Macroscopic Counterpart Research Articles

Macro–Micro-Coupled Simulations of Dilute Viscoelastic Fluids

Modeling the flow of polymer solutions requires knowledge at various length and time scales. The macroscopic behavior is described by the overall velocity, pressure, and stress. The polymeric contribution to the stress requires knowledge of the evolution of polymer chains. In this work, we use a microscopic model, the finitely extensible nonlinear elastic (FENE) model, to capture the polymer’s behavior. The benefit of using microscopic models is that they remain faithful to the polymer dynamics without information loss via averaging. Their downside is the computational cost incurred in solving the thousands to millions of differential equations describing the microstructure. Here, we describe a multiscale flow solver that utilizes GPUs for massively parallel, efficient simulations. We compare and contrast the microscopic model with its macroscopic counterpart under various flow conditions. In particular, significant differences are observed under nonlinear flow conditions, where the polymers become highly stretched and oriented.

Spinristor: A Spin‐Filtering Memristor

AbstractIn this paper, an in silico proof of concept of a spinristor is proposed and provided; a new electronic component that combines a spin‐filter and a memristor in a single molecule, useful for in‐memory processing. It builds on the idea of an open‐shell transition metal ion enclosed within an elliptical fullerene connected to a pair of electrodes. The spin‐ and electronic‐polarization induced by the enclosed open‐shell metallic ion leads to differential rectification of the electrons at low voltages applied between the source–drain electrodes, VSD. The position of the encapsulated ion can be switched by a high VSD which leads to a change in the direction of the rectification and the spin‐filtering ratio. The system can thus be used as a switching rectifier, that is, a memristor and a spin‐filter; therefore, a spinristor. The effect of different linkers on the function of the proposed device is further analyzed to show that linkers reduce the overall conductivity by an order of magnitude, but improve the spin‐filtering ratio. The computations suggest that nitrile and isocyanide linkers enhance the rectification, too. To the best of the authors’ knowledge, spinristor has no macroscopic counterpart in electronics, so far.

A continuum model for morphology formation from interacting ternary mixtures: Simulation study of the formation and growth of patterns

Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target system is derived in the literature as the rigorous hydrodynamic limit of a suitably scaled interacting particle system of Blume–Capel-type driven by Kawasaki dynamics. The system describes in a rather implicit way the interaction within a ternary mixture that is the macroscopic counterpart of a mix of two populations of interacting solutes in the presence of a solvent. Our discussion is based on the qualitative behavior of numerical simulations of finite volume approximations of smooth solutions to our system and their quantitative postprocessing in terms of two indicators (correlation and structure factor calculations). Our results show many similar qualitative features (e.g. general shape and approximate coarsening rates) which have been observed in previous works on the stochastic Blume–Capel model with three interacting species. The properties of the obtained morphologies (shape, connectivity, and so on) can play a key role in, e.g., the design of the active layer for efficient organic solar cells.

Spontaneous Takeoff of Single Sulfur Nanoparticles during Sublimation Studied by Dark-Field Microscopy.

The Leidenfrost effect describes a fascinating phenomenon in which a liquid droplet, when deposited onto a very hot substrate, will levitate on its own vapor layer and undergo frictionless movements. Driven by the significant implications for heat transfer engineering and drag reduction, intensive efforts have been made to understand, manipulate, and utilize the Leidenfrost effect on macrosized objects with a typical size of millimeters. The Leidenfrost effect of nanosized objects, however, remains unexplored. Herein, we report on an unprecedented Leidenfrost effect of single nanosized sulfur particles at room temperature. It was discovered when advanced dark-field optical microscopy was employed to monitor the dynamic sublimation process of single sulfur nanoparticles sitting on a flat substrate. Despite the phenomenological similarity, including the vapor-cushion-induced levitation and the extended lifetime, the Leidenfrost effect at the nanoscale exhibited two extraordinary features that were obviously distinct from its macroscopic counterpart. First, there was a critical size below which single sulfur nanoparticles began to levitate. Second, levitation occurred in the absence of the temperature difference between the nanoparticle and the substrate, which was barely possible for macroscopic objects and underscored the value of bridging the gap connecting the Leidenfrost effect and nanoscience. The sublimation-triggered spontaneous takeoff of single sulfur nanoparticles shed new light on its further applications, such as nanoflight.

