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Cosserat elasticity as the weak-field limit of Einstein–Cartan relativity

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arXiv 2024年

作者： Maitra, Matthew Tromp, Jeroen Institut für Geophysik ETH Zürich Sonneggstrasse 5 Zürich8092 Switzerland Department of Geosciences and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

The weak-field limit of Einstein–Cartan (EC) relativity is studied. The equations of EC theory are rewritten such that they formally resemble those of Einstein General Relativity (EGR);this allows ideas from post-Newtonian theory to be imported without essential change. The equations of motion are then written both at first post-Newtonian (1PN) order and at 1.5PN order. EC theory’s 1PN equations of motion are found to be those of a micropolar/Cosserat elastic medium, along with a decoupled evolution equation for non-classical, spin-related fields. It seems that a necessary condition for these results to hold is that one chooses the non-classical fields to scale with the speed of light in a certain empirically reasonable way. Finally, the 1.5PN equations give greater insight into the coupling between energy-momentum and spin within slowly moving, weakly gravitating matter. Specifically, the weakly relativistic modifications to Cosserat theory involve a gravitational torque and an augmentation of the gravitational force due to a ‘dynamic mass moment density’ with an accompanying ‘dynamic mass moment density flux’, and new forms of linear momentum density captured by a ‘dynamic mass density flux’ and a ‘dynamic momentum density’. Copyright © 2024, The Authors. All rights reserved.

关键词： Equations of motion

Comparison between a priori and a posteriori slope limiters for high-order finite volume schemes

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arXiv 2024年

作者： Palafoutas, Jonathan Velasco Romero, David A. Teyssier, Romain Program in Applied & Computational Mathematics Princeton University Washington Road PrincetonNJ08544 United States Department of Astrophysical Sciences Princeton University 171 Broadmead Street PrincetonNJ08540 United States

High-order finite volume and finite element methods offer impressive accuracy and cost efficiency when solving hyperbolic conservation laws with smooth solutions. However, if the solution contains discontinuities, these high-order methods can introduce unphysical oscillations and severe overshoots/undershoots. Slope limiters are an effective remedy, combating these oscillations by preserving monotonicity. Some limiters can even maintain a strict maximum principle in the numerical solution. They can be classified into one of two categories: a priori and a posteriori limiters. The former revises the high-order solution based only on data at the current time tn, while the latter involves computing a candidate solution at tn+1 and iteratively recomputing it until some conditions are satisfied. These two limiting paradigms are available for both finite volume and finite element methods. In this work, we develop a methodology to compare a priori and a posteriori limiters for finite volume solvers at arbitrarily high order. We select the maximum principle preserving scheme presented in [1, 2] as our a priori limited scheme. For a posteriori limiting, we adopt the methodology presented in [3] and search for so-called troubled cells in the candidate solution. We revise them with a robust MUSCL fallback scheme. The linear advection equation is solved in both one and two dimensions and we compare variations of these limited schemes based on their ability to maintain a maximum principle, solution quality over long time integration and computational cost. This analysis reveals a fundamental tradeoff between these three aspects. The high-order a posteriori limited solutions boast great quality at long time-scales, taking full advantage of the sharp gradients of the high-order finite volume method. However, they introduce consistent maximum principle violations. On the other hand, the high-order a priori limited solutions can preserve a strict maximum principle. Interestingly, thi

关键词： Polynomials

Parameter Estimation for Partially Observed McKean-Vlasov Diffusions

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arXiv 2024年

作者： Jasra, Ajay Maama, Mohamed Tempone, Raul School of Data Science The Chinese University of Hong Kong CN Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Chair of Mathematics for Uncertainty Quantification RWTH Aachen University Aachen52062 Germany

In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the framework of [5] we develop a new randomized multilevel Monte Carlo method for estimating the parameters, based upon Markovian stochastic approximation methodology. New Markov chain Monte Carlo algorithms for the POMV model are introduced facilitating the application of [5]. We prove, under assumptions, that the expectation of our estimator is biased, but with expected small and controllable bias. Our approach is implemented on several examples. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Langevin Equations in the Small-Mass Limit: Higher-Order Approximations

