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arXiv 2024年

作者： Sohn, Wuhyun Wang, Dong-Gang Fergusson, James R. Shellard, E.P.S. Korea Astronomy and Space Science Institute Daejeon34055 Korea Republic of Centre for Theoretical Cosmology Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom

In this paper, we present the first comprehensive CMB data analysis of cosmological collider physics. New heavy particles during inflation can leave imprints in the primordial correlators which are observable in today’s cosmological surveys. This remarkable detection channel provides an unsurpassed opportunity to probe new physics at extremely high energies. Here we initiate the search for these relic signals in the cosmic microwave background (CMB) data from the Planck legacy release. On the theory side, guided by recent progress from the cosmological bootstrap, we first propose a family of analytic bispectrum templates that incorporate the distinctive signatures of cosmological collider physics. Our consideration includes the oscillatory signals in the squeezed limit, the angular dependence from spinning fields, and several new shapes from nontrivial sound speed effects. On the observational side, we apply the recently developed pipeline, CMB Bispectrum Estimator (CMB-BEST), to efficiently analyze the three-point statistics and search directly for these new templates in the Planck 2018 temperature and polarization data. We report stringent CMB constraints on these new templates. Furthermore, we perform parameter scans to search for the best-fit values with maximum significance. For a benchmark example of collider templates, we find fNL = −91 ± 40 at the 68% confidence level. After accounting for the look-elsewhere effect, the biggest adjusted significance we get is 1.8σ. In general, we find no significant evidence of cosmological collider signals in the Planck data. However, our innovative analysis, together with the recent work [107] using the BOSS data, sets the stage for probing cosmological collider and demonstrates the potential for discovering new heavy particles during inflation in forthcoming cosmological surveys. © 2024, CC BY.

关键词： Cosmology

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POINTWISE ESTIMATES FOR THE FUNDAMENTAL SOLUTIONS OF HIGHER ORDER SCHRÖDINGER EQUATIONS IN ODD DIMENSIONS I: LOW DIMENSIONAL CASE

arXiv

引用

arXiv 2024年

作者： Cheng, Han Huang, Shanlin Huang, Tianxiao Zheng, Quan Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Sun Yat-sen University Guangdong Zhuhai519082 China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, for any odd n and any integer m ≥ 1 with n tu(x, t) = ((−∆)m + V(x))u(x, t), t ∈ , x ∈ n, where V is a real-valued potential with certain decay. Let Pac(H) denote the projection onto the absolutely continuous spectrum space of H = (−∆)m + V, and assume that H has no positive embedded eigenvalue. Our main result says that e−itHPac(H) has integral kernel K(t, x, y) satisfying (Equation presented), where the constants C, h > 0, and h can be specified by m, n and the zero energy resonances of H. A similar result for smoothing operators like (Equation presented) is also given. One of the main novelties lies in a new and unified approach to obtain the asymptotic expansions of perturbed resolvents under various types of zero energy resonances. © 2024, CC0.

关键词： Schrodinger equation

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Multilevel Monte Carlo for a class of Partially Observed Processes in Neuroscience

arXiv

引用

arXiv 2023年

作者： Maama, Mohamed Jasra, Ajay Kamatani, Kengo 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 School of Data Science The Chinese University of Hong Kong CN Shenzhen China Institute of Statistical Mathematics Tokyo190-0014 Japan

In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus upon the case of neuroscience. The data are assumed to be observed regularly in time and driven by the SDE model with unknown parameters. In practice the SDE may not have an analytically tractable solution and this leads naturally to a time-discretization. We adapt the multilevel Markov chain Monte Carlo method of [15], which works with a hierarchy of time discretizations and show empirically and theoretically that this is preferable to using one single time discretization. The improvement is in terms of the computational cost needed to obtain a pre-specified numerical error. Our approach is illustrated on models applied to examples of Bayesian inference problems using both simulated and real observed data from neuroscience. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

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The influence of magnetic particle incorporation on bisphenol A removal by β-cyclodextrin-derived sorbent

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Chemosphere 2023年第1期338卷 139538页

作者： Lukasik, Natalia Wikarska, Sandra Świątek, Hanna Lapiński, Marcin Klimczuk, Tomasz Hemine, Koleta Department of Chemistry and Technology of Functional Materials Faculty of Chemistry Gdańsk University of Technology 11/12 Narutowicza Street Gdańsk80-233 Poland Division of Strongly Correlated Electronic Systems Institute of Nanotechnology and Materials Science Faculty of Applied Physics and Mathematics Gdańsk University of Technology 11/12 Narutowicza Street Gdańsk80-233 Poland Division of Nanomaterials Physics Institute of Nanotechnology and Materials Science Faculty of Applied Physics and Mathematics Gdańsk University of Technology 11/12 Narutowicza Street Gdańsk80-233 Poland

