Macroscopic Observables Research Articles

Phase space mixing in the equatorial plane of a Kerr black hole

It is shown that a collisionless, relativistic kinetic gas configuration propagating in the equatorial plane of a Kerr black hole undergoes a relaxation process and eventually settles down to a stationary, axisymmetric configuration surrounding the black hole. The underlying mechanism for this relaxation process is due to phase space mixing, which implies that although the one-particle distribution function $f$ satisfying the collisionless Boltzmann equation which describes the microscopic state of the gas is quasi-periodic in time, the associated macroscopic observables computed from averages over $f$ possess well-defined limits as time goes to infinity. The final state of the gas is described by an effective distribution function depending only on constants of motion which can be predicted from the initial distribution function.

Thermal hysteresis of the Campbell response as a probe for bulk pinning landscape spectroscopy

In type-II superconductors, the macroscopic response of vortex matter to an external perturbation depends on the local interaction of flux lines with the pinning landscape (pinscape). The (Campbell) penetration depth $\lambda_{\mathrm{\scriptscriptstyle C}}$ of an $ac$ field perturbation is often associated with a phenomenological pinning curvature. However, this basic approach is unable to capture thermal hysteresis effects observed in a variety of superconductors. The recently developed framework of strong-pinning theory has established a quantitative relationship between the microscopic pinscape and macroscopic observables. Specifically, it identifies history-dependent vortex arrangements as the primary source for thermal hysteresis in the Campbell response. In this work, we show that this interpretation is well suited to capture the experimental results of the clean superconductor $\mathrm{Nb}\mathrm{Se}_{2}$; as observed through Campbell response (linear $ac$ susceptibility) and small-angle neutron scattering measurements. Furthermore, we exploit the hysteretic Campbell response upon thermal cycling to extract the temperature dependence of microscopic pinning parameters from bulk measurements; specifically the pinning force and pinning length. This spectroscopic tool may stimulate further pinscape characterization in other superconducting systems.

Biomolecular simulations: From dynamics and mechanisms to computational assays of biological activity

Biomolecular simulation is increasingly central to understanding and designing biological molecules and their interactions. Detailed, physics‐based simulation methods are demonstrating rapidly growing impact in areas as diverse as biocatalysis, drug delivery, biomaterials, biotechnology, and drug design. Simulations offer the potential of uniquely detailed, atomic‐level insight into mechanisms, dynamics, and processes, as well as increasingly accurate predictions of molecular properties. Simulations can now be used as computational assays of biological activity, for example, in predictions of drug resistance. Methodological and algorithmic developments, combined with advances in computational hardware, are transforming the scope and range of calculations. Different types of methods are required for different types of problem. Accurate methods and extensive simulations promise quantitative comparison with experiments across biochemistry. Atomistic simulations can now access experimentally relevant timescales for large systems, leading to a fertile interplay of experiment and theory and offering unprecedented opportunities for validating and developing models. Coarse‐grained methods allow studies on larger length‐ and timescales, and theoretical developments are bringing electronic structure calculations into new regimes. Multiscale methods are another key focus for development, combining different levels of theory to increase accuracy, aiming to connect chemical and molecular changes to macroscopic observables. In this review, we outline biomolecular simulation methods and highlight examples of its application to investigate questions in biology.This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Free Energy Methods

Addendum to “Is long-term autogenous shrinkage a creep phenomenon induced by capillary effects due to self-desiccation?”

Prof. F.-J. Ulm brought to our attention that we forgot to include an important reference in our manuscript. Indeed, Ulm et al. [1] showed that, for 5 concretes that differed in their water-to-cement ratio and for which basic creep and autogenous shrinkage were measured by Le Roy [2], the long-term kinetics of autogenous shrinkage could be explained by creep of the solid skeleton under the action of an internal pore pressure. Their conclusion was based on the observed linearity of the relationship between basic creep compliance and increase in autogenous shrinkage in the long term. From the slope of this linear relationship, they back-calculated an “effective pore pressure” displayed in Fig. 1. Interestingly, this uniaxial “effective pore pressure” – merely calculated from macroscopic observables – is in very good agreement (both in terms of magnitude and in terms of trend with water-to-cement ratio) with the capillary stresses that we estimated at the pore scale with the help of micromechanics (see Fig. 6 in our manuscript). The reason for this agreement lies in Eq. 16 of our manuscript, which reads Σ∞ = σ∞ and shows that, in the linear viscoelastic case with a viscoelastic Poisson's ratio of the matrix equal to 0.2, the long-term “effective” macroscopic stress Σ∞ that acts at the scale of the concrete sample is equal to the long-term microscopic stress σ∞ that acts on the C-S-H gel.