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Annales Henri Poincare 2020年第6期21卷 1765-1811页

作者： Birrell, Jeremiah Wehr, Jan Department of Mathematics and Statistics University of Massachusetts Amherst Amherst 01003 MA United States Department of Mathematics and Program in Applied Mathematics University of Arizona Tucson 8572 AZ United States

We study the small-mass (overdamped) limit of Langevin equations for a particle in a potential and/or magnetic field with matrix-valued and state-dependent drift and diffusion. We utilize a bootstrapping argument to derive a hierarchy of approximate equations for the position degrees of freedom that are able to achieve accuracy of order m^ℓ ^/ ² over compact time intervals for any ℓ∈ Z⁺. This generalizes prior derivations of the homogenized equation for the position degrees of freedom in the m→ 0 limit, which result in order m^{1 / 2} approximations. Our results cover bounded forces, for which we prove convergence in L^p norms and unbounded forces, in which case we prove convergence in probability. © 2020, Springer Nature Switzerland AG.

关键词： 60H10 82C31

Efficient Power Transfer via Induced Virtual Critical Coupling in an Overcoupled Silicon Nitride Microresonator

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Efficient Power Transfer via Induced Virtual Critical Coupli...

2023 Conference on Lasers and Electro-Optics, CLEO 2023

作者： Hinney, Jakob Kim, Seunghwi Flatt, Graydon J.K. Datta, Ipshita Alii, Andrea Lipson, Michal Department of Electrical Engineering Columbia University New YorkNY10027 United States Photonics Advanced Science Research Catm City University of New Yor New YorkNY10031 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Physics Program Graduate Center City University of New York New YorkNY10016 United States

We induce virtual critical coupling in an overcoupled photonic microresonator using complex-frequency pulses. We observe efficient cavity storage as an incident pulse of time constant 138 ps suppresses the resonant tr... 详细信息

ISBN: (纸本)9781957171258

关键词： Microresonators

Interval graphs for Genome-Fragment combinations

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Interval graphs for Genome-Fragment combinations

2023 International Conference on Mathematical and Statistical Physics, Computational Science, Education and Communication, ICMSCE 2023

作者： Kao, Shin-Shin Wu, Tzong-Yuan Department of Applied Mathematics Program of International Master of Business Administration Chung Yuan Christian University No. 200 Jong-Bei Road Chung-Li District Tao-Yuan320314 Taiwan Department of Bioscience Technology Chung Yuan Christian University No. 200 Jong-Bei Road Chung-Li District Tao-Yuan320314 Taiwan

ISBN: (纸本)9781510671768

The main purpose of this research work is to apply the theory of "interval graphs" to a specific viral genome, reconstruct the sequence from the unknown-ordered fragments for possible combinations for further studies. We use the restriction digestion method to cut the chromosome into many segments with several restriction enzymes. These cut segments can be separated by agarose gel electrophoresis according to their molecular size and are not in order of the original sequence. Besides, the segments cut out by each enzyme are different, so there will be intersections (sub-segments). The method of interval graph, suggested by14, attempts to use the information at the intersection to reorganize the original sequence. We selected our own patented insect viral gene sequence and conducted research on the above-mentioned interval graph method. More specifically, the isolated recombinant baculovirus, tentatively named ABM, and the widely-used prototype of baculovirus species, which is Autographa californica multiple nucleopolyhedrovirus (AcMNPV), were used as the model system. Although the length of the insect viral genome sequence we used is relatively short as compared with the genome of organisms, this study failed to achieve the purpose of sorting by the method of interval graph. The two main reasons can be summarized as follows: First, the enzyme experiment detected multiple short segments that did not intersect with other segments, and the interval graph method could not determine their positions in the original sequence. Secondly, any "graph" is made up of vertices and edges. Representing gene sequences with interval graphs means translating segments and intersecting segments with vertices and edges. Even if the improved method was adopted, the number of vertices and edges that can be loaded by the existing hardware makes this research unable to complete all the steps of the basic interval graph construction. This paper illustrates the experimental methods, mathematic

