonstrate analytically and verify numerically that the out-of-time order correlator is given by the thermal average of Loschmidt echo signals. This provides a direct link between the out-of-time-order correlator—a recently suggested measure of information scrambling in quantum chaotic systems—and the Loschmidt echo, a well-appreciated familiar diagnostic that captures the dynamical aspect of chaotic behavior in the time domain, and is accessible to experimental studies.
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Abstract Solvent selection is a pressing challenge in developing efficient and selective liquid phase catalytic processes, as predictive understanding of the solvent effect remains lacking. In this work, an attenuated total reflection infrared spectroscopy technique is developed to quantitatively measure adsorption isotherms on porous materials in solvent and decouple the thermodynamic contributions of van der Waals interactions within zeolite pore walls from those of pore-phase proton transfer. While both the pore diameter and the solvent identity dramatically impact the confinement (adsorption) step, the solvent identity plays a dominant role in proton-transfer. Combined computational and experimental investigations show increasingly favorable pore-phase proton transfer to pyridine in the order: water < acetonitrile < 1,4 – dioxane. Equilibrium methods unaffected by mass transfer limitations are outlined for quantitatively estimating fundamental thermodynamic values using statistical thermodynamics.
In this work, we review recent work by the authors to revisit the concept of extrapolating thermodynamic properties of classical systems using statistical mechanical principles. Specifically, we discuss how the combination of these principles with biased sampling techniques enables the prediction of free energy landscapes and other detailed information, such as structural properties, of the system in question. Remarkably accurate estimates of physical properties across a broad range of conditions have been achieved using this approach, greatly reducing the number of simulations needed to explore a given system's behaviour. While approximate, these extrapolations significantly amplify the amount of reasonably accurate information that can be extracted from simulations enabling a small set of them to feed data-intensive regression algorithms such as neural networks. Thus, this extrapolation methodology represents a useful tool for performing tasks such as high-throughput screening of physical properties, optimising force field parameters, exploring equilibrium phase behaviour, and enabling theory-guided data science for these systems.
Originally detected in rare earth pyrochlores, spin ice physics is now being artificially extended to a variety of geometries that control collective behavior and exotic properties, making graph theory their proper framework. We relate spin ice notions, such as ice rule, ice manifold, Coulomb phases, charges, and monopoles, to graph-theoretical notions, such as balance, in/out-degrees, and Euler paths. We then propose a field-theoretical treatment in which topological charges and monopoles are the degrees of freedom, while the binary spins are subsumed in an entropic interaction among charges. We show that for a spin ice on a graph in a Gaussian approximation, the kernel of the entropic interaction is the inverse of the graph Laplacian, and we compute screening functions from the graph spectra as Green operators for the screened Poisson problem on a graph. We then apply the treatment to star graphs, tournaments, cycles, and regular spin ice in different dimensions. Our aim is twofold: to set spin ice physics in a proper graph setting, where only topological rather than geometrical notions hold, and to invite graph theorists to contribute their powerful tools to the field of spin ice.
In this work, different machine learning (ML) methods were explored for the prediction of self-diffusion in Lennard-Jones (LJ) fluids. Using a database of diffusion constants obtained from the molecular dynamics simulation literature, multiple Random Forest (RF) and Artificial Neural Net (ANN) regression models were developed and characterized. The role and improved performance of feature engineering coupled to the RF model development was also addressed. The performance of these different ML models was evaluated by comparing the prediction error to an existing empirical relationship used to describe LJ fluid diffusion. It was found that the ANN regression models provided superior prediction of diffusion in comparison to the existing empirical relationships.
Several closely related ab initio thermal mean-field theories for fermions, both well-established and new ones, are compared with one another at the formalism level and numerically. The theories considered are Fermi–Dirac theory; thermal Hartree–Fock (HF) theory; two modifications of the thermal single-determinant and the first-order finite-temperature many-body perturbation theory based on a zero-temperature or thermal HF reference. Furthermore, thermal full-configuration-interaction theory is used as the benchmark.
