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#Matrix

53 posts48 participants4 posts today

📰 "Micro-swimmer locomotion and hydrodynamics in Brinkman Flows"
arxiv.org/abs/2505.08047 #Physics.Flu-Dyn #Physics.Bio-Ph #Cond-Mat.Soft #Matrix #Force

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arXiv.orgMicro-swimmer locomotion and hydrodynamics in Brinkman FlowsMicro-swimmer locomotion in heterogeneous media is increasingly relevant in biological physics due to the prevalence of microorganisms in complex environments. A model for such porous media is the Brinkman fluid which accounts for a sparse matrix of stationary obstacles via a linear resistance term in the momentum equation. We investigate two models for the locomotion and the flow field generated by a swimmer in such a medium. First, we analyze a dumbbell swimmer composed of two spring-connected spheres and driven by a flagellar force and derive its exact swimming velocity as a function of the Brinkman medium resistance, showing that the swimmer monotonically slows down as the medium drag monotonically increases. In the limit of no resistance the model reduces to the classical Stokes dipole swimmer, while finite resistance introduces hydrodynamic screening that attenuates long-range interactions. Additionally, we derive an analytical expression for the far-field flow generated by a Brinkmanlet force-dipole, which can be used for propulsive point-dipole swimmer models. Remarkably, this approximation reproduces the dumbbell swimmer's flow field in the far-field regime with high accuracy. These results provide new analytical tools for understanding locomotion in complex fluids and offer foundational insights for future studies on collective behavior in active and passive suspensions within porous or structured environments.

📰 "Divisible and indivisible Stochastic-Quantum dynamics"
arxiv.org/abs/2505.08785 #Physics.Data-An #Quant-Ph #Dynamics #Matrix

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arXiv.orgDivisible and indivisible Stochastic-Quantum dynamicsThis work presents a complete geometrical characterisation of divisible and indivisible time-evolution at the level of probabilities for systems with two configurations, open or closed. Our new geometrical construction in the space of stochastic matrices shows the existence of conical bounds separating divisible and indivisible dynamics, bearing analogy with the relativistic causal structure, with an emerging time pointing towards information erasure when the dynamics are divisible. Indivisible dynamics, which include quantum dynamics, are characterised by a time-flow against the information-erasure time coordinate or by being tachyonic with respect to the cones in the stochastic matrix space. This provides a geometric counterpart of other results in the literature, such as the equivalence between information-decreasing and divisible processes. The results apply under minimal assumptions: (i) the system has two configurations, (ii) one can freely ascribe initial probabilities to both and (iii) probabilities at other times are linearly related to the initial ones through conditional probabilities. The optional assumption of (iv) continuity places further constraints on the system, removing one of the past cones. Discontinuous stochastic dynamics in continuous time include cases with divisible blocks of evolution which are not themselves divisible. We show that the connection between continuity and multiplicity of divisors holds for any dimension. We extend methods of coarse graining and dilations by incorporating dynamics and uncertainty, connecting them with divisibility criteria. This is a first step towards a full geometric characterisation of indivisible stochastic dynamics for any number of configurations which, as they cannot at the level of probabilities be reduced to a composition of evolution operators, constitute fundamental elements of probabilistic time-evolution.

📰 "$\mathcal{H}$-HIGNN: A Scalable Graph Neural Network Framework with Hierarchical Matrix Acceleration for Simulation of Large-Scale Particulate Suspensions"
arxiv.org/abs/2505.08174 #Physics.Comp-Ph #Forces #Matrix

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arXiv.org$\mathcal{H}$-HIGNN: A Scalable Graph Neural Network Framework with Hierarchical Matrix Acceleration for Simulation of Large-Scale Particulate SuspensionsWe present a fast and scalable framework, leveraging graph neural networks (GNNs) and hierarchical matrix ($\mathcal{H}$-matrix) techniques, for simulating large-scale particulate suspensions, which have broader impacts across science and engineering. The framework draws on the Hydrodynamic Interaction Graph Neural Network (HIGNN) that employs GNNs to model the mobility tensor governing particle motion under hydrodynamic interactions (HIs) and external forces. HIGNN offers several advantages: it effectively captures both short- and long-range HIs and their many-body nature; it realizes a substantial speedup over traditional methodologies, by requiring only a forward pass through its neural networks at each time step; it provides explainability beyond black-box neural network models, through direct correspondence between graph connectivity and physical interactions; and it demonstrates transferability across different systems, irrespective of particles' number, concentration, configuration, or external forces. While HIGNN provides significant speedup, the quadratic scaling of its overall prediction cost (with respect to the total number of particles), due to intrinsically slow-decaying two-body HIs, limits its scalability. To achieve superior efficiency across all scales, in the present work we integrate $\mathcal{H}$-matrix techniques into HIGNN, reducing the prediction cost scaling to quasi-linear. Through comprehensive evaluations, we validate $\mathcal{H}$-HIGNN's accuracy, and demonstrate its quasi-linear scalability and superior computational efficiency. It requires only minimal computing resources; for example, a single mid-range GPU is sufficient for a system containing 10 million particles. Finally, we demonstrate $\mathcal{H}$-HIGNN's ability to efficiently simulate practically relevant large-scale suspensions of both particles and flexible filaments.

