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Mass spectrum of spin-one hadrons in dense two-color QCD: Novel predictions by extended linear sigma model

Physical Review D 2024年第7期109卷 074031-074031页

作者： Daiki Suenaga Kotaro Murakami Etsuko Itou Kei Iida Few-body Systems in Physics Laboratory RIKEN Nishina Center Wako 351-0198 Japan Research Center for Nuclear Physics Osaka University Ibaraki 567-0048 Japan Department of Physics Tokyo Institute of Technology 2-12-1 Ookayama Megro Tokyo 152-8551 Japan Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) RIKEN Wako 351-0198 Japan Yukawa Institute for Theoretical Physics Kyoto University Kyoto 606-8502 Japan Department of Mathematics and Physics Kochi University 2-5-1 Akebono-cho Kochi 780-8520 Japan

We construct an extended version of the linear sigma model in such a way as to describe spin-1 hadrons as well as spin-0 hadrons in two-color QCD (QC2D) by respecting the Pauli-Gürsey SU(4) symmetry. Within a mean-field approximation, we therefrom examine a mass spectrum of the spin-1 hadrons at finite quark chemical potential (μq) and zero temperature. Not only mean fields of scalar mesons and scalar-diquark baryons but also of vector mesons and vector-diquark baryons are incorporated. As a result, we find that, unless all of those four types of mean fields are taken into account, neither lattice result for the critical μq that corresponds to the onset of baryon superfluidity nor for μq dependence of the pion mass can be reproduced. We also find that a slight suppression of the ρ meson mass in the superfluid phase, which was suggested by the lattice simulation, is reproduced by subtle mixing effects between spin-0 and spin-1 hadrons. Moreover, we demonstrate the emergence of an axial-vector condensed phase and possibly of a vector condensed phase by identifying the values of μq at which the corresponding hadron masses vanish. The possible presence of isotriplet 1− diquarks that may be denoted by a tensor-type quark bilinear field is also discussed.

关键词： Lattice QCD Nuclear matter in neutron stars Sigma models Hadrons Superfluids Chiral symmetry

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Marginally-Stable Thermal Equilibria of Rayleigh-Bénard Convection

arXiv

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arXiv 2021年

作者： O’Connor, Liam Lecoanet, Daniel Anders, Evan H. Department of Engineering Sciences and Applied Mathematics Northwestern University EvanstonIL60208 United States Center for Interdisciplinary Exploration and Research in Astrophysics Northwestern University EvanstonIL60201 United States

Natural convection exhibits turbulent flows which are difficult or impossible to resolve in direct numerical simulations. In this work, we investigate a quasilinear form of the Rayleigh-Bénard problem which describes the bulk one-dimensional properties of convection without resolving the turbulent dynamics. We represent perturbations away from the mean using a sum of marginally-stable eigenmodes. By constraining the perturbation amplitudes, the marginal stability criterion allows us to evolve the background temperature profile under the influence of multiple eigenmodes representing flows at different length scales. We find the quasilinear system evolves to an equilibrium state where advective and diffusive fluxes sum to a constant. These marginally-stable thermal equilibria (MSTE) are exact solutions of the quasilinear equations. The mean MSTE temperature profiles have thinner boundary layers and larger Nusselt numbers than thermally-equilibrated 2D and 3D simulations of the full nonlinear equations. MSTE solutions exhibit a classic boundary-layer scaling of the Nusselt number Nu with the Rayleigh number Ra of Nu ∼ Ra1/3. When an MSTE is used as initial conditions for a 2D simulation, we find that Nu quickly equilibrates without the burst of turbulence often induced by purely conductive initial conditions, but we also find that the kinetic energy is too large and viscously attenuates on a long viscous time scale. © 2021, CC0.

关键词： Nonlinear equations

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On the existence of the maximum likelihood estimate and convergence rate under gradient descent for multi-class logistic regression

arXiv

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arXiv 2020年

作者： Nwaigwe, Dwight Rychlik, Marek Program in Applied Mathematics The University of Arizona Tucson United States Department of Mathematics The University of Arizona Tucson United States

We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The notion of data separability is not needed, which is in contrast to the classical set up of multi-class logistic regression in which each data sample belongs to one class. We also provide a general and constructive estimate of the convergence rate to the maximum likelihood estimate when gradient descent is used as the optimizer. Our estimate involves bounding the condition number of the Hessian of the maximum likelihood function. The approaches used in this article rely on a simple operator-theoretic *** Codes 62J12, 65K10, 47N10 Copyright © 2020, The Authors. All rights reserved.

