arXiv subjects

Tomer Markovich

Publications and source records attributed to Tomer Markovich.

At least 19 recordsLinked to original sources

arXiv2026

Static and dynamic density correlations of interacting active Brownian particles

We develop a stochastic Dean--Kawasaki field theory to predict the static structure factor and collective intermediate scattering function of interacting active Brownian particles. Starting from the microscopic overdamped dynamics, we derive coupled stochastic equations for the density and polarization fields using an angular-moment closure. Gaussian linearization then yields closed analytical expressions for static and dynamic density correlations in terms of propulsion speed, mean number density, interaction potential, translational and rotational diffusivities. The coupling between density and polarization predicts a crossover from exponential relaxation to damped oscillations despite the absence of inertia. For Gaussian-core potential, the predictions contain no fitting parameters. Brownian dynamics simulations show quantitative agreement at low activity and long wavelengths, and reproduce the crossover behaviour. For Weeks--Chandler--Andersen potential, the nonintegrable core makes both the Fourier transform of the potential and the self-interaction correction term in the Dean--Kawasaki field theory ill-defined. We therefore introduce an approximation that replaces the interaction potential with a passive direct-correlation function fitted separately at each density and temperature. This approximation requires no additional activity-dependent fitting parameters.

cond-mat.stat-mech↗

arXiv2026

Swimming versus Screening: How Activity Reshapes the Ionic Cloud of a Charged Particle

A major question in active matter is how interactions between particles are modified by activity. Here, we address this question for Coulomb interactions by considering a charged swimmer immersed in an electrolyte. A static charge is screened by an ionic cloud that decays over the Debye length $λ_D$. We show that the persistent motion of the swimmer can qualitatively modify the steady-state ionic charge-density profile. At low activity, the swimmer appears effectively quasistatic to the ions, and conventional Debye-Hückel screening is recovered. At higher activity, the ballistic-to-diffusive dynamics of the swimmer are reflected in distinct spatial regimes. A power-law decay is followed by a stretched-exponential decay at intermediate distances. At sufficiently large distances, exponential screening is restored, but with an increased screening length, $λ>λ_D$, revealing activity-induced underscreening. Thus, active motion modifies both the spatial form and the range of electrostatic screening. Our results motivate the study of active electrolytes composed of positively and negatively charged swimmers.

cond-mat.stat-mech↗

arXiv2026

Elastodynamics from Eulerian Poisson-bracket formalism: application to chiral odd solids

The Poisson-bracket (PB) formalism is widely used to derive dynamics of coarse-grained (CG) fields to capture large-scale physics, extending the role of PBs in classical particle mechanics to macroscopic fields. It has been applied to fluctuations in critical phenomena, hydrodynamics of liquid crystals, liquid crystal elastomers, tissues, and the emergence of odd viscosity from spinning particles. The PB formalism can be formulated in either the Lagrangian framework, using reference space, or the Eulerian framework, using real space. Conventionally, the Lagrangian formulation is used for elastic solids, and the Eulerian one for fluids. However, growing interest in Eulerian descriptions of solids has emerged for phenomena naturally defined in real space, such as viscoelastic responses, moving interfaces, and field-induced structural changes in particles. Here we develop a systematic formulation for applying the Eulerian PB formalism to elastic systems with potentials typically written in Lagrangian space, and clarify its consistency with the Lagrangian counterpart. We show that the Eulerian formulation generates additional nonlinearities absent in the Lagrangian framework. Such nonlinearities originate from CG volume changes under coordinate transformation and from particle flow across neighboring CG volumes. They must be retained when nonlinear effects are important. To illustrate, we study chiral active solids of finite-sized particles, where active torques drive internal particle rotations and generate geometric nonlinearities. These nonlinearities give rise to the odd elastic modulus, which non-reciprocally couples two different shear modes in stress-strain response. By recovering this modulus directly from the Eulerian PB formalism, we demonstrate its ability to capture emergent nonlinear elastic behavior in driven active solids, whose stresses are naturally measured in real space.