Glitch Rises as a Test for Rapid Superfluid Coupling in Neutron Stars

Abstract Pulsar glitches provide a unique way to study neutron star microphysics because short post-glitch dynamics are directly linked to strong frictional processes on small scales. To illustrate this connection between macroscopic observables and microphysics, we review calculations of vortex interactions focusing on Kelvin wave excitations and determine the corresponding mutual friction strength for realistic microscopic parameters in the inner crust. These density-dependent crustal coupling profiles are combined with a simplified treatment of the core coupling and implemented in a three-component neutron star model to construct a predictive framework for glitch rises. As a result of the density-dependent dynamics, we find the superfluid to transfer angular momentum to different parts of the crust and the core on different timescales. This can cause the spin frequency change to become non-monotonic in time, allowing for a maximum value much larger than the measured glitch size, as well as a delay in the recovery. The exact shape of the calculated glitch rise is strongly dependent on the relative strength between the crust and core mutual friction, providing the means to probe not only the crustal superfluid but also the deeper neutron star interior. To demonstrate the potential of this approach, we compare our predictive model with the first pulse-to-pulse observations recorded during the 2016 December glitch of the Vela pulsar. Our analysis suggests that the glitch rise behavior is relatively insensitive to the crustal mutual friction strength as long as  ≳ 10−3, while being strongly dependent on the core coupling strength, which we find to be in the range 3 × 10 − 5 ≲  core ≲ 10 − 4 .

Dynamical structure of entangled polymers simulated under shear flow.

The non-linear response of entangled polymers to shear flow is complicated. Its current understanding is framed mainly as a rheological description in terms of the complex viscosity. However, the full picture requires an assessment of the dynamical structure of individual polymer chains which give rise to the macroscopic observables. Here we shed new light on this problem, using a computer simulation based on a blob model, extended to describe shear flow in polymer melts and semi-dilute solutions. We examine the diffusion and the intermediate scattering spectra during a steady shear flow. The relaxation dynamics are found to speed up along the flow direction, but slow down along the shear gradient direction. The third axis, vorticity, shows a slowdown at the short scale of a tube, but reaches a net speedup at the large scale of the chain radius of gyration.

Equivalence of nonequilibrium ensembles in turbulence models.

Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of nonequilibrium statistical mechanics. In the case of fluid dynamical systems, one issue is to test whether different models for viscosity lead to the same macroscopic properties of the fluid systems in different regimes. Such models include, besides the standard choice of constant viscosity, cases where the time symmetry of the evolution equations is exactly preserved, as it must be in the corresponding microscopic systems, when available. Here a time-reversible dynamics is obtained by imposing the conservation of global observables. We test the equivalence of reversible and irreversible ensembles for the case of a multiscale shell model of turbulence. We verify that the equivalence is obeyed for the mean values of macroscopic observables, up to an error that vanishes as the system becomes more and more chaotic.

Eigenstate Thermalization for Degenerate Observables.

Under unitary time evolution, expectation values of physically reasonable observables often evolve towards the predictions of equilibrium statistical mechanics. The eigenstate thermalization hypothesis (ETH) states that this is also true already for individual energy eigenstates. Here we aim at elucidating the emergence of the ETH for observables that can realistically be measured due to their high degeneracy, such as local, extensive, or macroscopic observables. We bisect this problem into two parts, a condition on the relative overlaps and one on the relative phases between the eigenbases of the observable and Hamiltonian. We show that the relative overlaps are unbiased for highly degenerate observables and demonstrate that unless relative phases conspire to cumulative effects, this makes such observables verify the ETH. Through this we elucidate potential pathways towards proofs of thermalization.

Multiscale Kinetic Modeling of a Cl−/H+ Antiporter: Integrating Simulation and Experiment to Characterize A Complex Ion Exchange Process

One of the central challenges in modern biophysics is understanding the molecular nature, and hence both the thermodynamics and kinetics, of coupled biomolecular transport mechanisms. The coupled ion exchange mechanism in Cl-/H+ antiporters offers an important and intriguing case study for this challenge. Herein, our new approach to multiscale kinetic modeling (MKM) and its application to characterize the Cl-/H+ exchange process in ClC-ec1 will be presented. We first calculate essential state-to-state rate coefficients with reactive and polarizable molecular dynamics simulations. A kinetic (Markov state) model is then used to optimize the rate coefficients within their calculated error to reproduce specific experimental rates and stoichiometry. This results in a set of solutions that not only predicts new, testable properties (e.g., rates at different pH values and the relative contribution of protein orientations), but also reveals insight into the series of transitions, the balance of rate-limiting steps, the molecular origin of the 2.2:1 Cl−/H+ stoichiometry, and the influence of protein orientation. Our results suggest that the consistent exchange ratio is a consequence of kinetic coupling wherein residue E148 plays an essential role through protonation-dependent anion transport, and an anion-dependent pKa value. They further demonstrate that a large conformational change is not essential at this level of modeling for the ion exchange mechanism, suggesting a more facile possible evolutionary connection to chloride channels. Finally, the results demonstrate how an ensemble of different exchange pathways, as opposed to a single series of transitions, culminates in the macroscopic observables and thereby explains the molecular mechanism.