Free Dynamics of Feature Learning Processes

Regression models usually tend to recover a noisy signal in the form of a combination of regressors, also called features in machine learning, themselves being the result of a learning process. The alignment of the prior covariance feature matrix with the signal is known to play a key role in the generalization properties of the model, i.e. its ability to make predictions on unseen data during training. We present a statistical physics picture of the learning process. First we revisit the ridge regression to obtain compact asymptotic expressions for train and test errors, rendering manifest the conditions under which efficient generalization occurs. It is established thanks to an exact test-train sample error ratio combined with random matrix properties. Along the way in the form of a self-energy emerges an effective ridge penalty—precisely the train to test error ratio—which offers a very simple parameterization of the problem. This formulation appears convenient to tackle the learning process of the feature matrix itself. We derive an autonomous dynamical system in terms of elementary degrees of freedom of the problem determining the evolution of the relative alignment between the population matrix and the signal. A macroscopic counterpart of these equations is also obtained and various dynamical mechanisms are unveiled, allowing one to interpret the dynamics of simulated learning processes and to reproduce trajectories of single experimental run with high precision.

Macroscopic limits of non-local kinetic descriptions of vehicular traffic

We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle dynamics produce a first order macroscopic model with non-local flux. Next, we show that non-local follow-the-leader vehicle dynamics have a universal macroscopic counterpart in the second order Aw-Rascle-Zhang traffic model, at least when the non-locality of the interactions is sufficiently small. Finally, we show that the same qualitative result holds also for a general class of follow-the-leader dynamics based on the headway of the vehicles rather than on their speed. We also investigate the correspondence between the solutions to particle models and their macroscopic limits by means of numerical simulations.

Thermodynamics of evolution and the origin of life

We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for minimization of the loss function is employed to derive a canonical ensemble of organisms (population), the corresponding partition function (macroscopic counterpart of fitness), and free energy (macroscopic counterpart of additive fitness). We further define the biological counterparts of temperature (evolutionary temperature) as the measure of stochasticity of the evolutionary process and of chemical potential (evolutionary potential) as the amount of evolutionary work required to add a new trainable variable (such as an additional gene) to the evolving system. We then develop a phenomenological approach to the description of evolution, which involves modeling the grand potential as a function of the evolutionary temperature and evolutionary potential. We demonstrate how this phenomenological approach can be used to study the "ideal mutation" model of evolution and its generalizations. Finally, we show that, within this thermodynamics framework, major transitions in evolution, such as the transition from an ensemble of molecules to an ensemble of organisms, that is, the origin of life, can be modeled as a special case of bona fide physical phase transitions that are associated with the emergence of a new type of grand canonical ensemble and the corresponding new level of description.

Variational formulation of dynamical homogenization towards nonlocal effective media

The dynamical homogenization of heterogeneous materials is performed in the low and high frequency regimes using a variational formulation of dynamical equilibrium combined with the Laplace or Fourier-Floquet-Bloch decomposition of the mechanical fields (displacement, velocity, momentum, stress). The assumed periodicity of the initial heterogeneous structure entails that the homogenization process can be carried out at the scale of a reference unit cell over which periodicity conditions apply. A dynamical Hill type macrohomogeneity condition is formulated that plays a central role in this work. The weak form of the unit cell dynamical equilibrium is formulated as the minimization of the mean field action integral expressed versus the Floquet components of the displacement and velocity. The effective dynamical moduli are evaluated in reciprocal space as unit cell averages of the microscopic properties and localization operators relating the local velocity and strain to their macroscopic counterpart. More specific dynamical models involving locality in space (thus valid for long wavelengths) but nonlocality in time (thus describing both low and high frequency regimes) are formulated, considering Cauchy type and strain gradient effective models. The range of validity of the developed dynamical generalized continuum theories is assessed by comparing the phase velocity-wavenumber plots for inclusion based composites with reference plots obtained from Bloch's theorem. The benchmark of dynamical models evidences that the nonlocal dynamical model proves able to predict with a good accuracy the dynamical behavior of 2D periodic inclusion based composites.

