arXiv subjects

Michael te Vrugt

Publications and source records attributed to Michael te Vrugt.

At least 37 records · Page 2Linked to original sources

arXiv2023

Passive and active field theories for disease spreading

The worldwide COVID-19 pandemic has led to a significant growth of interest in the development of mathematical models that allow to describe effects such as social distancing measures, the development of vaccines, and mutations. Several of these models are based on concepts from soft matter theory. Considerably less well investigated is the reverse direction, i.e., how results from epidemiological research can be of interest for the physics of colloids and polymers. In this work, we consider the SIR-DDFT model, a combination of the susceptible-infected-recovered (SIR) model from epidemiology with dynamical density functional theory (DDFT) from nonequilibrium soft matter physics, which allows for an explicit modeling of social distancing. We extend the SIR-DDFT model both from an epidemiological perspective by incorporating vaccines, asymptomaticity, reinfections, and mutations, and from a soft matter perspective by incorporating noise and self-propulsion and by deriving a phase field crystal (PFC) model that allows for a simplified description. On this basis, we investigate via computer simulations how epidemiological models are affected by the presence of non-reciprocal interactions. This is done in a numerical study of a zombie outbreak.

cond-mat.soft↗

arXiv2023

Thermodynamics of an Empty Box

A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermodynamics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory.

cond-mat.stat-mech↗

arXiv2022

How to derive a predictive active field theory: a step-by-step tutorial

The study of active soft matter has developed into one of the most rapidly growing areas of physics. Field theories, which can be developed either via phenomenological considerations or by coarse-graining of a microscopic model, are a very useful tool for understanding active systems. Here, we provide a detailed review of a particular coarse-graining procedure, the interaction-expansion method (IEM). The IEM allows for the systematic microscopic derivation of predictive field theories for systems of interacting active particles. We explain in detail how it can be used for a microscopic derivation of active model B+, which is a widely used scalar active matter model. Extensions and possible future applications are also discussed.

cond-mat.soft↗

arXiv2022

Orientation-dependent propulsion of active Brownian spheres: from self-advection to programmable cluster shapes

Applications of active particles require a method for controlling their dynamics. While this is typically achieved via direct interventions, indirect interventions based, e.g., on an orientation-dependent self-propulsion speed of the particles, become increasingly popular. In this work, we investigate systems of interacting active Brownian spheres in two spatial dimensions with orientation-dependent propulsion using analytical modeling and Brownian dynamics simulations. It is found that the orientation-dependence leads to self-advection, circulating currents, and programmable cluster shapes.

cond-mat.soft↗

arXiv2022

Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

We discuss an active phase field crystal (PFC) model that describes a mixture of active and passive particles. First, a microscopic derivation from dynamical density functional theory (DDFT) is presented that includes a systematic treatment of the relevant orientational degrees of freedom. Of particular interest is the construction of the nonlinear and coupling terms. This allows for interesting insights into the microscopic justification of phenomenological constructions used in PFC models for active particles and mixtures, the approximations required for obtaining them, and possible generalizations. Second, the derived model is investigated using linear stability analysis and nonlinear methods. It is found that the model allows for a rich nonlinear behavior with states ranging from steady periodic and localized states to various time-periodic states. The latter include standing, traveling, and modulated waves corresponding to spatially periodic and localized traveling, wiggling, and alternating peak patterns and their combinations.

cond-mat.soft↗

arXiv2022

Perspective: New directions in dynamical density functional theory

Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

cond-mat.soft↗

arXiv2022

Is thermodynamics fundamental?

It is a common view in philosophy of physics that thermodynamics is a non-fundamental theory. This is motivated in particular by the fact that thermodynamics is considered to be a paradigmatic example for a theory that can be reduced to another one, namely statistical mechanics. For instance, the statement "temperature is mean molecular kinetic energy" has become a textbook example for a successful reduction, despite the fact that this statement is not correct for a large variety of systems. In this article, we defend the view that thermodynamics is a fundamental theory, a position that we justify based on four case studies from recent physical research. We explain how entropic gravity (1) and black hole thermodynamics (2) can serve as case studies for the multiple realizability problem which blocks the reduction of thermodynamics. Moreover, we discuss the problem of the reducibility of phase transitions and argue that bifurcation theory (3) allows the modelling of "phase transitions" on a thermodynamic level even in finite systems. It is also shown that the derivation of irreversible transport equations in the Mori-Zwanzig formalism (4) does not, despite recent claims to the contrary, constitute a reduction of thermodynamics to quantum mechanics. Finally, we briefly discuss some arguments against the fundamentality of thermodynamics that are not based on reduction.

