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Flagellum Pumping Efficiency in Shear-Thinning Viscoelastic Fluids

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arXiv 2023年

作者： Barrett, Aaron Fogelson, Aaron L. Gregory Forest, M. Gruninger, Cole Lim, Sookkyung Griffith, Boyce E. Department of Mathematics University of Utah Salt Lake CityUT United States Departments of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Department of Mathematical Sciences University of Cincinnati CincinnatiOH United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear-thinning of the viscoelastic environment. Copyright © 2023, The Authors. All rights reserved.

关键词： Shear thinning

Embodied Runtime Monitoring of Learning-enabled Robot Perception Components

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Embodied Runtime Monitoring of Learning-enabled Robot Percep...

IEEE International Conference on Automation Science and Engineering (CASE)

作者： Deebul Nair Sathwik Panchangam Miguel A. Olivares-Mendez Nico Hochgeschwender Institute for Artificial Intelligence and Autonomous Systems Bonn-Rhein-Sieg University of Applied Sciences Sankt Augustin Germany Space Robotics Research Group (SpaceR) Interdisciplinary Centre for Security Reliability and Trust (SnT) University of Luxembourg Luxembourg Department of Mathematics and Computer Science University of Bremen Germany

ISBN: (数字)9798350358513

ISBN: (纸本)9798350358520

Monitoring during runtime, the estimated uncertainty from learning-enabled robot perception components, is a vital tool for assuring and evaluating model correctness. By utilizing different uncertainty estimation methods, monitors exploit the perceived sensor data and predictions generated by the perception model to make informed decisions, such as in safety-critical situations. In robotics, informed decisions should be aligned with embodied information regarding space and time. We argue and show that runtime monitors of learning-enabled components can be made more robust by including the embodiment information of the robot. However, it remains challenging to build uncertainty-based runtime monitors with embodiment information using only real-world datasets, which are tedious to collect. To this end, we propose a solution that leverages simulation-based datasets to characterize expected uncertainty estimates with robot embodiment. By constructing a nominal runtime monitor model based on simulated datasets, we establish a reference for the expected uncertainty along with the embodiment information that can be subsequently used to monitor real-world deployed perception components. We demonstrate the zero-shot sim-to-real transfer of our approach on a Kinova Gen3 manipulator picking task, for which the runtime monitor reliability model was trained using simulation-based data containing embodiment information of distance from the object being selected.

关键词： Runtime Uncertainty Computational modeling Estimation Predictive models Robot sensing systems Manipulators Reliability engineering Data models Monitoring

A physics informed neural network approach to simulating ice dynamics governed by the shallow ice approximation

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arXiv 2025年

作者： Chawla, Kapil Holmes, William Department of Mathematics Institute for Scientific Computing and Applied Mathematics Indiana University IN47405 United States Department of Mathematics Cognitive Science Program Indiana University IN47405 United States

In this article we develop a Physics Informed Neural Network (PINN) approach to simulate ice sheet dynamics governed by the Shallow Ice Approximation. This problem takes the form of a time-dependent parabolic obstacle problem [17]. Prior work has used this approach to address the stationary obstacle problem and here we extend it to the time dependent problem [4]. Through comprehensive 1D and 2D simulations, we validate the model’s effectiveness in capturing complex free-boundary conditions. By merging traditional mathematical modeling with cutting-edge deep learning methods, this approach provides a scalable and robust solution for predicting temporal variations in ice thickness. To illustrate this approach in a real world setting, we simulate the dynamics of the Devon Ice Cap, incorporating aerogeophysical data from 2000 [6] and 2018 [22]. © 2025, CC BY.

关键词： Approximation theory

A First-Principles and Calphad-Assisted Phase-Field Model for Microstructure Evolution: Application to Mo-V Binary Alloy Systems

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SSRN

SSRN 2023年

作者： Thakur, Abhishek Kumar Kovacevic, Sasa Manga, Venkateswara Rao Deymier, Pierre Alix Muralidharan, Krishna Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Department of Civil and Environmental Engineering Imperial College London LondonSW7 2AZ United Kingdom Lunar and Planetary Laboratory University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics India

A multiscale computational framework combining the first-principles calculations and the CALPHAD approach with the phase-field method is presented to simulate the microstructure evolution in multicomponent steel alloys. We demonstrate the potential of the framework by predicting the microstructural evolution in elastically periodic arrays of the Mo-V binary sub-system. The framework utilizes the first-principles calculations using special quasi-random structures. Hitherto unavailable thermodynamic and material properties of the alloy are obtained by employing the first-principles calculations and the CALPHAD approach and fed into the phase-field model to predict the microstructure evolution at different temperatures within the miscibility gap region. In addition to the temperature and cooling rates, the model incorporates the role of mechanical fields in decomposition kinetics in the Mo-V binary alloy system. Regimes for temperatures and cooling rates at which spinodal decomposition occurs are identified. Applying external loading leads to directional phase separation in the Mo-V binary system. The elastic inhomogeneity in terms of material properties between the two phases initiates the directional alignment while eigenstrains and applied external loading control the degree of alignment. The framework developed is general and extendable to higher multicomponent sub-systems in steel alloys. © 2023, The Authors. All rights reserved.

