arXiv subjects

Michał Bogdan

Publications and source records attributed to Michał Bogdan.

5 recordsLinked to original sources

arXiv2026

Topological cell-openness index for porous materials

We propose a method of estimating and parametrising the proportion of open and closed cells in a porous material based on measuring Betti numbers on the structures. We define a cell-openness index τ which can be used to complement the proportion of open-celled volume reported by gas pycnometry, which is the current gold standard for pore type characterization. We discuss in what types of structures mismatches between the two measures can occur and how such mismatches convey additional information about the structure. We demonstrate examples of significant correlations between τ and measurable physical quantities in both numerical and experimental structures. We also discuss how Betti curves can be used to estimate characteristic feature sizes in porous structures.

cond-mat.soft↗

arXiv2026

Direction-aware topological descriptors for elastic stiffness tensor prediction in porous materials

Classical topological descriptors used in topological data analysis (TDA) are invariant under permutations of spatial axes and therefore cannot represent the loading direction, which is essential for modeling anisotropic mechanical response. Here, this limitation is addressed by introducing a direction-aware TDA framework in which the loading axis is explicitly embedded into filtration functions used to compute both persistent homology and Euler characteristic profile descriptors. We apply this framework to predict the full elastic stiffness tensor of porous microstructures using non-directional as well as direction-aware descriptors of the structures as well as convolutional neural networks trained directly on the voxelized structure. We show that the performance of all those are comparable on the diagonal uniaxial, Poisson, and shear components. However for the twelve off-diagonal, normal shear coupling components - which govern elastic anisotropy and are the hardest to predict - only direction-aware topology retains meaningful predictive power, with all baselines, non-directional descriptors and the CNN collapsing to near-chance accuracy. When used as inputs to gradient-boosted tree models, the proposed descriptors match or exceed the accuracy of the convolutional neural network specifically on these hardest-to-predict coupling terms, despite relying on a compact, physically interpretable representation that is orders of magnitude smaller than the raw voxel grid. Overall, the results establish direction-aware TDA as a practical route for linking porous microstructure to the full anisotropic elastic response, capturing coupling terms that conventional descriptors and end-to-end deep learning models fail to resolve.

physics.comp-ph↗

arXiv2022

Stochastic jetting and dripping in confined soft granular flows

We report new dynamical modes in confined soft granular flows, such as stochastic jetting and dripping, with no counterpart in continuum viscous fluids. The new modes emerge as a result of the propagation of the chaotic behaviour of individual grains -- here, monodisperse emulsion droplets to the level of the entire system as the emulsion is focused into a narrow orifice by an external viscous flow. We observe avalanching dynamics and the formation of remarkably stable jets -- singlefile granular chains -- which occasionally break, resulting in a non-Gaussian distribution of cluster sizes. We find that the sequences of droplet rearrangements that lead to the formation of such chains resemble unfolding of cancer cell clusters in narrow capillaries, overall demonstrating that microfluidic emulsion systems could serve to model various aspects of soft granular flows, including also tissue dynamics at the meso-scale.

cond-mat.soft↗

arXiv2018

Fingering instabilities in tissue invasion: an active fluid model

Metastatic tumors often invade healthy neighboring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model of a self-propelled, growing biological tissue. The theory involves only four mechanical parameters and remains analytically trackable in various settings. As an application of the model, we study the evolution of a 2D circular droplet made of our active and expanding fluid, and embedded in a passive non-growing tissue. This system could be used to model the evolution of a carcinoma in an epithelial layer. We find that our description can explain the propensity of tumor tissues to fingering instabilities, as conditioned by both the magnitude of active traction and the growth kinetics. We are also able to derive predictions for the tumor size at the onset of metastasis, and for the number of subsequent invasive fingers. Our active fluid model may help describe a wider range of biological processes, including wound healing and developmental patterning.

physics.bio-ph↗

arXiv2017

Errors in energy landscapes measured with particle tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet, video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame acquisition time. We show that these errors result in systematic and non-trivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials, by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors, but decreased by static errors. Our formula allows for the development of efficient corrections schemes, which we also present in this paper.

cond-mat.soft↗