Article
Mathematics, Applied
Michele Dolce, Theodore D. Drivas
Summary: The transport of vorticity in two-dimensional ideal fluids is crucial for predicting their long-term behavior, and the mixing of vorticity and conservation of kinetic energy alone cannot rule out the possibility of weak convergence to equilibrium.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2022)
Article
Mathematics, Applied
Bjoern Gebhard, Jozsef J. Kolumban
Summary: We study the two-dimensional Euler equations with local energy balance and show that the corresponding relaxation process can be simplified compared to the relaxation process without local energy balance. For bounded solutions, we provide a criterion that allows a globally dissipative subsolution to induce infinitely many globally dissipative solutions with the same initial data, pressure, and dissipation measure. This criterion can be easily verified in the case of a flat vortex sheet causing the Kelvin-Helmholtz instability. Additionally, we show the existence of initial data such that the associated globally dissipative solutions can achieve any dissipation measure from an open set in C-0(T-2 x [0, T]). In fact, the set of such initial data is dense in the space of solenoidal L-2(T-2; R-2) vector fields.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2022)
Article
Physics, Multidisciplinary
Matthew T. Reeves, Kwan Goddard-Lee, Guillaume Gauthier, Oliver R. Stockdale, Hayder Salman, Timothy Edmonds, Xiaoquan Yu, Ashton S. Bradley, Mark Baker, Halina Rubinsztein-Dunlop, Matthew J. Davis, Tyler W. Neely
Summary: We experimentally study the emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. The resulting long-time vortex distributions are in excellent agreement with the mean-field Poisson Boltzmann equation for the system, and a point-vortex model with phenomenological damping and noise can quantitatively reproduce the equilibration dynamics.
Article
Physics, Fluids & Plasmas
M. Onorato, G. Dematteis, D. Proment, A. Pezzi, M. Ballarin, L. Rondoni
Summary: In this study, we predict the presence of negative temperature states in the discrete nonlinear Schodinger (DNLS) equation and provide exact solutions using the associated wave kinetic equation. We define an entropy within the wave kinetic approach that monotonically increases in time and reaches a stationary state in accordance with classical equilibrium statistical mechanics. Our analysis shows that fluctuations of actions at fixed wave numbers relax to their equilibrium behavior faster than the spectrum reaches equilibrium. Numerical simulations of the DNLS equation confirm our theoretical results. The boundedness of the dispersion relation is found to be critical for observing negative temperatures in lattices characterized by two invariants.
Article
Multidisciplinary Sciences
M. C. Lopes Filho, H. J. Nussenzveig Lopes
Summary: In this work, the authors proved that physically realizable weak solutions of the incompressible two-dimensional Euler equations on a torus conserve kinetic energy. Physically realizable weak solutions refer to solutions that can be obtained as limits of vanishing viscosity. The authors extended the previous research by adding forcing to the flow.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Mathematics, Applied
S. Lanthaler, S. Mishra, C. Pares-Pulido
Summary: We prove the conservation of energy for weak and statistical solutions of the two-dimensional Euler equations, characterized by a uniform decay of the structure function. Through numerical experiments, we validate this theory and observe energy conservation in a wide variety of two-dimensional incompressible flows.
Article
Physics, Fluids & Plasmas
F. Lucco Castello, P. Tolias
Summary: Through molecular dynamics simulations, the thermodynamic and structural properties of two-dimensional dense Yukawa liquids are studied. The precise thermodynamic properties play a crucial role in determining the equation of state and structural properties, leading to high accuracy in terms of static correlations and thermodynamics.
Article
Mathematics, Applied
Jacob Bedrossian, Roberta Bianchini, Michele Coti Zelati, Michele Dolce
Summary: This study investigates the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, under a Gevrey perturbation of size epsilon. It is proven that the system experiences a shear-buoyancy instability, with density variation and velocity undergoing inviscid damping while vorticity and density gradient grow. The proof relies on suitable symmetrization and a variation of the Fourier time-dependent energy method.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Physics, Fluids & Plasmas
V. K. Mezentsev, E. Podivilov, I. A. Vaseva, M. P. Fedoruk, A. M. Rubenchik, S. K. Turitsyn
Summary: The article explores the possibility of utilizing the nonlinear lens effect to localize initially broad field distributions, describing two-dimensional localized solitary waves in a specific physical system. By using standard variational analysis, it is demonstrated that these solitons correspond to the minimum of the Hamiltonian.
Article
Physics, Fluids & Plasmas
Jae Dong Noh
Summary: We investigate the eigenstate thermalization properties of the spin-1/2 XXZ model in two-dimensional rectangular lattices. The numerical analysis supports that the model follows the eigenstate thermalization hypothesis, and this hypothesis is still valid within each subspace where the total spin is a good quantum number.
Article
Physics, Fluids & Plasmas
Jonathan Skipp, Jason Laurie, Sergey Nazarenko
Summary: We rigorously derive a precise point vortex model from the two-dimensional nonlinear Schrodinger equation, considering the Hamiltonian perspective. This derivation is carried out in the limit of well-separated, subsonic vortices on a spatially infinite strong condensate. As a result, we accurately calculate the self-energy of an isolated elementary Pitaevskii vortex.
