arXiv subjects

Patrick Ilg

Publications and source records attributed to Patrick Ilg.

At least 19 recordsLinked to original sources

arXiv2025

Time is length in self-similar logarithmic aging of physically cross-linked semiflexible polymer networks

Physical aging in polymers is a fundamental yet poorly understood phenomenon, as diverse macromolecular systems exhibit remarkably similar slow dynamics. Through molecular dynamics simulations of physically crosslinked networks composed of semiflexible polymers, we identify a previously unexplored class of self-similar aging. The network undergoes ultra-slow coarsening characterized by a logarithmically growing mesh size, $L(t)\sim \ln t$, which governs the spatial organization, cohesive and bending energies, and the aging dynamics of the system. This single time-dependent length scale defines an internal clock, giving rise to spatio- temporal self-similarity of both structure and dynamics - offering a perspective on aging in soft and disordered materials.

cond-mat.soft↗

arXiv2025

Quantitative Stain Mapping in X-ray Virtual Histology

Virtual histology is an emerging field in biomedicine that enables three-dimensional tissue visualization using X-ray micro-computed tomography. However, the method still lacks the specificity of conventional histology, in which parts of the tissue are selectively highlighted using targeted stains. Though some first X-ray stains have been developed to address this issue, their precise location and quantity inside the tissue volume remain largely unknown. In this work, we present a novel approach to virtual histology that simultaneously captures electron number density and X-ray attenuation values through modulation-based X-ray imaging with a structured phase modulator. These complementary measurements enable decomposition of tissue volumes into basis materials, which allows the extraction of three-dimensional maps of molar contrast agent distribution alongside morphological details on the micrometer scale -- here demonstrated on murine kidneys. The concentration values are validated against the established method of K-edge subtraction imaging. We also create a direct bridge from X-ray to visible light imaging by detecting the same stain both using classical histology and our proposed X-ray approach. Our methodology opens new possibilities for biomedical research into disease progression by providing quantitative three-dimensional stain mapping across entire tissue volumes alongside high-contrast morphology, enabling deeper insights into disease mechanisms.

physics.med-ph↗

arXiv2025

Analytic solution for the nonlinear response of magnetic nanoparticles to large-amplitude oscillatory fields

Nonlinear responses of physical systems to strong perturbations are notoriously difficult to tackle analytically. Here, we present analytic results for the nonlinear response of magnetic nanoparticles to large amplitude oscillatory magnetic fields based on a particular model for the magnetization dynamics. A number of characteristic features of the in-phase and out-of-phase higher-harmonic response are found and analyzed. In particular we find that the magnitude of higher harmonic contributions Rn depends on the field amplitude and frequency only via a single scaling variable that combines the two quantities. The decrease of |Rn|with increasing order nof harmonics is a key quantity monitored in biomedical applications such as magnetic particle spectroscopy and magnetic particle imaging. Except for the first few harmonics, we find that this decrease is exponential with a rate that depends on the scaling variable only. For not too high frequencies and not loo large amplitudes, we find that these exact results for one particular model of magnetization dynamics hold approximately also for other, more frequently used models. Our results therefore offer not only deeper insight into strongly nonlinear responses of magnetic nanoparticles, especially for higher harmonics that are very difficult to determine numerically, but also suggest analyzing data in terms of a scaling variable.

cond-mat.soft↗

arXiv2024

Magneto-Permeability Effect in Ferrofluid Flow through Porous Media studied via Multiparticle Collision Dynamics