Multiscale Kinetic Modeling Reveals an Ensemble of Cl-/H+ Exchange Pathways in ClC-ec1 Antiporter.

Despite several years of research, the ion exchange mechanisms in chloride/proton antiporters and many other coupled transporters are not yet understood at the molecular level. Here, we present a novel approach to kinetic modeling and apply it to ion exchange in ClC-ec1. Our multiscale kinetic model is developed by (1) calculating the state-to-state rate coefficients with reactive and polarizable molecular dynamics simulations, (2) optimizing these rates in a global kinetic network, and (3) predicting new electrophysiological results. The model shows that the robust Cl:H exchange ratio (2.2:1) can indeed arise from kinetic coupling without large protein conformational changes, indicating a possible facile evolutionary connection to chloride channels. The E148 amino acid residue is shown to couple chloride and proton transport through protonation-dependent blockage of the central anion binding site and an anion-dependent pKa value, which influences proton transport. The results demonstrate how an ensemble of different exchange pathways, as opposed to a single series of transitions, culminates in the macroscopic observables of the antiporter, such as transport rates, chloride/proton stoichiometry, and pH dependence.

Mechanical Response of Two-Dimensional Polymer Networks: Role of Topology, Rate Dependence, and Damage Accumulation

The skeleton of many natural and artificial soft materials can be abstracted as networks of fibers/polymers interacting in a nonlinear fashion. Here, we present a numerical model for networks of nonlinear, elastic polymer chains with rate-dependent crosslinkers similar to what is found in gels. The model combines the worm-like chain (WLC) at the polymer level with the transition state theory for crosslinker bond dynamics. We study the damage evolution and the force—displacement response of these networks under uniaxial stretching for different loading rates, network topology, and crosslinking density. Our results suggest a complex nonmonotonic response as the loading rate or the crosslinking density increases. We discuss this in terms of the microscopic deformation mechanisms and suggest a novel framework for increasing toughness and ductility of polymer networks using a bio-inspired sacrificial bonds and hidden length (SBHL) mechanism. This work highlights the role of local network characteristics on macroscopic mechanical observables and opens new pathways for designing tough polymer networks.

Path-space moderate deviation principles for the random field Curie-Weiss model

We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie Weiss model (i.e., standard Curie-Weiss model embedded in a site dependent, i.i.d. random environment). We obtain path space large deviation principles via a general analytic approach based on convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton Jacobi equations. The moderate asymptotics depend crucially on the phase we consider and moreover, the space-time scale range for which fluctuations can be proven is restricted by the addition of the disorder.

Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions

We investigate the stationary and dynamic properties of the celebrated Nosé–Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé–Hoover dynamics aim to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé–Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé–Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé–Hoover and canonical equilibrium.

Stochastic approach to irreversible thermodynamics.

An extension of classical irreversible thermodynamics pioneered by Ilya Prigogine is developed, in which fluctuations of macroscopic observables accounting for microscopic-scale processes are incorporated. The contribution of the fluctuations to the entropy production is derived from a generalized entropy balance equation and expressed in terms of the fluctuating variables, via an extended local equilibrium Ansatz and in terms of the probability distributions of these variables. The approach is illustrated on reactive systems involving linear and nonlinear steps, and the role of the distance from equilibrium and of the nonlinearities is assessed.

Thermonuclear burst oscillations and the dense matter equation of state

AbstractMatter in neutron star cores reaches extremely high densities, forming states of matter that cannot be generated in the laboratory. The Equation of State (EOS) of the matter links to macroscopic observables, such as mass M and radius R, via the stellar structure equations. A promising technique for measuring M and R exploits hotspots (burst oscillations) that form on the stellar surface when material accreted from a companion star undergoes a thermonuclear explosion. As the star rotates, the hotspot gives rise to a pulsation, and relativistic effects encode information about M and R into the pulse profile. However the burst oscillation mechanism remains unknown, introducing uncertainty when inferring the EOS. I review the progress that we are making towards cracking this long-standing problem, and establishing burst oscillations as a robust tool for measuring M and R. This is a major goal for future large area X-ray telescopes.