In-situ capillary pressure and wettability in natural porous media: Multi-scale experimentation and automated characterization using X-ray images

HypothesisGeometrical analyses of pore-scale fluid-fluid-rock interfaces have recently been used for in-situ characterization of capillary pressure and wettability in natural porous media. Nevertheless, more robust techniques and multi-scale, well-characterized experimental data are needed to rigorously validate these techniques and enhance their efficacy when applied to saturated porous media. Experiments and Image analysisWe present two new techniques for automated measurements of in-situ capillary pressure and contact angle, which offer several advancements over previous methodologies. These approaches are methodically validated using synthetic data and X-ray images of capillary rise experiments, and subsequently, applied on pore-scale fluid occupancy maps of a miniature Berea sandstone sample obtained during steady-state drainage and imbibition flow experiments. FindingsThe results show encouraging agreement between the image-based capillary pressure-saturation function and its macroscopic counterpart obtained from a porous membrane experiment. However, unlike the macroscopic behavior, the micro-scale measurements demonstrate a nonmonotonic increase with saturation due to the intermittency of the pore-scale displacement events controlling the overall flow behavior. This is further explained using the pertinent micro-scale mechanisms such as Haines jumps. The new methods also enable one to generate in-situ contact angle distributions and distinguish between the advancing and receding values while automatically excluding invalid measurements.

Single- and dual-mode Rayleigh–Taylor instability at microscopic scale

The microscopic Rayleigh–Taylor instability (RTI) is studied via molecular dynamics (MD) simulation for single- and dual-mode interfaces under a strong acceleration. The growth behavior of microscopic RTI as well as the underlying regime exhibits considerable differences from the macroscopic counterpart. At a microscopic scale, the flow Reynolds number is very low and thus viscosity effect plays an important role, namely, it suppresses the growth of overall perturbation amplitude and also damps the growth of harmonics. As a result, the microscopic RTI presents a much weaker nonlinearity. Also, the motion of atoms produces random fluctuations to the evolving interface, which cause the detachment of droplets from the spike under the action of surface tension at late stages. In addition, the mode coupling behavior in dual-mode RTI at a microscopic scale is evidently different from the macroscopic counterpart, and a new prescription dominating the growth of each mode is proposed. Based on these findings, a semi-empirical model applicable to the microscopic RTI from early to late stages is developed, which gives a satisfactory prediction of the MD results.

Gellan Gum Microgels as Effective Agents for a Rapid Cleaning of Paper.

Microgel particles have emerged in the past few years as a favorite model system for fundamental science and for innovative applications ranging from the industrial to biomedical fields. Despite their potentialities, no works so far have focused on the application of microgels for cultural heritage preservation. Here we show their first use for this purpose, focusing on wet paper cleaning. Exploiting their retentive properties, microgels are able to clean paper, ensuring more controlled water release from the gel matrix, in analogy to their macroscopic counterpart, i.e., hydrogels. However, differently from these, the reduced size of microgels makes them suitable to efficiently penetrate in the porous structure of the paper and to easily adapt to the irregular surfaces of the artifacts. To test their cleaning abilities, we prepare microgels made of Gellan gum, a natural and widespread material already used as a hydrogel for paper cleaning, and apply them to modern and ancient paper samples. Combining several diagnostic methods, we show that microgels performances in the removal of cellulose degradation byproducts for ancient samples are superior to commonly employed hydrogels and water bath treatments. This is due to the composition and morphology of ancient paper, which facilitates microgels penetration. For modern paper cleaning, performances are at least comparable to the other methods. In all cases, the application of microgels takes place on a time scale of a few minutes, opening the way for widespread use as a rapid and efficient cleaning protocol.

On the Fokker–Planck approach to the stochastic thermodynamics of reactive systems

Stochastic thermodynamics is an extension of classical nonequilibrium thermodynamics that aims at including the effect of fluctuations occurring at small scales. In many cases, the starting point of such approaches is a Fokker–Planck equation for the probability density associated to the underlying stochastic variables. It is known that for chemically reactive systems, the usual equation for entropy production derived in this framework is not consistent with its macroscopic counterpart. It moreover also differs from the expression obtained with the master equation, from which the aforementioned Fokker–Planck equation derives. In the present work, we obtain a Fokker–Planck based alternative formula for entropy production in reactive systems that converges to the correct expression in the thermodynamic limit and is moreover consistent with expressions obtained with the master-equation based approach.

Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics

Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation period of the fastest atomic motion, rendering long-time simulations very expensive. To resolve this bottleneck, we propose a supervised parallel-in-time algorithm for stochastic dynamics (SPASD) to accelerate long-time Lagrangian particle simulations. Our method is inspired by bottom-up coarse-graining projections that yield mean-field hydrodynamic behavior in the continuum limit. Here as an example, we use the dissipative particle dynamics (DPD) as the Lagrangian particle simulator that is supervised by its macroscopic counterpart, i.e., the Navier-Stokes simulator. The low-dimensional macroscopic system (here, the Navier-Stokes solver) serves as a predictor to supervise the high-dimensional Lagrangian simulator, in a predictor-corrector type algorithm. The results of the Lagrangian simulation then correct the mean-field prediction and provide the proper microscopic details (e.g., consistent fluctuations, correlations, etc.). The unique feature that sets SPASD apart from other multiscale methods is the use of a low-fidelity macroscopic model as a predictor. The macro-model can be approximate and even inconsistent with the microscale description, but SPASD anticipates the deviation and corrects it internally to recover the true dynamics. We first present the algorithm and analyze its theoretical speedup, and subsequently we present the accuracy and convergence of the algorithm for the time-dependent plane Poiseuille flow, demonstrating that SPASD converges exponentially fast over iterations, irrespective of the accuracy of the predictor. Moreover, the fluctuating characteristics of the stochastic dynamics are identical to the unsupervised (serial in time) DPD simulation. We also compare the performance of SPASD to the conventional spatial decomposition method, which is one of the most parallel-efficient methods for particle simulations. We find that the parallel efficiency of SPASD and the conventional spatial decomposition method are similar for a small number of computing cores, but for a large number of cores the performance of SPASD is superior. Furthermore, SPASD can be used in conjunction with spatial decomposition for enhanced performance. Lastly, we simulate a two-dimensional cavity flow that requires more iterations to converge compared to the Poiseuille flow, and we observe that SPASD converges to the correct solution. Although a DPD solver is used to demonstrate the results, SPASD is a general framework and can be readily applied to other Lagrangian approaches including molecular dynamics and Langevin dynamics.

Surrogate-assisted microscopic traffic simulation-based optimisation of routing parameters

Reactive and predictive routing algorithms have to work fast and reliably for a large number of traffic participants. Therefore, simple rules and thresholds guide the routing decisions rather than extensive data collection and machine learning. In this paper, we optimise some of the thresholds governing the behaviour of a reactive and predictive routing algorithm by using the microscopic traffic simulator TraffSim. Microscopic traffic simulation is more exact than its macroscopic counterpart and very well suited to test the efficiency of a reactive and predictive routing algorithm. Unfortunately, it is also tremendously more computationally expensive, impairing the applicability of 'conventional' heuristic optimisation techniques like genetic algorithms or evolution strategies. Extensive use of surrogate models in an optimisation procedure is a promising alternative. Several variations of the efficient global optimisation (EGO) algorithm are tested and compared. Furthermore, a new type of surrogate model geared towards the parameter optimisation is presented.

Correlating Thermal Machines and the Second Law at the Nanoscale

Thermodynamics at the nanoscale is known to differ significantly from its familiar macroscopic counterpart: The possibility of state transitions is not determined by free energy alone but by an infinite family of free-energy-like quantities; strong fluctuations (possibly of quantum origin) allow one to extract less work reliably than what is expected from computing the free-energy difference. However, these known results rely crucially on the assumption that the thermal machine is not only exactly preserved in every cycle but also kept uncorrelated from the quantum systems on which it acts. Here, we lift this restriction: We allow the machine to become correlated with the microscopic systems on which it acts while still exactly preserving its own state. Surprisingly, we show that this possibility restores the second law in its original form: Free energy alone determines the possible state transitions, and the corresponding amount of work can be invested or extracted from single systems exactly and without any fluctuations. At the same time, the work reservoir remains uncorrelated from all other systems and parts of the machine. Thus, microscopic machines can increase their efficiency via clever “correlation engineering” in a perfectly cyclic manner, which is achieved by a catalytic system that can sometimes be as small as a single qubit (though some setups require very large catalysts). Our results also solve some open mathematical problems on majorization which may lead to further applications in entanglement theory.Received 31 August 2018Revised 17 November 2018DOI:https://doi.org/10.1103/PhysRevX.8.041051Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsQuantum statistical mechanicsQuantum thermodynamicsResource theoriesQuantum InformationStatistical Physics

A multiscale approach for spatially inhomogeneous disease dynamics

In this paper we introduce an agent-based epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the mean-field limit. The chain of equations acquired via the multiscale approach are investigated, analytically as well as numerically. The outcome of these results provide strong evidence of the models' robustness and justifies their applicability in describing disease dynamics, in particularly when mobility is involved.