关键词： Temperature

Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data

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arXiv 2023年

作者： Nguyen, Kyle Rutter, Erica M. Flores, Kevin Biomathematics Graduate Program North Carolina State University RaleighNC United States Center for Research in Scientific Computation North Carolina State University RaleighNC United States Department of Applied Mathematics University of California Merced MercedCA United States Department of Mathematics North Carolina State University RaleighNC United States

Reaction diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates, however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of Glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models’ performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions. © 2023, CC BY.

关键词： Parameter estimation

Phase Diagram of a Deep Potential Water Model

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Physical Review Letters 2021年第23期126卷 236001-236001页

作者： Linfeng Zhang Han Wang Roberto Car Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and Beijing Institute of Big Data Research Beijing 100871 People’s Republic of China

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII′′ and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

关键词： Classical statistical mechanics First order phase transitions Interatomic & molecular potentials Phase diagrams Potential energy surfaces Water First-principles calculations Machine learning Molecular dynamics

Can One Hear the Shape of a Crystal?

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arXiv 2025年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics PrincetonNJ08544 United States

Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question "Can one hear the shape of a drum?" concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in d-dimensional Euclidean space Rd is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function g2(r). While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an n-particle basis (n ≥ 2). Here, we ask, What is nmin(d), the minimum value of n for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension d? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multi-particle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral 4-, 3- and 2-particle bases in one, two and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identical g2(r) up to infinite r. Based on our analyses, we conjecture that nmin(d) = 4, 3, 2 for d = 1, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with n = 3, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radia

关键词： Eigenvalues and eigenfunctions

Wigner non-negative states that verify the Wigner entropy conjecture

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arXiv 2024年

作者： Qian, Qipeng Gagatsos, Christos N. Program in Applied Mathematics The University of Arizona TucsonAZ85721 United States Department of Electrical and Computer Engineering The University of Arizona TucsonAZ85721 United States Wyant College of Optical Sciences The University of Arizona TucsonAZ85721 United States

We present further progress, in the form of analytical results, on the Wigner entropy conjecture set forth in [Phys. Rev. A 104, 042211 (2021)] and [J. Phys. A: Math. Theor. 50 385301]. Said conjecture asserts that the differential entropy defined for non-negative, yet physical, Wigner functions is minimized by pure Gaussian states while the minimum entropy is equal to 1 + ln π. We prove this conjecture for the qubits formed by Fock states |0) and |1) that correspond to non-negative Wigner functions. In particular, we derive an explicit form of the Wigner entropy for those states lying on the boundary of the set of Wigner non-negative qubits. We then consider general mixed states and derive a sufficient condition for the conjecture’s validity. Lastly, we elaborate on the states which are in accordance with our condition. Copyright © 2024, The Authors. All rights reserved.

关键词： Entropy

Viscoelastic fluid flow in a slowly varying planar contraction: the role of finite extensibility on the pressure drop

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arXiv 2024年

作者： Mahapatra, Bimalendu Ruangkriengsin, Tachin Stone, Howard A. Boyko, Evgeniy Faculty of Mechanical Engineering Technion – Israel Institute of Technology Haifa3200003 Israel Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States

We analyze the steady viscoelastic fluid flow in slowly varying contracting channels of arbitrary shape and present a theory based on the lubrication approximation for calculating the flow rate–pressure drop relation at low and high Deborah (De) numbers. Unlike most prior theoretical studies leveraging the Oldroyd-B model, we describe the fluid viscoelasticity using a FENE-CR model and examine how the polymer chains’ finite extensibility impacts the pressure drop. We employ the low-Deborah-number lubrication analysis to provide analytical expressions for the pressure drop up to O(De4). We further consider the ultra-dilute limit and exploit a one-way coupling between the parabolic velocity and elastic stresses to calculate the pressure drop of the FENE-CR fluid for arbitrary values of the Deborah number. Such an approach allows us to elucidate elastic stress contributions governing the pressure drop variations and the effect of finite extensibility for all De. We validate our theoretical predictions with two-dimensional numerical simulations and find excellent agreement. We show that, at low Deborah numbers, the pressure drop of the FENE-CR fluid monotonically decreases with De, similar to the previous results for the Oldroyd-B and FENE-P fluids. However, at high Deborah numbers, in contrast to a linear decrease for the Oldroyd-B fluid, the pressure drop of the FENE-CR fluid exhibits a non-monotonic variation due to finite extensibility, first decreasing and then increasing with de. Nevertheless, even at sufficiently high Deborah numbers, the pressure drop of the FENE-CR fluid in the ultra-dilute and lubrication limits is lower than the corresponding Newtonian pressure drop. © 2024, CC BY.

关键词： Non Newtonian flow