As more and more promising applications of magnetic nanoparticles in complicated environments are explored, their flow properties in porous media are of increasing interest. We here propose a hybrid approach based on the Multiparticle Collision Dynamics Method extended to porous media via friction forces and coupled with Brownian Dynamics simulations of the rotational motion of magnetic nanoparticles' magnetic moment. We simulate flow in planar channels homogeneously filled with a porous medium and verify our implementation by reproducing the analytical velocity profile of the Darcy-Brinkman model in the non-magnetic case. In the presence of an externally applied magnetic field, the non-equilibrium magnetization and friction forces lead to field-dependent velocity profiles that result in effective, field-dependent permeabilities. We provide a theoretical expression for this magneto-permeability effect in analogy with the magneto-viscous effect. Finally, we study the flow through planar channels, where only the walls are covered with a porous medium. We find a smooth crossover from the Poiseuille profile in the center of the channel to the Brinkman-Darcy flow in the porous layers. We propose a simple estimate of the thickness of the porous layer based on the flow rate and maximum flow velocity.

cond-mat.soft↗

arXiv2022

Multiparticle Collision Dynamics for Ferrofluids

Detailed studies of the intriguing field-dependent dynamics and transport properties of confined flowing ferrofluids require efficient mesoscopic simulation methods that account for fluctuating ferrohydrodynamics. Here, we propose such a new mesoscopic model for the dynamics and flow of ferrofluids, where we couple the multi-particle collision dynamics method as a solver for the fluctuating hydrodynamics equations to the stochastic magnetization dynamics of suspended magnetic nanoparticles. This hybrid model is validated by reproducing the magnetoviscous effect in Poiseuille flow, obtaining the rotational viscosity in quantitative agreement with theoretical predictions. We also illustrate the new method for the benchmark problem of flow around a square cylinder. Interestingly, we observe that the length of the recirculation region is increased whereas the drag coefficient is decreased in ferrofluids when an external magnetic field is applied, compared with the field-free case at the same effective Reynolds number. The presence of thermal fluctuations and the flexibility of this particle-based mesoscopic method provides a promising tool to investigate a broad range of flow phenomena of magnetic fluids and could also serve as an efficient way to simulate solvent effects when colloidal particles are immersed in ferrofluids.

cond-mat.soft↗

arXiv2018

Magnetic susceptibility, nanorheology, and magnetoviscosity of magnetic nanoparticles in viscoelastic environments

While magnetic nanoparticles suspended in Newtonian solvents (ferrofluids) have been intensively studied in recent years, the effects of viscoelasticity of the surrounding medium on the nanoparticle dynamics are much less understood. Here we investigate a mesoscopic model for the orientational dynamics of isolated magnetic nanoparticles subject to external fields, viscous and viscoelastic friction as well as the corresponding random torques. We solve the model analytically in the overdamped limit for weak viscoelasticity. By comparison to Brownian Dynamics simulations we establish the limits of validity of the analytical solution. We find that viscoelasticity does not only slow down the magnetization relaxation, shift the peak of the imaginary magnetic susceptibility $χ''$ to lower frequencies and increase the magnetoviscosity, it also leads to non-exponential relaxation and a broadening of $χ''$. The model we study also allows to test a recent proposal for using magnetic susceptibility measurements as a nanorheological tool using a variant of the Germant-DiMarzio-Bishop relation. We find for the present model and certain parameter ranges that the relation of the magnetic susceptibility to the shear modulus is satisfied to a good approximation.

cond-mat.soft↗

arXiv2017

Time correlation functions in the Lebwohl-Lasher model of liquid crystals

Time correlation functions in the Lebwohl-Lasher model of nematic liquid crystals are studied using theory and molecular dynamics simulations. In particular, the autocorrelation functions of angular momentum and nematic director fluctuations are calculated in the long-wavelength limit. The constitutive relations for the hydrodynamic currents are derived using a standard procedure based on non-negativity of the entropy production. The continuity equations are then linearized and solved to calculate the correlation functions. We find that the transverse angular momentum fluctuations are coupled to the director fluctuations, and are both propagative. The propagative nature of the fluctuations suppress the anticipated hydrodynamic long-time tails in the single-particle autocorrelation functions. The fluctuations in the isotropic phase are however diffusive, leading to $t^{-d/2}$ long-time tails in $d$ spatial dimensions. The Frank elastic constant measured using the time-correlation functions are in good agreement with previously reported results.