A novel, biomass-derived hybrid sorbent Ban-CD-EPI-Fe was successfully synthesized in a coprecipitation method, in which β-cyclodextrin copolymerized with banana peel extract and epichlorohydrin was grafted onto an iron oxide surface. The composition, presence of functional groups, morphology, thermal stability, and magnetic properties of the obtained material were characterized by Powder X-Ray Diffraction (XRD), X-Ray Photoelectron Spectroscopy (XPS), Fourier Transform Infrared Spectroscopy (FTIR), Scanning Electron Microscopy and Energy Dispersive X-Ray Spectroscopy (SEM-EDS), Thermogravimetric Analysis (TGA), and Physical Properties Measurement System (PPMS). The material bearing around 28% of β-cyclodextrin units has mesoporous structure with plate-like morphology and active surface area determined by BET and Langmuir models equal to 38.35 and 53.59 m2 g−1, respectively. The sorption studies aimed to remove an endocrine disruptor – bisphenol A (BPA), from water. The results showed that the time evolution could be fitted with pseudo-second kinetic order with a rate constant k equal to 0.05 g mg−1 min−1. According to the Langmuir isotherm, a monolayer is created during BPA sorption, and the maximum sorption capacity was estimated as 93.5 mg g−1. After BPA sorption, the hybrid material could be easily separated by an external magnet and regenerated under mild conditions keeping its recyclability in at least eight cycles. © 2023 Elsevier Ltd

关键词： Cyclodextrins

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Completely entangled subspaces of entanglement depth k

arXiv

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arXiv 2023年

作者： Demianowicz, Maciej Vogtt, Kajetan Augusiak, Remigiusz Institute of Physics and Applied Computer Science Faculty of Applied Physics and Mathematics Gdańsk University of Technology Narutowicza 11/12 Gdańsk80-233 Poland Center for Theoretical Physics Polish Academy of Sciences Aleja Lotników 32/46 Warsaw02-668 Poland Faculty of Physics University of Warsaw Pasteura 5 Warsaw02-093 Poland

We introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth k (k-CESs). These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least k. We present an efficient construction of k-CESs of any achievable dimensionality in any multipartite scenario. Further, we discuss the relation between these subspaces and unextendible product bases (UPBs). In particular, we establish that there is a non-trivial bound on the cardinality of a UPB whose orthocomplement is a k-CES. Further, we discuss the existence of such UPBs for qubit systems. © 2023, CC BY.

关键词： Quantum entanglement

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Towards a Laser-Induced Microbubble during Lithotripsy Process in Soft Tissue

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Bulletin of the Russian Academy of sciences: physics 2022年第1期86卷 S1-S7页

作者： Abu-Bakr, A.F. Abu-Nab, A.K. Theoretical and Mathematical Physics Department Institute of Natural Sciences and Mathematics Ural Federal University Ekaterinburg620083 Russia Department of Mathematics and Computer Science Faculty of Science Menoufia University Shebin El-Koom32511 Egypt Phystech School of Applied Mathematics and Informatics Moscow Institute of Physics and Technology Dolgoprudny141700 Russia

Abstract: The present paper proposes the theoretical study and mathematical approach of laser induced cavitation microbubble during lithotripsy process in soft tissue. The mathematical model is constructed via the potential function and Lagrangian equation of radial and translational dynamics of microbubble. The given model of laser-induced cavitation microbubble (as like Rayleigh–Plesset equation) is analytically solved and investigated via Plesset–Zwick method to investigate the behaviour of laser-induced cavitation microbubble and energy produced by laser-induced cavitation microbubble during lithotripsy in soft tissue. From our results, we get the energy produced by laser-induced cavitation bubble increases with increasing of the time and decreasing of the parameter Kexp which is calculated experimentally. The present mathematical approach and its analytical results are satisfied by comparing with the published experimentally results. © 2022, Allerton Press, Inc.

关键词： Tissue

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Multi-Scale Electromagnetic Simulation Through Parallel Adaptive Mesh Refinement FDTD Method with Symmetric Positive Semi-Definite Subgridding Scheme

Multi-Scale Electromagnetic Simulation Through Parallel Adap...

引用

International applied Computational Electromagnetics Society Symposium (ACES)

作者： Hanyu Li Haijing Zhou Xianfeng Bao Xiaojie Chen School of Physical Science and Technology Southwest Jiaotong University Chengdu China Institute of Applied Physics and Computational Mathematics Beijing China Software Center for High Performance Numerical Simulation CAEP Beijing China

FDTD method is a common approach for electromagnetic propagation, scattering and coupling simulation. Conventional FDTD with universal mesh requires numerous computations to represent solve problems with multi-scale structures. In this paper, adaptive mesh refinement (AMR) strategy is performed to reduce the calculations along with symmetric positive semi-definite subgridding scheme to guarantee stability. Numerical example of a missile seeker coupling simulation shows that the computation time decrease down to 2% while preserving excellent precision.