A Stronger Theorem Against Macro-realism

Macro-realism is the position that certain macroscopic observables must always possess definite values: e.g. the table is in some definite position, even if we do not know what that is precisely. The traditional understanding is that by assuming macro-realism one can derive the Leggett-Garg inequalities, which constrain the possible statistics from certain experiments. Since quantum experiments can violate the Leggett-Garg inequalities, this is taken to rule out the possibility of macro-realism in a quantum universe. However, recent analyses have exposed loopholes in the Leggett-Garg argument, which allow many types of macro-realism to be compatible with quantum theory and hence violation of the Leggett-Garg inequalities. This paper takes a different approach to ruling out macro-realism and the result is a no-go theorem for macro-realism in quantum theory that is stronger than the Leggett-Garg argument. This approach uses the framework of ontological models: an elegant way to reason about foundational issues in quantum theory which has successfully produced many other recent results, such as the PBR theorem.

Magnetic phenomena in exchange coupled spin systems

We study theoretically a cluster of several interacting spins modelling a hypothetical single-molecule magnet. Starting from a spin Hamiltonian, we obtain the individual energy levels and their evolution in an applied magnetic field. By substituting the energy levels into the partition function, we compute macroscopic observables like the magnetisation and the susceptibility of the system.

Retention and release of hydrogen isotopes in tungsten plasma-facing components: the role of grain boundaries and the native oxide layer from a joint experiment-simulation integrated approach

Fusion fuel retention (trapping) and release (desorption) from plasma-facing components are critical issues for ITER and for any future industrial demonstration reactors such as DEMO. Therefore, understanding the fundamental mechanisms behind the retention of hydrogen isotopes in first wall and divertor materials is necessary. We developed an approach that couples dedicated experimental studies with modelling at all relevant scales, from microscopic elementary steps to macroscopic observables, in order to build a reliable and predictive fusion reactor wall model. This integrated approach is applied to the ITER divertor material (tungsten), and advances in the development of the wall model are presented. An experimental dataset, including focused ion beam scanning electron microscopy, isothermal desorption, temperature programmed desorption, nuclear reaction analysis and Auger electron spectroscopy, is exploited to initialize a macroscopic rate equation wall model. This model includes all elementary steps of modelled experiments: implantation of fusion fuel, fuel diffusion in the bulk or towards the surface, fuel trapping on defects and release of trapped fuel during a thermal excursion of materials. We were able to show that a single-trap-type single-detrapping-energy model is not able to reproduce an extended parameter space study of a polycrystalline sample exhibiting a single desorption peak. It is therefore justified to use density functional theory to guide the initialization of a more complex model. This new model still contains a single type of trap, but includes the density functional theory findings that the detrapping energy varies as a function of the number of hydrogen isotopes bound to the trap. A better agreement of the model with experimental results is obtained when grain boundary defects are included, as is consistent with the polycrystalline nature of the studied sample. Refinement of this grain boundary model is discussed as well as the inclusion in the model of a thin defective oxide layer following the experimental observation of the presence of an oxygen layer on the surface even after annealing to 1300 K.

Influence of Vapor Deposition on Structural and Charge Transport Properties of Ethylbenzene Films.

Organic glass films formed by physical vapor deposition exhibit enhanced stability relative to those formed by conventional liquid cooling and aging techniques. Recently, experimental and computational evidence has emerged indicating that the average molecular orientation can be tuned by controlling the substrate temperature at which these “stable glasses” are grown. In this work, we present a comprehensive all-atom simulation study of ethylbenzene, a canonical stable-glass former, using a computational film formation procedure that closely mimics the vapor deposition process. Atomistic studies of experimentally formed vapor-deposited glasses have not been performed before, and this study therefore begins by verifying that the model and method utilized here reproduces key structural features observed experimentally. Having established agreement between several simulated and experimental macroscopic observables, simulations are used to examine the substrate temperature dependence of molecular orientation. The results indicate that ethylbenzene glasses are anisotropic, depending upon substrate temperature, and that this dependence can be understood from the orientation present at the surface of the equilibrium liquid. By treating ethylbenzene as a simple model for molecular semiconducting materials, a quantum-chemical analysis is then used to show that the vapor-deposited glasses exhibit decreased energetic disorder and increased magnitude of the mean-squared transfer integral relative to isotropic, liquid-cooled films, an effect that is attributed to the anisotropic ordering of the molecular film. These results suggest a novel structure–function simulation strategy capable of tuning the electronic properties of organic semiconducting glasses prior to experimental deposition, which could have considerable potential for organic electronic materials design.

Macroscopic and microscopic thermal equilibrium

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro‐canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (MITE). The distinction between MITE and MATE is particularly relevant for systems with many‐body localization (MBL) for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions ψ) in an energy shell, then for generic macroscopic systems, including those with MBL, most ψ are in both MATE and MITE. We explore here the properties of MATE and MITE and compare the two notions, thereby elaborating on ideas introduced in . image