cond-mat.soft↗

arXiv2015

Influence of inherent structure shear stress of supercooled liquids on their shear moduli

Configurations of supercooled liquids residing in their local potential minimum (i.e. in their inherent structure, IS) were found to support a non-zero shear stress. This IS stress was attributed to the constraint to the energy minimization imposed by boundary conditions, which keep size and shape of the simulation cell fixed. In this paper we further investigate the influence of these boundary conditions on the IS stress. We investigate its importance for the computation of the low frequency shear modulus of a glass obtaining a consistent picture for the low- and high frequency shear moduli over the full temperature range. Hence, we find that the IS stress corresponds to a non-thermal contribution to the fluctuation term in the Born-Green expression. This leads to an unphysical divergence of the moduli in the low temperature limit if no proper correction for this term is applied. Furthermore, we clarify the IS stress dependence on the system size and put its origin on a more formal basis.

cond-mat.soft↗

arXiv2014

Nonequilibrium Thermodynamics of the Soft Glassy Rheology Model

The Soft Glassy Rheology (SGR) model is a mesoscopic framework which proved to be very successful in describing flow and deformation of various amorphous materials phenomenologically (e.g. pastes, slurries, foams etc). In this paper, we cast SGR in a general, model independent framework for nonequilibrium thermodynamics called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC). This leads to a new formulation of SGR which clarifies how it can properly be coupled to hydrodynamic fields, resulting in a thermodynamically consistent, local, continuum version of SGR. Additionally, we find that compliance with thermodynamics imposes the existence of a modification to the stress tensor as predicted by SGR.

cond-mat.soft↗

arXiv2014

Soft modes and non-affine rearrangements in the inherent structures of supercooled liquids

We find that the hierarchical organization of the potential energy landscape in a model supercooled liquid can be related to a change in the spatial distribution of soft normal modes. For groups of nearby minima, between which fast relaxation processes typically occur, the localization of the soft modes is very similar. The spatial distribution of soft regions changes, instead, for minima between which transitions relevant to structural relaxation occur. This may be the reason why the soft modes are able to predict spatial heterogeneities in the dynamics. Nevertheless, the very softest modes are only weakly correlated with dynamical heterogeneities, and instead show higher statistical overlap with regions in the local minima that would undergo non-affine rearrangements if subjected to a shear deformation. This feature of the supercooled liquid is reminiscent of the behavior of non-affine deformations in amorphous solids, where the very softest modes identify the {\it loci} of plastic instabilities.

cond-mat.dis-nn↗

arXiv2012

Deformation of inherent structures to detect long-range correlations in supercooled liquids

We propose deformations of inherent structures as a suitable tool for detecting structural changes underlying the onset of cooperativity in supercooled liquids. The non-affine displacement (NAD) field resulting from the applied deformation shows characteristic differences between the high temperature liquid and supercooled state, that are typically observed in dynamic quantities. The average magnitude of the NAD is very sensitive to temperature changes in the supercooled regime and is found to be strongly correlated with the inherent structure energy. In addition, the NAD field is characterized by a correlation length that increases upon lowering the temperature towards the supercooled regime.

cond-mat.dis-nn↗

arXiv2010

Probing a critical length scale at the glass transition

We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external, static perturbation to extract the structural information from the system's response. In particular, we consider the transformation behavior of the local minima of the underlying potential energy landscape (inherent structures), under a static deformation. The finite-size scaling analysis of our numerical results indicate that the correlation length diverges at a temperature $T_c$, below the temperatures here the system can be equilibrated. Our numerical results are consistent with random first order theory, which predicts such a divergence with a critical exponent $ν=2/3$ at the Kauzmann temperature, where the extrapolated configurational entropy vanishes.

cond-mat.stat-mech↗

arXiv2010

Bridging length and time scales in sheared demixing systems: from the Cahn-Hilliard to the Doi-Ohta model

We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is to identify the relevant coarse-grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarse-grained variables, which in the long wavelength limit recovers the familiar phenomenological Doi-Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn-Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established.