In this work we investigate the behaviour of molecules at the nanoscale using scanning tunnelling microscopy in order to explore the origin of the cooperativity in the formation of self-assembled molecular networks (SAMNs) at the liquid/solid interface. By studying concentration dependence of alkoxylated dimethylbenzene, a molecular analogue to 5-alkoxylated isophthalic derivatives, but without hydrogen bonding moieties, we show that the cooperativity effect can be experimentally evaluated even for low-interacting systems and that the cooperativity in SAMN formation is its fundamental trait. We conclude that cooperativity must be a local effect and use the nearest-neighbor Ising model to reproduce the coverage vs. concentration curves. The Ising model offers a direct link between statistical thermodynamics and experimental parameters, making it a valuable tool for assessing the thermodynamics of SAMN formation.
The protein folding process often proceeds through partially folded transient states. Therefore, a structural understanding of these disordered states is crucial for developing mechanistic models of the folding process. Characterization of unfolded states remains challenging due to their disordered nature, and incorporating multiple methods is necessary. Combining the time-resolved x-ray solution scattering (TRXSS) signal with molecular dynamics (MD), we are able to characterize transient partially folded states of bovine α-lactalbumin, a model system widely used for investigation of molten globule states, during its unfolding triggered by a temperature jump. We track the unfolding process between 20 μs and 70 ms and demonstrate that it passes through three distinct kinetic states. The scattering signals associated with these transient species are then analyzed with TRXSS constrained MD simulations to produce protein structures that are compatible with the input signals. Without utilizing any experimentally extracted kinetic information, the constrained MD simulation successfully drove the protein to an intermediate molten globule state; signals for two later disordered states are refined to terminal unfolded states. From our examination of the structural characteristics of these disordered states, we discuss the implications disordered states have on the folding process, especially on the folding pathway. Finally, we discuss the potential applications and limitations of this method.
We present a machine learning interatomic potential for ammonia designed to capture its complex multiphase behavior, including both molecular and superionic phases. The potential is based on the atomic cluster expansion (ACE) formulation and has been parameterized to facilitate high-fidelity molecular dynamics simulations of ammonia under extreme conditions, for pressures up to 100 GPa and for temperatures above 500 K and up to 6000 K. A diverse range of configurations was generated through high-quality ab initio molecular dynamics simulations, covering insulating and superionic ice phases, liquid ammonia, molecular nitrogen (N 2 ) and hydrogen (H 2 ), and metastable compounds that form upon dissociation, including $NH^{+}_{4}$, $H^{+}_{3}$, N 2 H 4 , and N 3 H. We demonstrate that the ammonia ACE potential accurately reproduces experimental and density functional theory predicted isotherms and Hugoniots. Crucially, the potential is able to capture the intricate phase behavior of ammonia, including the transition from insulating molecular fluid to the superionic phase. This work provides a robust interatomic potential that can be used for large-scale, accurate simulations of ammonia under extreme thermodynamic conditions, offering a powerful tool for investigating its behavior in various phases and applications.
A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.
Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. In this report an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.
The characteristics of the hadron-to-quark first-order phase transition differ depending on whether charge neutrality is locally or globally fulfilled. In 𝛽-equilibrated matter, these two possibilities correspond to the Maxwell and Gibbs constructions. Recently, we presented a new framework in which a continuously varying parameter allows one to describe a first-order phase transition in intermediate scenarios to the two extremes of fully local and fully global charge neutrality. In this work, we extend the previous framework to finite temperatures and out-of-𝛽 equilibrium conditions, making it available for simulations of core-collapse supernovae and binary neutron star mergers. We investigate its impact on key thermodynamic quantities across a range of baryon densities, temperatures, and electron fractions. We find that when matter is not in 𝛽 equilibrium, the pressure in the mixed phase is not constant even for the case of fully local charge neutrality. Moreover, we compute the thermal index using three different approaches, demonstrating that the finite-temperature extension of an equation of state using a constant thermal index can be ill defined when applied to the mixed phase.
Summary: 1. Equations of state furnish thermodynamic properties of a material. 2. Usually involve P, p (or V), and T, or P, r, and E 3. Necessary ingredient to solve compressible flow problems. 4. Varieties: i. Analytical expressions (ideal gas, Grüneisen) – fast, convenient for verification and test problems ii. Graphs and charts – good for hand calculations iii. Tables and databases – generally most accurate, require interpolation i. Steam tables ii. NIST database iii. SESAME EOS Library 5. Constructed by using semi-empirical models from Statistical Mechanics and fitting to available data