📰 "A comprehensive protocol for PDMS fabrication for use in cell culture"
doi.org/doi:10.1371/journal.po
pubmed.ncbi.nlm.nih.gov/403544
#Mechanical #Matrix #Cell

doi.orgA comprehensive protocol for PDMS fabrication for use in cell cultureCells exhibit remarkable sensitivity to the mechanical properties of their surrounding matrix, particularly stiffness changes, a phenomenon known as cellular mechanotransduction. In vivo, tissues exhibit a wide range of stiffness, from kilopascals (kPa) to megapascals (MPa), which can alter with aging and disease. Traditional cell culture methods employ plastic substrates with stiffness in the gigapascal range, which does not accurately mimic the physiological conditions of most biological tissues. Therefore, employing substrates that can be engineered to span a wide range of stiffnesses, closely resembling the native tissue environment, is crucial for obtaining results that more accurately reflect cellular responses in vivo. Polydimethylsiloxane (PDMS) substrates are widely used in cell culture for their ability to simulate tissue stiffness, but their optimization presents several challenges. Fabrication requires precise control over mixing, weighing, and curing to ensure reproducible mechanical properties. Inconsistent preparation can lead to improperly cured PDMS substrates, compromising experimental outcomes. Additionally, PDMS’s inherent hydrophobicity poses challenges for cell attachment, necessitating surface modifications to enhance adhesion. Moreover, the risk of contamination during the sterilization process necessitates stringent protocols to maintain cell culture integrity. These challenges are further compounded by substrate autofluorescence which can cause difficulties when imaging cells. The aim of this study is to develop a standardized method for fabricating PDMS substrates with tuneable stiffness, ranging from kPa to MPa, suitable for diverse cell types using standard laboratory equipment. This method aims to minimize the complexity and equipment required for PDMS fabrication, ensuring reproducibility and ease of use. Achieving consistent and contaminant-free PDMS substrates will facilitate a broader adoption of these substrates in mechanobiology research and improve the relevance of in vitro models to in vivo conditions. Ultimately, contributing to a more comprehensive understanding of cellular responses to mechanical cues in health and disease.

Is there any possibility to log into the #Matrix webinterface when you forgot the password, but you are still logged in with a mobile app (#Schildi in this case). The app provides an access token, but how to use it in the browser?

Goddamn! My Conduit server's registration was open, and now my server is banned by many, many Matrix servers because I had 232 spam accounts posting spam originating from my server. Well deserved, I guess.

Any hints on how to get unbanned? I already contacted moderation:gnome.org as this was the server where I noticed the ban. But my logs are full of servers refusing to federate. I guess there's a blocklist involved somewhere. Any hints?

📰 "Hyperbolic and Elliptic Points Tracking Algorithm (HEPTA) in two-dimensional non-stationary velocity fields defined on a discrete grid"
arxiv.org/abs/2505.05975 #Physics.Ao-Ph #Dynamics #Matrix

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arXiv.orgHyperbolic and Elliptic Points Tracking Algorithm (HEPTA) in two-dimensional non-stationary velocity fields defined on a discrete gridThis article presents a new algorithm, the Hyperbolic and Elliptic Points Tracking Algorithm (HEPTA), designed for automated tracking of elliptic and hyperbolic stationary points in two-dimensional non-stationary velocity fields defined on a discrete grid. HEPTA analyzes the stability, bifurcations, and Lagrangian dynamics of stationary points. By leveraging bilinear interpolation, Jacobian matrix analysis, and trajectory tracking, the algorithm accurately identifies the locations of vortex centers (elliptic points) and strain zones (hyperbolic points). A methodology has been developed to address bifurcation events and transitions across grid cell boundaries that occur during the evolution of stationary points in a discrete velocity field. The algorithm was tested on AVISO satellite altimetry data in the Kuroshio Current region, which is characterized by intense eddy formation. These data represent a two-dimensional discrete velocity field with a daily time step. The results show that HEPTA accurately identifies and tracks both cyclonic and anticyclonic eddies, even under conditions of rapid eddy drift and complex hydrodynamic conditions. This study provides a reliable and efficient tool for analyzing the dynamics of mesoscale formations, which may be useful in oceanographic research, climate modeling, and operational oceanography.