cond-mat.stat-mech↗

arXiv2009

Multiscale Modeling and Coarse Graining of Polymer Dynamics: Simulations Guided by Statistical Beyond-Equilibrium Thermodynamics

We review some recent coarse-graining and multi-scale methods, but also put forward some new ideas for addressing such issues. We find that, if one is guided by nonequilibrium statistical mechanics and thermodynamics, it is possible to design well-founded multi-scale modeling tools that can link microscopic models with macroscopic constitutive equations. Such multi-scale modeling tools benefit from recently proposed approaches for static coarse graining which are mainly built on potentials of mean force. For dynamical properties, however, coarse-grained models need to account for dissipative effects that arise due to fast degrees of freedom that are eliminated in favor of the remaining slowly varying ones. The proper definition of the set of the state variables, effectively representing the nonequilibrium states is the first key to the success of such an approach. Linking the microscopic model with a macroscopic model built on these slowly relaxing variables is the second key. We illustrate the new approach for a flowing, low-molecular polymer melt.

cond-mat.soft↗

arXiv2008

Systematic time-scale-bridging molecular dynamics applied to flowing polymer melts

We present a novel thermodynamically guided, low-noise, time-scale bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for low-molecular polymeric systems subjected to homogeneous flow fields. We use established concepts of nonequilibrium thermodynamics and an alternating Monte-Carlo--molecular dynamics iteration scheme in order to obtain the model equations for the slow variables. For chosen flow situations of interest, the established model predicts structural as well as material functions beyond the regime of linear response. As a by-product, we present the first steady state equibiaxial simulation results for polymer melts. The method is simple to implement and allows for the calculation of time-dependent behavior through quantities readily available from the nonequilibrium steady states.

cond-mat.soft↗

arXiv2008

Non-affine deformations of inherent structure as signature of cooperativity in supercooled liquids

We unveil the existence of non-affinely rearranging regions in the inherent structures (IS) of supercooled liquids by numerical simulations of two- and three-dimensional model glass formers subject to static shear deformations combined with local energy minimizations. In the liquid state IS, we find a broad distribution of rather large rearrangements which are correlated only over small distances. At low temperatures, the onset of the cooperative dynamics corresponds to much smaller displacements correlated over larger distances. This finding indicates the presence of non-affinely rearranging domains of relevant size in the IS deformation, which can be seen as the static counterpart of the cooperatively rearranging regions in the dynamics. This idea provides new insight into possible structural signatures of slow cooperative dynamics of supercooled liquids and supports the connections with elastic heterogeneities found in amorphous solids.

cond-mat.stat-mech↗

arXiv2007

Driven activation versus thermal activation

Activated dynamics in a glassy system undergoing steady shear deformation is studied by numerical simulations. Our results show that the external driving force has a strong influence on the barrier crossing rate, even though the reaction coordinate is only weakly coupled to the nonequilibrium system. This "driven activation" can be quantified by introducing in the Arrhenius expression an effective temperature, which is close to the one determined from the fluctuation-dissipation relation. This conclusion is supported by analytical results for a simplified model system.

cond-mat.stat-mech↗

arXiv2006

Effective temperatures in a simple model of non-equilibrium, non-Markovian dynamics

The concept of effective temperatures in nonequilibrium systems is studied within an exactly solvable model of non-Markovian diffusion. The system is coupled to two heat baths which are kept at different temperatures: one ('fast') bath associated with an uncorrelated Gaussian noise and a second ('slow') bath with an exponential memory kernel. Various definitions of effective temperatures proposed in the literature are evaluated and compared. The range of validity of these definitions is discussed. It is shown in particular, that the effective temperature defined from the fluctuation-dissipation relation mirrors the temperature of the slow bath in parameter regions corresponding to a separation of time scales. On the contrary, quasi-static and thermodynamic definitions of an effective temperature are found to display the temperature of the fast bath in most parameter regions.

cond-mat.stat-mech↗