cond-mat.soft↗

arXiv2026

Odd elasticity in disordered chiral active materials

Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacterial flagella, and self-spinning starfish embryos. These materials break both time reversal and mirror-image (parity) symmetries due to injection of torques at the microscale. It was recently discovered that chiral active materials show a new type of elastic response termed `odd' elasticity. Currently, odd elasticity is understood microscopically only in ordered structures, e.g., lattice designs of metamaterials. It remains to explore how odd elasticity emerges in natural or biological systems, which are usually disordered. To address this, we propose a minimal generic model for disordered `odd solids', using micropolar (Cosserat) elasticity in the presence of local active torques. We find that odd elasticity naturally emerges as a nonlinear effect of internal particle rotations. Exploring the viscoelasticity of such a solid, when immersed in an odd fluid, we discover new dynamically unstable regions driven by the odd solid-fluid coupling, and, in the underdamped regime, also by inertia. Remarkably, in the overdamped limit, this odd solid-fluid coupling allows for bulk wave propagation near these unstable regions.

cond-mat.soft↗

arXiv2026

Non-Hermitian chiral surface waves in disordered odd solids

Chiral surface waves are surface-localized modes that propagate unidirectionally along a boundary, enabling directed transport and minimal back-scattering. While first identified in quantum systems, they were recently shown to emerge in classical metamaterials in the presence of `odd elasticity'. Owing to the non-reciprocality of odd elasticity, these waves exhibit growing amplitudes during propagation, reminiscent of the non-Hermitian skin effect. To date, studies of odd elastic systems have mainly focused on ordered structures. Whether structurally-disordered materials can host non-Hermitian chiral surface waves (NHCSW) remains unexplored. We address this question using a minimal model of torque-driven disordered odd solids. Such solids are abundant, from biological gels such as the cytoskeleton driven by motor-proteins to synthesized systems such as magnetic colloidal gels. We find that torque-driven disordered odd solids have unique NHCSW with stronger surface localization and stable boundary velocity, in contrast to previous lattice models of odd solids. These distinct features stem from an intrinsic interplay between boundary torques and odd elasticity in torque-driven odd solids. Our results offer a new strategy to control NHCSW using active torques.

cond-mat.soft↗

arXiv2025

Control of active field theories at minimal dissipation

Advances in experimental techniques enable the precise manipulation of a large variety of active systems, which constantly dissipate energy to sustain nonequilibrium phenomena without any equilibrium equivalent. To design novel materials out of active systems, an outstanding challenge is to rationalize how material properties can be optimally controlled by applying external perturbations. However, equilibrium thermodynamics is inadequate to guide the control of such nonequilibrium systems. Therefore, there is a dire need for a novel framework to provide a systematic toolbox for the thermodynamic control of active matter. Here, we build an optimization procedure for generic active field theories within a thermodynamically consistent formulation. Central to our approach is the distinction between the protocol heat, which is dissipated only during manipulation, and the total heat, which also accounts for the post-manipulation dissipation. We demonstrate that the latter generically features a global minimum with respect to the protocol duration. We deploy our versatile approach to an active theory of phase separation, and examine the scalings of the optimal protocol duration with respect to activity and system size. Remarkably, we reveal that the landscape of steady-state dissipation regulates the crossover between optimal control strategies for a finite duration.

cond-mat.stat-mech↗

arXiv2024

Chiral active fluids: what can we learn from the total momentum?

Chiral active materials are those that break both time-reversal symmetry and parity microscopically, which results in average rotation of the material's complex molecules around their center-of-mass (CM). These materials are far from equilibrium due to their local non-vanishing spin angular momentum. In this paper we show that, unlike passive fluids, the non vanishing spin angular momentum brings about a difference between the CM momentum and the total momentum, which accounts for the momentum of all atoms that compose the complex rotating molecules. This is in stark contrast to equilibrium fluids where the CM stress and the total momentum are essentially equivalent. In fact, we find that generally the CM dynamics are insufficient to describe the dynamics of a chiral active material. The total momentum, other than being experimentally accessible in simple rheological experiments, also imposes another constraint -- its stress must be allowed to be written in a symmetric way. We find that the latter imposes a relation between possible central-force interactions and spin-spin interactions, and constraints the ammount of {\it odd} viscosities in the system to the well-known odd (Hall) viscosity and the odd pressure.