Fick and Fokker–Planck Diffusion Law in Inhomogeneous Media

We discuss diffusion of particles in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric interpretation in terms of weights associated to un--oriented edges and vertices. We consider the hydrodynamic diffusive scaling that gives, as a macroscopic evolution equation, the Fokker--Planck equation corresponding to the evolution of the probability distribution of a reversible spatially inhomogeneous diffusion process. The geometric macroscopic counterpart of reversibility is encoded into a tensor metrics and a positive function. The Fick's law with inhomogeneous diffusion matrix is obtained in the case when the spatial inhomogeneity is associated exclusively with the edge weights. We discuss also some related properties of the systems like a non-homogeneous Einstein relation and the possibility of uphill diffusion.

A Hybrid Multiscale Model of Miscible Reactive Fronts

AbstractSubsurface processes can be simulated at multiple scales with variable degrees of fidelity. Some microscopic (pore‐scale) features of reactive transport cannot be properly resolved in macroscopic (Darcy‐scale) models. While microscopic descriptors might be closer to reality, they are computationally unfeasible when deployed on a macroscale. Hybrid algorithms combine the physical fidelity of a microscopic model with the computational efficiency of its macroscopic counterpart. We develop a hybrid model of dynamic reactive fronts in an open fracture, with a chemical reaction occurring in the zone of contact between two dissolved species. Away from the front, both fluid flow and solute transport are described by one‐dimensional models. In the front's proximity, two‐dimensional Stokes equations are used to model fluid flow, and solute transport is described with advection‐diffusion‐reaction equations. These two descriptors are coupled via an iterative procedure, which enforces the continuity of concentrations and mass fluxes across the interface between the two models. Our numerical experiments demonstrate that the hybrid model outperforms its microscopic and macroscopic counterparts in terms of computational time and representational accuracy, respectively.

Hybrid quantum systems with trapped charged particles

We study theoretically the possibilities of coupling the quantum mechanical motion of a trapped charged particle (e.g. ion or electron) to quantum degrees of freedom of superconducting devices, nano-mechanical resonators and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e. the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples, using parameters that are experimentally attainable in the foreseeable future. We conclude that those hybrid quantum system considered involving an atomic ion are unfavorable, compared to using an electron, since the coupling rates between the charged particle and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates which significantly exceed decoherence rates. Moreover it might have appealing properties such as fast entangling gates, long coherence and flexible electron interconnectivity topology. Realizing such a system, however, is technologically challenging, since it requires accommodating both trapping technology and superconducting circuitry in a compatible manner. We review some of the challenges involved, such as the required trap parameters, electron sources, electrical circuitry and cooling schemes in order to promote further investigations towards the realization of such a hybrid system.

Fluctuation shift of the nematic–isotropic phase transition temperature

A macroscopic counterpart to the microscopic mechanism of the straightening dimer mesogens conformations, proposed recently by S.M. Saliti, M.G. Tamba, S.N. Sprunt, C. Welch, G.H. Mehl, A. Jakli, and J.T. Gleeson [Phys. Rev. Lett. 116, 217801 (2016)] to explain their experimental observation of the unprecedentedly large shift of the nematic–isotropic transition temperature is discussed. The proposed interpretation is based on singular longitudinal fluctuations of the nematic order parameter. Since these fluctuations are governed by the Goldstone director fluctuations, they exist only in the nematic state. External magnetic field suppresses the singular longitudinal fluctuations of the order parameter (similarly as is the case for the transverse director fluctuations, although with a different scaling over the magnetic field). The reduction of the fluctuations changes the equilibrium value of the magnitude of the order parameter in the nematic state. Therefore, it leads to additional (with respect to the mean field contribution) fluctuation shift of the nematic–isotropic transition temperature. Our mechanism works for any nematic liquid crystals, however the magnitude of the fluctuation shift increases with decrease in the Frank elastic moduli. Since some of these moduli supposed to be anomalously small for so-called bent-core or dimer nematic liquid crystals, just these liquid crystals are promising candidates for the observation of the predicted fluctuation shift of the phase transition temperature.