arXiv subjects

Martin Kröger

Publications and source records attributed to Martin Kröger.

14 recordsLinked to original sources

arXiv2025

RN-SDEs: Limited-Angle CT Reconstruction with Residual Null-Space Diffusion Stochastic Differential Equations

Computed tomography is a widely used imaging modality with applications ranging from medical imaging to material analysis. One major challenge arises from the lack of scanning information at certain angles, resulting in distortion or artifacts in the reconstructed images. This is referred to as the Limited Angle Computed Tomography (LACT) reconstruction problem. To address this problem, we propose the use of Residual Null-Space Diffusion Stochastic Differential Equations (RN-SDEs), which are a variant of diffusion models that characterize the diffusion process with mean-reverting (MR) stochastic differential equations. To demonstrate the generalizability of RN-SDEs, we conducted experiments with two different LACT datasets, ChromSTEM and C4KC-KiTS. Through extensive experiments, we demonstrate that by leveraging learned MR-SDEs as a prior and emphasizing data consistency using Range-Null Space Decomposition (RNSD) based rectification, we can recover high-quality images from severely degraded ones and achieve state-of-the-art performance in most LACT tasks. Additionally, we present a quantitative comparison of RN-SDE with other networks, in terms of computational complexity and runtime efficiency, highlighting the superior effectiveness of our proposed approach.

eess.IV↗

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↗

arXiv2024

Characterizing hydrogel behavior under compression with gel-freezing osmometry

Hydrogels are particularly versatile materials that are widely found in both Nature and industry. One key reason for this versatility is their high water content, which lets them dramatically change their volume and many of their mechanical properties -- often by orders of magnitude -- as they swell and dry out. Currently, we lack techniques that can precisely characterize how these properties change with water content. To overcome this challenge, here we develop Gel-Freezing Osmometry (GelFrO): an extension of freezing-point osmometry. We show how GelFrO can measure a hydrogel's mechanical response to compression and osmotic pressure, while only using small, $O(100μ$L$)$ samples. Because the technique allows measurement of properties over an unusually wide range of water contents, it allows us to accurately test theoretical predictions. We find simple, power-law behavior for both mechanical response to compression, and osmotic pressure, while these are not well-captured by classical Flory-Huggins theory. We interpret this power-law behavior as a hallmark of a microscopic fractal structure of the gel's polymer network, and propose a simple way to connect the gel's fractal dimension to its mechanical and osmotic properties. This connection is supported by observations of hydrogel microstructures using small-angle x-ray scattering. Finally, our results motivate us to propose an updated constitutive model describing hydrogel swelling, and mechanical response.

cond-mat.soft↗

arXiv2024

Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally-defined domains observed by single cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as Rad21 degradation.

physics.bio-ph↗

arXiv2023

Increase in rod diffusivity emerges even in Markovian nature

Rod-shaped particles embedded in certain matrices have been reported to exhibit an increase in their center of mass diffusivity upon increasing the matrix density. This increase has been considered to be caused by a kinetic constraint in analogy with tube models. We investigate a mobile rod-like particle in a sea of immobile point obstacles using a kinetic Monte Carlo scheme equipped with a Markovian process, that generates gas-like collision statistics, so that such kinetic constraints do essentially not exist. Even in such a system, provided the particle's aspect ratio exceeds a threshold value of about 24, the unusual increase in the rod diffusivity emerges. This result implies that the kinetic constraint is not a necessary condition for the increase in the diffusivity.

cond-mat.stat-mech↗

arXiv2023

Siloxane molecules: Nonlinear elastic behavior and fracture characteristics

Fracture phenomena in soft materials span multiple length- and timescales. This poses a major challenge in computational modeling and predictive materials design. To pass quantitatively from molecular- to continuum scales, a precise representation of the material response at the molecular level is vital. Here, we derive the nonlinear elastic response and fracture characteristics of individual siloxane molecules using molecular dynamics (MD) studies. For short chains, we find deviations from classical scalings for both the effective stiffness and mean chain rupture times. A simple model of a non-uniform chain of Kuhn segments captures the observed effect and agrees well with MD data. We find that the dominating fracture mechanism depends on the applied force scale in a non-monotonic fashion. This analysis suggests that common polydimethylsiloxane (PDMS) networks fail at crosslinking points. Our results can be readily lumped into coarse-grained models. Although focusing on PDMS as a model system, our study presents a general procedure to pass beyond the window of accessible rupture times in MD studies employing mean first passage time theory, which can be exploited for arbitrary molecular systems.

cond-mat.soft↗

arXiv2020

Time correlation functions of equilibrium and nonequilibrium Langevin dynamics: Derivations and numerics using random numbers