cond-mat.soft↗

arXiv2024

Second Law of Thermodynamics without Einstein Relation

Materials that are constantly driven out of thermodynamic equilibrium, such as active and living systems, typically violate the Einstein relation. This may arise from active contributions to particle fluctuations which are unrelated to the dissipative resistance of the surrounding medium. We show that in these cases the widely used relation between informatic entropy production and heat dissipation does not hold. Consequently, fluctuation relations for the mechanical work, such as the Jarzynski and Crooks theorems, are invalid. We relate the breaking of the correspondence between entropy production and heat dissipation to departure from the fluctuation-dissipation theorem. We propose a temperaturelike variable that restores this correspondence and gives rise to a generalized second law of thermodynamics, whereby the dissipated heat is necessarily non-negative and vanishes at equilibrium. The Clausius inequality, Carnot maximum efficiency theorem, and relation between the extractable work and the change of free energy are recovered as well.

cond-mat.stat-mech↗

arXiv2024

Nonreciprocity and odd viscosity in chiral active fluids

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid ${\rm He}^3$, quantum-Hall fluids, and recently in the context of chiral active matter. In most of these studies, odd terms in the viscosity obey Onsager reciprocal relations. Although this is expected in equilibrium systems, it is not obvious that Onsager relations hold in active materials. By directly coarse graining the kinetic energy and independently using both the Poisson-bracket formalism and a kinetic theory derivation, we find that the appearance of a non-vanishing angular momentum density, which is a hallmark of chiral active materials, necessarily breaks Onsager reciprocal relations. This leads to a non-Hermitian dynamical matrix for the total hydrodynamic momentum and to the appearance of odd viscosity and other non-dissipative contributions to the viscosity. Furthermore, by accounting for both the angular momentum density and interactions that lead to odd viscosity, we find regions in the parameter space in which 3D odd mechanical waves propagate and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting a possible non-reciprocal phase transition.

cond-mat.soft↗

arXiv2024

Consistent expansion of the Langevin propagator with application to entropy production

Stochastic thermodynamics is a developing theory for systems out of thermal equilibrium. It allows to formulate a wealth of nontrivial relations among thermodynamic quantities such as heat dissipation, excess work, and entropy production in generic nonequilibrium stochastic processes. A key quantity for the derivation of these relations is the propagator - the probability to observe a transition from one point in phase space to another after a given time. Here, applying stochastic Taylor expansions, we devise a formal expansion procedure for the propagator of overdamped Langevin dynamics. The three leading orders are obtained explicitly. The technique resolves the shortcomings of the current mathematical machinery for the calculation of the propagator. For the evaluation of the first two displacement cumulants, the leading order Gaussian propagator is sufficient. However, some functionals of the propagator, such as the entropy production, which we refer to as "first derivatives of the trajectory", need to be evaluated to a previously-unrecognized higher order. The method presented here can be extended to arbitrarily higher orders in order to accurately compute any other functional of the propagator.

cond-mat.stat-mech↗

arXiv2024

Field theory for mechanical criticality in disordered fiber networks

Strain-controlled criticality governs the elasticity of jamming and fiber networks. While the upper critical dimension of jamming is believed to be $d_u$=2, non mean-field exponents are observed in numerical studies of 2D and 3D fiber networks. The origins of this remains unclear. In this study we propose a minimal mean-field model for strain-controlled criticality of fiber networks. We then extend this to a phenomenological field theory, in which non mean-field behavior emerges as a result of the disorder in the network structure. We predict that the upper critical dimension for such systems is $d_u$=4 using a Gaussian approximation. Moreover, we identify an order parameter for the phase transition, which has been lacking for fiber networks to date.

cond-mat.soft↗

arXiv2023

Effective Medium Theory for Mechanical Phase Transitions of Fiber Networks

Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen. These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects via an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results.

cond-mat.soft↗

arXiv2023

Non-affine deformation of semiflexible polymer and fiber networks

Networks of semiflexible or stiff polymers such as most biopolymers are known to deform inhomogeneously when sheared. The effects of such non-affine deformation have been shown to be much stronger than for flexible polymers. To date, our understanding of non-affinity in such systems is limited to simulations or specific 2D models of athermal fibers. Here, we present an effective medium theory (EMT) for non-affine deformation of semiflexible polymer and fiber networks, which is general to both 2D and 3D and in both thermal and athermal limits. The predictions of this model are in good agreement with both prior computational and experimental results for linear elasticity. Moreover, the framework we introduce can be extended to address nonlinear elasticity and network dynamics.

