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📰 "Implicit Incompressible Porous Flow using SPH"
arxiv.org/abs/2504.07739 #Physics.Flu-Dyn #Adhesion #Forces #Cs.Gr

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arXiv.orgImplicit Incompressible Porous Flow using SPHWe present a novel implicit porous flow solver using SPH, which maintains fluid incompressibility and is able to model a wide range of scenarios, driven by strongly coupled solid-fluid interaction forces. Many previous SPH porous flow methods reduce particle volumes as they transition across the solid-fluid interface, resulting in significant stability issues. We instead allow fluid and solid to overlap by deriving a new density estimation. This further allows us to extend modern SPH pressure solvers to take local porosity into account and results in strict enforcement of incompressibility. As a result, we can simulate porous flow using physically consistent pressure forces between fluid and solid. In contrast to previous SPH porous flow methods, which use explicit forces for internal fluid flow, we employ implicit non-pressure forces. These we solve as a linear system and strongly couple with fluid viscosity and solid elasticity. We capture the most common effects observed in porous flow, namely drag, buoyancy and capillary action due to adhesion. To achieve elastic behavior change based on local fluid saturation, such as bloating or softening, we propose an extension to the elasticity model. We demonstrate the efficacy of our model with various simulations that showcase the different aspects of porous flow behavior. To summarize, our system of strongly coupled non-pressure forces and enforced incompressibility across overlapping phases allows us to naturally model and stably simulate complex porous interactions.

📰 "Identity-Based Language Shift Modeling"
arxiv.org/abs/2504.01552 #Physics.Soc-Ph #Dynamics #Math.Na #Cs.Na #Cell

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arXiv.orgIdentity-Based Language Shift ModelingThe preservation of endangered languages is a widely discussed issue nowadays. Languages represent essential cultural heritage and can provide valuable botanical, biological, and geographical information. Therefore, it is necessary to develop efficient measures to preserve and revitalize endangered languages. However, the language shift process is complex and requires an interdisciplinary approach, including mathematical modeling techniques. This paper develops a new mathematical model that extends previous works on this topic. We introduce the factor of ethnic identity, which is a proxy for a more complex nexus of variables involved in an individual's self-identity and/or a group's identity. This proxy is socially constructed rather than solely inherited, shaped by community-determined factors, with language both indexing and creating the identity. In our model, we divide speakers into groups depending on with which language they identify themselves with. Moreover, every group includes monolinguals and bilinguals. The proposed model naturally allows us to consider cases of language coexistence and describe a broader class of linguistic situations. For example, the simulation results show that our model can result in cyclic language dynamics, drawing a parallel to cell population models. In this way, the proposed mathematical model can serve as a useful tool for developing efficient measures for language preservation and revitalization.

📰 "The Granule-In-Cell Method for Simulating Sand--Water Mixtures"
arxiv.org/abs/2504.00745 #Physics.Flu-Dyn #Forces #Cs.Gr #Cell

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arXiv.orgThe Granule-In-Cell Method for Simulating Sand--Water MixturesThe simulation of sand--water mixtures requires capturing the stochastic behavior of individual sand particles within a uniform, continuous fluid medium, such as the characteristic of migration, deposition, and plugging across various scenarios. In this paper, we introduce a Granule-in-Cell (GIC) method for simulating such sand--water interaction. We leverage the Discrete Element Method (DEM) to capture the fine-scale details of individual granules and the Particle-in-Cell (PIC) method for its continuous spatial representation and particle-based structure for density projection. To combine these two frameworks, we treat granules as macroscopic transport flow rather than solid boundaries for the fluid. This bidirectional coupling allows our model to accommodate a range of interphase forces with different discretization schemes, resulting in a more realistic simulation with fully respect to the mass conservation equation. Experimental results demonstrate the effectiveness of our method in simulating complex sand--water interactions, while maintaining volume consistency. Notably, in the dam-breaking experiment, our simulation uniquely captures the distinct physical properties of sand under varying infiltration degree within a single scenario. Our work advances the state of the art in granule--fluid simulation, offering a unified framework that bridges mesoscopic and macroscopic dynamics.