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WHEN GNNS MEET SYMMETRY IN ILPS: AN ORBIT-BASED FEATURE AUGMENTATION APPROACH

arXiv

引用

arXiv 2025年

作者： Chen, Qian Li, Lei Li, Qian Wu, Jianghua Wang, Akang Sun, Ruoyu Luo, Xiaodong Chang, Tsung-Hui Shi, Qingjiang School of Science and Engineering The Chinese University of Hong Kong Shenzhen China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data China School of Data Science The Chinese University of Hong Kong Shenzhen China School of Artificial Intelligence The Chinese University of Hong Kong Shenzhen China School of Software Engineering Tongji University Shanghai China

A common characteristic in integer linear programs (ILPs) is symmetry, allowing variables to be permuted without altering the underlying problem structure. Recently, GNNs have emerged as a promising approach for solving ILPs. However, a significant challenge arises when applying GNNs to ILPs with symmetry: classic GNN architectures struggle to differentiate between symmetric variables, which limits their predictive accuracy. In this work, we investigate the properties of permutation equivariance and invariance in GNNs, particularly in relation to the inherent symmetry of ILP formulations. We reveal that the interaction between these two factors contributes to the difficulty of distinguishing between symmetric variables. To address this challenge, we explore the potential of feature augmentation and propose several guiding principles for constructing augmented features. Building on these principles, we develop an orbit-based augmentation scheme that first groups symmetric variables and then samples augmented features for each group from a discrete uniform distribution. Empirical results demonstrate that our proposed approach significantly enhances both training efficiency and predictive performance. Copyright © 2025, The Authors. All rights reserved.

关键词： Integer linear programming

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Dynamics of a PDE Model with Size-Structure: Characterizing the Growth and Flocculation Effects of Unicellular Algae

SSRN

引用

SSRN 2022年

作者： Ni, Dongdong Ma, Wanbiao Banerjee, Malay Department of Applied Mathematics School of Mathematics and Physics University of Science and Technology Beijing Beijing100083 China Department of Mathematics and Statistics Indian Institute of Technology Kanpur Kanpur208016 India

The commercial production of algae is of great practical significance to the reduction of environmental pollution, the development of bioenergy and nutritional food. Heterotrophic culture is one of the most important methods in commercial production of algae, and flocculation is usually used to collect algae cells in the reactor. The size of algae cells has a direct impact on the nutrient absorption and the flocculation effect of algae cells. In this paper, a size-structured PDE model considering the size of algae cells is established, which depicts the evolutionary relationship of the growth of algae cells, the nutrient absorption and flocculation effect. In the construction of the model, it is assumed that the number of newborn algae cells is determined by nutrition and the weighted total number of algal cells. The numerical observation shows that the model has complex dynamics, such as the appearances of the backward bifurcation of equilibrium states and bistability. The main theoretical results are as follows: (1) The well-posedness of the solution is obtained by using the fixed point theorem. (2) Under the condition of threshold quantity R0> 1, the existence of the coexistence equilibrium state of algae is analyzed. Then, by using the theory of contraction semigroups, the sufficient condition for the local stability of the coexistence equilibrium state of algae is obtained. (3) Sufficient condition for the global stability of the algae-free equilibrium state is given. © 2022, The Authors. All rights reserved.

关键词： Algae

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Discrete unified gas kinetic scheme for the solution of electron Boltzmann transport equation with Callaway approximation

arXiv

引用

arXiv 2023年

作者： Lian, Meng Zhang, Chuang Guo, Zhaoli Lü, Jing-Tao School of Physics Institute for Quantum Science and Engineering Wuhan National High Magnetic Field Center Huazhong University of Science and Technology Wuhan430074 China Department of Physics Hangzhou Dianzi University Hangzhou310018 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China

Electrons are the carriers of heat and electricity in materials, and exhibit abundant transport phenomena such as ballistic, diffusive, and hydrodynamic behaviors in systems with different sizes. The electron Boltzmann transport equation (eBTE) is a reliable model for describing electron transport, but it is a challenging problem to efficiently obtain the numerical solutions of eBTE within one unified scheme involving ballistic, hydrodynamics and/or diffusive regimes. In this work, a discrete unified gas kinetic scheme (DUGKS) in finite-volume framework is developed based on the eBTE with the Callaway relaxation model for electron transport. By reconstructing the distribution function at the cell interface, the processes of electron drift and scattering are coupled together within a single time step. Numerical tests demonstrate that the DUGKS can be adaptively applied to multiscale electron transport, across different regimes. Copyright © 2023, The Authors. All rights reserved.

关键词： Distribution functions

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