We study the time correlation functions of coupled linear Langevin dynamics without and with inertia effects, both analytically and numerically. The model equation represents the physical behavior of a harmonic oscillator in two or three dimensions in the presence of friction, noise, and an external field with both rotational and deformational components. This simple model plays pivotal roles in understanding more complicated processes. The presented analytical solution serves as a test of numerical integration schemes, its derivation is presented in a fashion that allows to be repeated directly in a classroom. While the results in the absence of fields (equilibrium) or confinement (free particle) are omnipresent in the literature, we write down, apparently for the first time, the full nonequilibrium results that may correspond, e.g., to a Hookean dumbbell embedded in a macroscopically homogeneous shear or mixed flow field. We demonstrate how the inertia results reduce to their noninertia counterparts in the nontrivial limit of vanishing mass. While the results are derived using basic integrations over Dirac delta distributions, we mention its relationship with alternative approaches involving (i) Fourier transforms, that seems advantageous only if the measured quantities also reside in Fourier space, and (ii) a Fokker--Planck equation and the moments of the probability distribution. The results, verified by numerical experiments, provide additional means of measuring the performance of numerical methods for such systems. It should be emphasized that this manuscript provides specific details regarding the derivations of the time correlation functions as well as the implementations of various numerical methods, so that it can serve as a standalone piece as part of education in the framework of stochastic differential equations and calculus.

physics.comp-ph↗

arXiv2020

Unified analytic expressions for the entanglement length, tube diameter, and plateau modulus of polymer melts

By combining molecular dynamics simulations and topological analyses with scaling arguments, we obtain analytic expressions that quantitatively predict the entanglement length $N_e$, the plateau modulus $G$, and the tube diameter $a$ in melts that span the entire range of chain stiffnesses for which systems remain isotropic. Our expressions resolve conflicts between previous scaling predictions for the loosely entangled [Lin-Noolandi: $G\ell_K^3/k_\textrm{B}T \sim (\ell_K/p)^3$], semiflexible [Edwards/de Gennes: $G\ell_K^3/k_\textrm{B}T \sim (\ell_K/p)^2$], and tightly-entangled [Morse: $G\ell_K^3/k_\textrm{B}T \sim (\ell_K/p)^{1+ε}$] regimes, where $\ell_K$ and $p$ are respectively the Kuhn and packing lengths. We also find that maximal entanglement (minimal $N_e$) coincides with the onset of local nematic order.

cond-mat.soft↗

arXiv2020

Assessing numerical methods for molecular and particle simulation

We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more recently proposed "pairwise adaptive Langevin" (PAdL) method, which, like DPD but unlike Langevin dynamics, conserves momentum and better matches the relaxation rate of orientational degrees of freedom. PAdL is easy to code and suitable for a variety of problems in nonequilibrium soft matter modeling, our simulations of polymer melts indicate that this method can also provide dramatic improvements in computational efficiency. Moreover we show that PAdL gives excellent control of the relaxation rate to equilibrium. In the nonequilibrium setting, we further demonstrate that while PAdL allows the recovery of accurate shear viscosities at higher shear rates than are possible using the DPD method at identical timestep, it also outperforms Langevin dynamics in terms of stability and accuracy at higher shear rates.

physics.comp-ph↗

arXiv2018

Dynamics and wetting behavior of soft particles at a fluid-fluid interface

We investigate the conformation, position, and dynamics of core-shell nanoparticles (CSNPs) composed of a silica core encapsulated in a cross-linked poly-N-isopropylacrylamide shell at a water-oil interface for a systematic range of core sizes and shell thicknesses. We first present a free-energy model that we use to predict the CSNP wetting behavior at the interface as a function of its geometrical and compositional properties in the bulk phases, which gives good agreement with our experimental data. Remarkably, upon knowledge of the polymer shell deformability, the equilibrium particle position relative to the interface plane, an often elusive experimental quantity, can be extracted by measuring its radial dimensions after adsorption. For all the systems studied here, the interfacial dimensions are always larger than in bulk and the particle core resides in a configuration wherein it just touches the interface or is fully immersed in water. Moreover, the stretched shell induces a larger viscous drag at the interface, which appears to depend solely on the interfacial dimensions, irrespective of the portion of the CSNP surface exposed to the two fluids. Our findings indicate that tailoring the architecture of CSNPs can be used to control their properties at the interface, as of interest for applications including emulsion stabilization and nanopatterning.

cond-mat.soft↗

arXiv2009

Topological analysis of polymeric melts: Chain length effects and fast-converging estimators for entanglement length

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_e which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive and test new estimators which eliminate these systematic errors using information obtainable from the variation of entanglement characteristics with chain length. The new estimators produce accurate results for N_e from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

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↗

arXiv2002

Canonical Distribution Functions in Polymer Dynamics: II. Liquid--Crystalline Polymers

The quasi--equilibrium approximation is employed as a systematic tool for solving the problem of deriving constitutive equations from kinetic models of liquid--crystalline polymers. It is demonstrated how kinetic models of liquid--crystalline polymers can be approximated in a systematic way, how canonical distribution functions can be derived from the maximum entropy principle and how constitutive equations are derived therefrom. The numerical implementation of the constitutive equations based on the intrinsic dual structure of the quasi--equilibrium manifold thus derived is developed and illustrated for particular examples. Finally, a measure of the accuracy of the quasi--equilibrium approximation is proposed that can be implemented into the numerical integration of the constitutive equation.

cond-mat.stat-mech↗