关键词： Enzymes

Spatial Bayesian Neural Networks

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arXiv 2023年

作者： Zammit-Mangion, Andrew Kaminski, Michael D. Tran, Ba-Hien Filippone, Maurizio Cressie, Noel School of Mathematics and Applied Statistics University of Wollongong Australia Paris Research Centre Huawei Technologies France Statistics Program King Abdullah University of Science and Technology Saudi Arabia

Statistical models for spatial processes play a central role in analyses of spatial data. Yet, it is the simple, interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest. Here, we propose a new, flexible class of spatial-process models, which we refer to as spatial Bayesian neural networks (SBNNs). An SBNN leverages the representational capacity of a Bayesian neural network;it is tailored to a spatial setting by incorporating a spatial "embedding layer" into the network and, possibly, spatially-varying network parameters. An SBNN is calibrated by matching its finite-dimensional distribution at locations on a fine gridding of space to that of a target process of interest. That process could be easy to simulate from or we may have many realisations from it. We propose several variants of SBNNs, most of which are able to match the finite-dimensional distribution of the target process at the selected grid better than conventional BNNs of similar complexity. We also show that an SBNN can be used to represent a variety of spatial processes often used in practice, such as Gaussian processes, lognormal processes, and max-stable processes. We briefly discuss the tools that could be used to make inference with SBNNs, and we conclude with a discussion of their advantages and limitations. Copyright © 2023, The Authors. All rights reserved.

关键词： Bayesian networks

Lung Cancer Diagnosis Based on Object Detection Technology 14th

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Lung Cancer Diagnosis Based on Object Detection Technology

14th International Conference on Frontier Computing, FC 2024

作者： Xu, Jia-Lang Wang, Pei-Yun Huang, Tzu-Hsuan Hsu, Ying-Lin Huang, Kuo-Yang Chen, Mu-Yen Artificial Intelligence Development Center Changhua Christian Hospital Changhua Taiwan Doctoral Program in Data Science and Industrial Analytics National Chung Hsing University Taichung Taiwan Department of Applied Mathematics and Institute of Statistics National Chung Hsing University Taichung Taiwan Division of Chest Medicine Department of Internal Medicine Changhua Christian Hospital Changhua Taiwan Department of Engineering Science National Cheng Kung University Tainan Taiwan

ISBN: (纸本)9789819623945

With the rise of artificial intelligence, many people nowadays use artificial intelligence to help solve some problems in life, and the medical field is also with the rise of artificial intelligence, many people are slowly applying artificial intelligence to medical images to assist in decision-making, this study proposes a Yolov8 algorithm for object tracking of CT images of lung cancer, which can quickly tell the doctor where the cancer is and what the type of cancer is. The results of this study show that the Box_Loss, Cls_Loss, and Dfl_loss of the Yolov8 algorithm in detecting the location of lung cancer are 1.3689, 0.4552, and 1.5569 in the validation data, respectively, and thus this study suggests that this method can help physicians know the location of the tumor and what kind of tumor it belongs to. Therefore, this study suggests that this method can help physicians know the location of the tumor and the type of tumor. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Lung cancer

Embedded (4,5) pairs of explicit 7-stage Runge-Kutta methods with FSAL property

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arXiv 2021年

作者： Stepanov, Misha Department of Mathematics and Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

The general case of embedded (4,5) pairs of explicit 7-stage Runge-Kutta methods with FSAL property (a7 j = bj, 1 ≤ j ≤ 7, c7 = 1) is considered. Besides exceptional cases, the pairs form five 4-dimensional families. The pairs within two (already known) families satisfy the simplifying assumption ∑jaijcj = c2i/2, i ≥ *** Codes 65L05, 65L06 Copyright © 2021, The Authors. All rights reserved.

关键词： Runge Kutta methods