关键词： Gradient methods

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Optimization production and characterization of fish protein hydrolysate (FPH) from Sardinella Lemuru head with papain protease

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AIP Conference Proceedings 2025年第1期3186卷

作者： Jannatul Firdaus Evi Susanti Suharti Suharti Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Negeri Malang Jl. Semarang 5 Malang 65145 Indonesia Biotechnology Program Department of Applied Science Faculty of Mathematics and Natural Sciences Universitas Negeri Malang Jl. Semarang 5 Malang 65145 Indonesia

Sardinella lemuru head has potential as Fish Protein Hydrolysate (FPH). This study aims to determine the optimum conditions and characterization of FPH from lemuru fish heads produced enzymatically with papain. This study was conducted through the following stages with (1) isolation of crude extract of papain, (2) optimization of papain enzymatic FPH production methods, (3) characterization of FPH including determined of proximate value, FTIR analysis, molecular weight, the antibacterial and antioxidant activity FPH produced from lemuru fish head powder was a short peptide measuring about 25 kDa and less. FPH has water, protein, and fat value of 24.54; 28.76; and 0.224 % (w/w). The resulting yield was at an optimum condition of 18.87% under the following conditions: 1 g of fish head powder was hydrolyzed with 0.705 U papain in 8 mL of phosphate buffer pH 7 0.1 M, incubated for 3 hours at room temperature, continued for 90 minutes at 75°C and at 90°C for 5 minutes. At a concentration of 10,000 ppm, the FPH can inhibit the growth of Escherichia coli bacteria by producing an inhibition zone diameter of 4.537±0.265 and Staphylococcus aureus bacteria by 5.5±0.212 and has an IC50 value to inhibit DPPH free radical oxidation of 70.175 ppm.

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Frequency Response of the Diffuse-Charge Dynamics in Electrochemical Systems with a Graphene Electrode

SSRN

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SSRN 2024年

作者： Yavarian, Mahdi Melnik, Roderick Mišković, Zoran L. Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada MS2Discovery Interdisciplinary Research Institute M2Net Lab Wilfrid Laurier University 75 University Avenue WaterlooONN3L 3V6 Canada Waterloo Institute for Nanotechnology University of Waterloo WaterlooONN2L 3G1 Canada

We investigate the frequency response of diffuse-charge dynamics related to a 1:1 symmetric electrolyte containing a graphene electrode by solving the governing Poisson-Nernst-Planck equations subjected to appropriate boundary conditions in the asymptotic limit Ε = λD∕H → 0, where λD is the Debye screening length and H is the half-thickness of the electrolyte. Using the method of matched asymptotic expansion, we first solve the leading order non-linear problem for equilibrium state at a nonzero applied DC voltage in the presence of Stern layer(s). Then, we extend the leading order asymptotic analysis to derive an analytic expression for the impedance of the graphene-based electrochemical cell when a small AC voltage perturbation is added to the applied DC voltage. Finally, we use a suitable scaling of the impedance parameters to expose the impacts of the ion concentration and the DC bias voltage on the frequency response for possible applications involving the graphene-electrolyte interface. © 2024, The Authors. All rights reserved.

关键词： Graphene

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Liquid-Liquid Transition in Water from First Principles

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Physical Review Letters 2022年第25期129卷 255702-255702页

作者： Thomas E. Gartner, III Pablo M. Piaggi Roberto Car Athanassios Z. Panagiotopoulos Pablo G. Debenedetti Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

关键词： Classical statistical mechanics First order phase transitions First-principles calculations Liquid-liquid phase transition Phase transitions Thermodynamics Deep learning Density functional theory Molecular dynamics

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Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order-disorder transitions in LixCoO2

arXiv

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arXiv 2023年

作者： Teichert, G.H. Das, S. Shojaei, M. Faghih Holber, J. Mueller, T. Hung, L. Gavini, V. Garikipati, K. Department of Mechanical Engineering University of Michigan United States Toyota Research Institute Los AltosCA United States Department of Materials Science & Engineering University of Michigan United States Department of Mathematics University of Michigan United States Michigan Institute for Computational Discovery & Engineering University of Michigan United States Applied Physics Program University of Michigan United States Materials Science & Engineering Johns Hopkins University United States

LixTMO2 (TM=Ni, Co, Mn) forms an important family of cathode materials for Li-ion batteries, whose performance is strongly governed by Li composition-dependent crystal structure and phase stability. Here, we use LixCoO2 (LCO) as a model system to benchmark a machine learning-enabled framework for bridging scales in materials physics. We focus on two scales: (a) assemblies of thousands of atoms described by density functional theory-informed statistical mechanics, and (b) continuum phase field models to study the dynamics of order-disorder transitions in LCO. Central to the scale bridging is the rigorous, quantitatively accurate, representation of the free energy density and chemical potentials of this material system by coarsegraining formation energies for specific atomic configurations. We develop active learning workflows to train recently developed integrable deep neural networks for such high-dimensional free energy density and chemical potential functions. The resulting, first principles-informed, machine learning-enabled, phase-field computations allow us to study LCO cathodes’ phase evolution in terms of temperature, morphology, charge cycling and particle size. © 2023, CC BY-NC-SA.