cond-mat.soft↗

arXiv2022

Bjerrum Pairs in Ionic Solutions: a Poisson-Boltzmann Approach

Ionic solutions are often regarded as fully dissociated ions dispersed in a polar solvent. While this picture holds for dilute solutions, at higher ionic concentrations, oppositely charged ions can associate into dimers, referred to as Bjerrum pairs. We consider the formation of such pairs within the nonlinear Poisson-Boltzmann framework, and investigate their effects on bulk and interfacial properties of electrolytes. Our findings show that pairs can reduce the magnitude of the dielectric decrement of ionic solutions as the ionic concentration increases. We describe the effect of pairs on the Debye screening length, and relate our results to recent surface-force experiments. Furthermore, we show that Bjerrum pairs reduce the ionic concentration in bulk electrolyte and at the proximity of charged surfaces, while they enhance the attraction between oppositely charged surfaces.

cond-mat.soft↗

arXiv2022

Dielectric Constant of Ionic Solutions: Combined Effects of Correlations and Excluded Volume

The dielectric constant of ionic solutions is known to reduce with increasing ionic concentrations. However, the origin of this effect has not been thoroughly explored. In this paper we study two such possible sources: long-range Coulombic correlations and solvent excluded volume. Correlations originate from fluctuations of the electrostatic potential beyond the mean-field Poisson-Boltzmann theory, evaluated by employing a field-theoretical loop expansion of the free energy. The solvent excluded-volume, on the other hand, stems from the finite ion size, accounted for via a lattice-gas model. We show that both correlations and excluded volume are required in order to capture the important features of the dielectric behavior. For highly polar solvents, such as water, the dielectric constant is given by the product of the solvent volume fraction and a concentration-dependent susceptibility per volume fraction. The available solvent volume decreases as function of ionic strength due the increasing volume fraction of ions. A similar decrease occurs for the susceptibility due to correlations between the ions and solvent, reducing the dielectric response even further. Our predictions for the dielectric constant fit well with experiments for a wide range of concentrations for different salts in different temperatures, using a single fit parameter related to the ion size.

cond-mat.stat-mech↗

arXiv2022

Motor-free contractility of active biopolymer networks

Contractility in animal cells is often generated by molecular motors such as myosin, which require polar substrates for their function. Motivated by recent experimental evidence of motor-independent contractility, we propose a robust motor-free mechanism that can generate contraction in biopolymer networks without the need for substrate polarity. We show that contractility is a natural consequence of active binding/unbinding of crosslinkers that breaks the Principle of Detailed Balance, together with the asymmetric force-extension response of semiflexible biopolymers. We calculate the resulting contractile velocity using both a simple coarse-grained model and a more detailed microscopic model for a viscoelastic biopolymer network. Our model may provide an explanation of recent reports of motor-independent contractility in cells. Our results also suggest a mechanism for generating contractile forces in synthetic active materials.

cond-mat.soft↗

arXiv2022

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff -- which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing for simplicity on models with a purely diffusive scalar field, such as `Model B' which describes phase separation in binary fluid mixtures. We address the requirement that the steady state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for `active field theories' in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR) we must make a careful treatment of so-called `spurious drift' and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative, via off-diagonal couplings to additional fields that encode thermodynamically the underlying chemical processes responsible for activity. In this case the spurious drift terms need careful accounting, not just to evaluate correctly the EPR, but also to numerically implement the Langevin dynamics itself.

cond-mat.soft↗

arXiv2021

Non-linear stress relaxation of transient-crosslinked biopolymer networks

A long standing puzzle in the rheology of living cells is the origin of the experimentally observed long time stress relaxation. The mechanics of the cell is largely dictated by the cytoskeleton, which is a biopolymer network consisting of transient crosslinkers, allowing for stress relaxation over time. Moreover, these networks are internally stressed due to the presence of molecular motors. In this work we propose a theoretical model that uses a mode-dependent mobility to describe the stress relaxation of such prestressed transient networks. Our theoretical predictions agree favorably with experimental data of reconstituted cytoskeletal networks and may provide an explanation for the slow stress relaxation observed in cells.

physics.bio-ph↗