To my #CS #professor friends on MathsTodon.xyz: what #programming languages are you teaching as the "proper first language" to your freshmen, and what are the delights and dismays thereof?

Some 30y ago, I taught C and ML to the CS undergrads—my two favourite classic languages. But, boy, they were a handful to teach to novices. But then, you lot might well have an easier task now, given that a typical CS freshman today knows several languages already (at least #Python and/or #JavaScript🤦‍♂️), by the time they enter the uni.

📰 "Empirical Hyper Element Integration Method (EHEIM) with Unified Integration Criteria for Efficient Hyper Reduced FE$^2$ Simulations"
arxiv.org/abs/2503.19483 #Physics.Comp-Ph #Mechanical #Math.Na #Cs.Na #Ecm

arXiv.orgEmpirical Hyper Element Integration Method (EHEIM) with Unified Integration Criteria for Efficient Hyper Reduced FE$^2$ SimulationsNumerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood. However, the computational costs of this so-called FE$^2$ method are so high that reduction methods are essential. While the construction of a reduced basis for the microscopic nodal displacements using proper orthogonal decomposition (POD) has become a standard technique, the reduction of the computational effort for the projected nodal forces, the so-called hyper reduction, is an additional challenge, for which different strategies have been proposed in the literature. The empirical cubature method (ECM), which has been proven to be very robust, implemented the conservation of the total volume is used as a constraint in the resulting optimization problem, while energy-based criteria have been proposed in other contributions. The present contribution presents a unified integration criteria concept, involving the aforementioned criteria, among others. These criteria are used both with a Gauss point-based as well as with an element-based hyper reduction scheme, the latter retaining full compatibility with the common modular finite element framework. The methods are combined with a previously proposed clustered training strategy and a monolithic solver. Numerical examples empirically demonstrate that the additional criteria improve the accuracy for a given number of modes. Vice verse, less modes and thus lower computational costs are required to reach a given level of accuracy.

📰 "AI-driven control of bioelectric signalling for real-time topological reorganization of cells"
arxiv.org/abs/2503.13489 #Physics.Bio-Ph #Morphogenesis #Q-Bio.Qm #Q-Bio.Cb #Eess.Sy #Cs.Sy #Cs.Ai #Cell

arXiv.orgAI-driven control of bioelectric signalling for real-time topological reorganization of cellsUnderstanding and manipulating bioelectric signaling could present a new wave of progress in developmental biology, regenerative medicine, and synthetic biology. Bioelectric signals, defined as voltage gradients across cell membranes caused by ionic movements, play a role in regulating crucial processes including cellular differentiation, proliferation, apoptosis, and tissue morphogenesis. Recent studies demonstrate the ability to modulate these signals to achieve controlled tissue regeneration and morphological outcomes in organisms such as planaria and frogs. However, significant knowledge gaps remain, particularly in predicting and controlling the spatial and temporal dynamics of membrane potentials (V_mem), understanding their regulatory roles in tissue and organ development, and exploring their therapeutic potential in diseases. In this work we propose an experiment using Deep Reinforcement Learning (DRL) framework together with lab automation techniques for real-time manipulation of bioelectric signals to guide tissue regeneration and morphogenesis. The proposed framework should interact continuously with biological systems, adapting strategies based on direct biological feedback. Combining DRL with real-time measurement techniques -- such as optogenetics, voltage-sensitive dyes, fluorescent reporters, and advanced microscopy -- could provide a comprehensive platform for precise bioelectric control, leading to improved understanding of bioelectric mechanisms in morphogenesis, quantitative bioelectric models, identification of minimal experimental setups, and advancements in bioelectric modulation techniques relevant to regenerative medicine and cancer therapy. Ultimately, this research aims to utilize bioelectric signaling to develop new biomedical and bioengineering applications.