关键词： Cathodes

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Upscaling the Navier-Stokes-Cahn-Hilliard model for incompressible multiphase flow in inhomogeneous porous media

arXiv

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arXiv 2025年

作者： Zhang, Chunhua Liu, Peiyao Peng, Cheng Wang, Lian-Ping Guo, Zhaoli School of Energy and Power Engineering North University of China Shanxi Taiyuan030051 China State Key Laboratory of Coal and CBM Co-Mining North University of China Shanxi Taiyuan030051 China College of Mathematics Taiyuan University of Technology Shanxi Taiyuan030024 China Key Laboratory of High Efficiency and Clean Mechanical Manufacture Ministry of Education School of Mechanical Engineering Shandong University Shandong Jinan250061 China Guangdong Provincial Key Laboratory of Turbulence Research and Applications Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Guangdong Shenzhen518055 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China

In this work, we present a macroscopic model for the flow of two immiscible and incompressible fluids in inhomogeneous porous medium. At the pore scale, the flow is governed by the fully Navier-Stokes equations while the evolution of the phase interface is captured by the Cahn-Hilliard equation. Using the volume averaging method, the upscaled equations describing the averaged behavior of two fluids at the Darcy scale are obtained, with unclosed terms related to spatial deviations. Then, spatial derivations are carefully modeled up to some undetermined coefficients, which could be evaluated by solving simplified closure problems in each representative volume element. In particular, the wetting behavior is incorporated into the averaged chemical potential. The differences between the proposed equations and the empirical two-phase Darcy-type models are discussed. Finally, a phase-field-based lattice Boltzmann model for the averaged equations is presented, and numerical results demonstrate the abilities of the proposed model. Copyright © 2025, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Convergence of Mass Transfer Particle Tracking Schemes for the Simulation of Advection-Diffusion-Reaction Equations

SSRN

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SSRN 2024年

作者： Pankavich, Stephen D. Schauer, Lucas Schmidt, Michael J. Engdahl, Nicholas B. Bolster, Diogo Benson, David A. Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM87185 United States Department of Civil and Environmental Engineering Washington State University PullmanWA99164 United States Department of Civil and Environmental Engineering and Earth Sciences University of Notre Dame Notre DameIN46556 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States

Since their introduction, multi-species mass-transfer particle tracking (or MTPT) algorithms have been used to accurately simulate advective and dispersive transport of solutes, even within systems that feature nonlinear chemical reactions. The MTPT methods were originally derived from a probabilistic or first-principles perspective and have previously lacked a more rigorous derivation arising directly from the underlying advection-diffusion-reaction equation (ADRE). Herein, we provide a fully rigorous derivation of the MTPT method as a Lagrangian approximation of solutions to the ADRE, complete with a description of the error and order of accuracy generated by this approximation. Numerical simulations further detail the fidelity of MTPT methods and display parameter regimes wherein the numerical error is independent of the chosen time step, and thereby dependent only upon the numerical discretization of the spatial domain via the number of particles within a simulation. Finally, different normalizations of the local Green's function are shown to generate similar approximations of the underlying solution for stationary particles. © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

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Grapenet_Lv1 for the Prediction of Optimum Hand-Picking Time of Nagano Purple Grapes

SSRN

引用

SSRN 2025年

作者： Islam, Md. Parvez Shinagawa, K. Hatou, K. Abdurrakhman, Arief Dian, K. Department of Biomechanical Systems Faculty of Agriculture Ehime University 3-5-7 Tarumi Matsuyama790-8566 Japan United Graduate School of Agriculture Ehime University 3-5-7 Tarumi Matsuyama790-8566 Japan Department of Instrumentation Engineering Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Business Mathematics Program Study School of Applied STEM Universitas Prasetiya Mulya BSD Campus BSD City Kav. Edutown I.1 Tangerang15339 Indonesia Indonesia

We investigated the optimum hand-picking time of Nagano Purple, a rare Japanese table grape variety. The color sensitivity between pure red–purple–black and pure purple–black makes it difficult for farmers to harvest these fruits at the right time while maintaining high sweetness level. We manually extracted 13 color parameters, namely, X, Y, Z, x, y, L*, a*, b*, L, a, b, C*, and h, from 355 grape skin samples using a colorimeter, which is a time-consuming and expensive process. In addition, we developed a 15-layer shallow long short-term memory (LSTM) and bidirectional long short-term memory (BLSTM) neural network, namely, GrapeNet_Lv1, with a learnable parameter of 1.39E+06. This network is compact and requires low computational cost for training. Furthermore, it has the ability to prevent the problems of vanishing gradient and overfitting. The combination of all the 13 aforementioned parameters yielded promising results in predicting color and sweetness levels, with test accuracies of 0.83 and 0.76, respectively. In the prediction of color level, our proposed network GrapeNet_Lv1 achieves a high validation accuracy of 0.92, F1 score of 0.88, recall of 0.87, low validation loss of 0.39, and RMSE of 0.31. However, in the prediction of sweetness level, GrapeNet_Lv1 achieves a relatively low validation accuracy of 0.79, F1 score of 0.70, recall of 0.69, high validation loss of 0.72, and RMSE of 0.33. Further research can help improve the accuracy. GrapeNet_Lv1 can be applied to other crops, where, predicting the whose optimal hand-picking time is difficult to predict based on color recognition. Keywords: Neural network;LSTM-BLSTM;Nagano Purple, color, sweetness © 2025, The Authors. All rights reserved.

关键词： Long short-term memory

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