physics.hist-ph↗

arXiv2022

From a microscopic inertial active matter model to the Schrödinger equation

Field theories for the one-body density of an active fluid, such as the paradigmatic active model B+, are simple yet very powerful tools for describing phenomena such as motility-induced phase separation. No comparable theory has been derived yet for the underdamped case. In this work, we introduce active model I+, an extension of active model B+ to particles with inertia. The governing equations of active model I+ are systematically derived from the microscopic Langevin equations. We show that, for underdamped active particles, thermodynamic and mechanical definitions of the velocity field no longer coincide and that the density-dependent swimming speed plays the role of an effective viscosity. Moreover, active model I+ contains the Schrödinger equation in Madelung form as a limiting case, allowing to find analoga of the quantum-mechanical tunnel effect and of fuzzy dark matter in the active fluid. We investigate the active tunnel effect analytically and via numerical continuation.

cond-mat.soft↗

arXiv2022

Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals

Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the intrinsic positional order of smectic liquid crystals comes into play, we perform Monte-Carlo simulations of rod-like particles in a range of cavities with a cylindrical symmetry. Based on recent insights into the topology of smectic orientational grain boundaries in two dimensions, we analyze the emerging three-dimensional defect structures from the perspective of tetratic symmetry. Using an appropriate three-dimensional tetratic order parameter constructed from the Steinhardt order parameters, we show that those grain boundaries can be interpreted as a pair of tetratic disclination lines that are located on the edges of the nematic domain boundary. Thereby, we shed light on the fine structure of grain boundaries in three-dimensional confined smectics.

cond-mat.soft↗

arXiv2021

Understanding probability and irreversibility in the Mori-Zwanzig projection operator formalism

Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the Mori-Zwanzig formalism in philosophy of physics tend to focus on simple variants rather than on the more sophisticated ones used in modern physical research. In this work, I will close this gap by studying the problems of probability and irreversibility using the example of Grabert's time-dependent projection operator formalism. This allows to give a more solid mathematical foundation to various concepts from the philosophical literature, in particular Wallace's simple dynamical conjecture and Robertson's theory of autonomous macrodynamics. Moreover, I will explain how the Mori-Zwanzig formalism allows to resolve the tension between epistemic and ontic approaches to probability in statistical mechanics. Finally, I argue that the debate which interventionists and coarse-grainers should really be having is related not to the question why there is equilibration at all, but why it has the quantitative form it is found to have in experiments.

cond-mat.stat-mech↗

arXiv2021

How to distinguish between indistinguishable particles

A long and intense debate in philosophy is concerned with the question whether there can be haecceistic differences between possible worlds, that is, nonqualitative differences that only arise from different de re representations. According to haecceitism, it can give rise to a different situation if the positions of two qualitatively identical particles are exchanged, while according to anti-haecceitism, this is not the case. It has been suggested that classical statistical mechanics might provide evidence for one of these positions. However, most philosophers of physics argue that it does not. In this article, we show that order-preserving dynamics, a novel method from statistical mechanics developed for the description of nonergodic systems, changes this situation: It is intrinsically haecceistic and makes different experimental predictions than non-haecceistic alternatives. Thereby, it provides an empirical argument for the existence of modality de re.

physics.hist-ph↗

arXiv2021

Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem

Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse-graining extremely difficult. We here address this problem by extending the Mori-Zwanzig projection operator formalism, a highly successful coarse-graining method from statistical mechanics, towards general relativity. Using the Buchert equations, we derive a new dynamic equation for the Hubble parameter which captures the effects of averaging through a memory function. This gives an empirical prediction for the cosmic jerk.

gr-qc↗

arXiv2021

The Mereology of Thermodynamic Equilibrium

The special composition question (SCQ), which asks under which conditions objects compose a further object, establishes a central debate in modern metaphysics. Recent successes of inductive metaphysics, which studies the implications of the natural sciences for metaphysical problems, suggest that insights into the SCQ can be gained by investigating the physics of composite systems. In this work, I show that the minus first law of thermodynamics, which is concerned with the approach to equilibrium, leads to a new approach to the SCQ, the thermodynamic composition principle (TCP): Multiple systems in (generalized) thermal contact compose a single system. This principle, which is justified based on a systematic classification of possible mereological models for thermodynamic systems, can form the basis of an inductive argument for universalism. A formal analysis of the TCP is provided on the basis of mereotopology, which is a combination of mereology and topology. Here, "thermal contact" can be analyzed using the mereotopological predicate "self-connectedness". Self-connectedness has to be defined in terms of mereological sums to ensure that scattered objects cannot be self-connected.

physics.hist-ph↗

arXiv2021

Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models - Ghirardi-Rimini-Weber (GRW) theory, continuous spontaneous localization (CSL) model, Diósi-Penrose model, and dissipative GRW model - in the Wigner framework. The resulting master equations are approximated by Fokker-Planck equations. Moreover, we use the phase-space form of GRW theory to test, via molecular dynamics simulations, David Albert's suggestion that the stochasticity induced by spontaneous collapses is responsible for the emergence of thermodynamic irreversibility. The simulations show that, for initial conditions leading to anti-thermodynamic behavior in the classical case, GRW-type perturbations do not lead to thermodynamic behavior. Consequently, the GRW-based equilibration mechanism proposed by Albert is not observed.

quant-ph↗

arXiv2021

The Five Problems of Irreversibility

Thermodynamics has a clear arrow of time, characterized by the irreversible approach to equilibrium. This stands in contrast to the laws of microscopic theories, which are invariant under time-reversal. Foundational discussions of this "problem of irreversibility" often focus on historical considerations, and do therefore not take results of modern physical research on this topic into account. In this article, I will close this gap by studying the implications of dynamical density functional theory (DDFT), a central method of modern nonequilibrium statistical mechanics not previously considered in philosophy of physics, for this debate. For this purpose, the philosophical discussion of irreversibility is structured into five problems, concerned with the source of irreversibility in thermodynamics, the definition of equilibrium and entropy, the justification of coarse-graining, the approach to equilibrium and the arrow of time. For each of these problems, it is shown that DDFT provides novel insights that are of importance for both physicists and philosophers of physics.

physics.hist-ph↗

arXiv2021

Jerky active matter: a phase field crystal model with translational and orientational memory

Most field theories for active matter neglect effects of memory and inertia. However, recent experiments have found inertial delay to be important for the motion of self-propelled particles. A major challenge in the theoretical description of these effects, which makes the application of standard methods very difficult, is the fact that orientable particles have both translational and orientational degrees of freedom which do not necessarily relax on the same time scale. In this work, we derive the general mathematical form of a field theory for soft matter systems with two different time scales. This allows to obtain a phase field crystal model for polar (i.e., nonspherical or active) particles with translational and orientational memory. Notably, this theory is of third order in temporal derivatives and can thus be seen as a spatiotemporal jerky dynamics. We obtain the phase diagram of this model, which shows that, unlike in the passive case, the linear stability of the liquid state depends on the damping coefficients. Moreover, we investigate sound waves in active matter. It is found that, in active fluids, there are two different mechanisms for sound propagation. For certain parameter values and sufficiently high frequencies, sound mediated by polarization waves experiences less damping than usual passive sound mediated by pressure waves of the same frequency. By combining the different modes, acoustic frequency filters based on active fluids could be realized.

cond-mat.soft↗

arXiv2020

Containing a pandemic: Nonpharmaceutical interventions and the "second wave"

In response to the worldwide outbreak of the coronavirus disease COVID-19, a variety of nonpharmaceutical interventions such as face masks and social distancing have been implemented. A careful assessment of the effects of such containment strategies is required to avoid exceeding social and economical costs as well as a dangerous "second wave" of the pandemic. In this work, we combine a recently developed dynamical density functional theory model and an extended SIRD model with hysteresis to study effects of various measures and strategies using realistic parameters. Depending on intervention thresholds, a variety of phases with different numbers of shutdowns and deaths are found. Spatiotemporal simulations provide further insights into the dynamics of a second wave. Our results are of crucial importance for public health policy.

q-bio.PE↗

arXiv2020

Classical dynamical density functional theory: from fundamentals to applications

Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems. Originally developed for the treatment of simple and complex fluids, DDFT is now applied in fields as diverse as hydrodynamics, materials science, chemistry, biology, and plasma physics. In this review, we give a broad overview over classical DDFT. We explain its theoretical foundations and the ways in which it can be derived. The relations between the different forms of deterministic and stochastic DDFT as well as between DDFT and related theories, such as quantum-mechanical time-dependent DFT, mode coupling theory, and phase field crystal models, are clarified. Moreover, we discuss the wide spectrum of extensions of DDFT, which covers methods with additional order parameters (like extended DDFT), exact approaches (like power functional theory), and systems with more complex dynamics (like active matter). Finally, the large variety of applications, ranging from fluid mechanics and polymer physics to solidification, pattern formation, biophysics, and electrochemistry, is presented.

cond-mat.soft↗