Article
Mathematics, Applied
Hongyu Qin, Fengyan Wu, Deng Ding
Summary: In this study, a linearized compact ADI numerical method is developed to solve the nonlinear delayed Schrodinger equation in two-dimensional space. The convergence of the fully-discrete numerical method is analyzed using discrete energy estimate method, showing a numerical scheme of order O(Delta t(2) + h(4)) with time stepsize Delta t and space stepsize h. Several numerical examples are presented to confirm the theoretical analyses.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Physics, Multidisciplinary
Mason Kamb, Janie Byrum, Greg Huber, Guillaume Le Treut, Shalin Mehta, Boris Veytsman, David Yllanes
Summary: This study introduces a framework for studying ensembles of 2D time-invariant flow fields and estimating the probability for a particle to leave a finite area. The authors establish two upper bounds on this probability by leveraging different insights about the distribution of flow velocities, and complement their analytical results with numerical simulations.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Quantum Science & Technology
Jakub Rembielinski, Pawel Caban
Summary: This paper discusses deterministic nonlinear time evolutions satisfying convex quasi-linearity condition, proving that a family of linear non-trace-preserving maps satisfying the semigroup property will generate a family of convex quasilinear operations with the same property. The Gorini-Kossakowski-Sudarshan-Lindblad type equation for the considered evolution is generalized, with examples including general qubit evolution and extension of the Jaynes-Cummings model. The formalism is applied to spin density matrix of a charged particle in an electromagnetic field and flavor evolution of solar neutrinos.
Article
Computer Science, Interdisciplinary Applications
Ashesh Chattopadhyay, Ebrahim Nabizadeh, Eviatar Bach, Pedram Hassanzadeh
Summary: Data assimilation (DA) is a crucial part of forecasting models, allowing for better estimation of initial conditions in imperfect dynamical systems using observations. Ensemble Kalman filter (EnKF) is a widely-used DA algorithm, but its computational complexity is problematic for large systems. In this study, a hybrid ensemble Kalman filter (H-EnKF) is proposed, utilizing a data-driven surrogate to generate a large ensemble and accurately compute the background error covariance matrix. H-EnKF outperforms EnKF without the need for ad-hoc localization strategies, making it applicable to high-dimensional systems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Melanie Kobras, Valerio Lucarini, Maarten H. P. Ambaum
Summary: In this study, a minimal dynamical system derived from the classical Phillips two-level model is introduced to investigate the interaction between eddies and mean flow. The study finds that the horizontal shape of the eddies can lead to three distinct dynamical regimes, and these regimes undergo transitions depending on the intensity of external baroclinic forcing. Additionally, the study provides insights into the continuous or discontinuous transitions of atmospheric properties between different regimes.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Julien Nespoulous, Guillaume Perrin, Christine Funfschilling, Christian Soize
Summary: This paper focuses on optimizing driver commands to limit energy consumption of trains under punctuality and security constraints. A four-step approach is proposed, involving simplified modeling, parameter identification, reformulation of the optimization problem, and using evolutionary algorithms. The challenge lies in integrating uncertainties into the optimization problem.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Alain Bourdier, Jean-Claude Diels, Hassen Ghalila, Olivier Delage
Summary: In this article, the influence of a turbulent atmosphere on the growth of modulational instability, which is the cause of multiple filamentation, is studied. It is found that considering the stochastic behavior of the refractive index leads to a decrease in the growth rate of this instability. Good qualitative agreement between analytical and numerical results is obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Feiting Fan, Minzhi Wei
Summary: This paper focuses on the existence of periodic and solitary waves for a quintic Benjamin-Bona-Mahony (BBM) equation with distributed delay and diffused perturbation. By transforming the corresponding traveling wave equation into a three-dimensional dynamical system and applying geometric singular perturbation theory, the existence of periodic and solitary waves are established. The uniqueness of periodic waves and the monotonicity of wave speed are also analyzed.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Wangbo Luo, Yanxiang Zhao
Summary: We propose a generalized Ohta-Kawasaki model to study the nonlocal effect on pattern formation in binary systems with long-range interactions. In the 1D case, the model displays similar bubble patterns as the standard model, but Fourier analysis reveals that the optimal number of bubbles for the generalized model may have an upper bound.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Corentin Correia, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
Summary: The emergence of clustering of rare events is due to periodicity, where fast returns to target sets lead to a bulk of high observations. In this research, we explore the potential of a new mechanism to create clustering of rare events by linking observable functions to a finite number of points belonging to the same orbit. We show that with the right choice of system and observable, any given cluster size distribution can be obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Enyu Fan, Changpin Li
Summary: This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, Yuzuru Sato
Summary: The predictability of weather and climate is influenced by the state-dependent nature of atmospheric systems. The presence of special atmospheric states, such as blockings, is associated with anomalous instability. Chaotic systems, like the attractor of the Lorenz '96 model, exhibit heterogeneity in their dynamical properties, including the number of unstable dimensions. The variability of unstable dimensions is linked to the presence of finite-time Lyapunov exponents that fluctuate around zero. These findings have implications for understanding the structural stability and behavior modeling of high-dimensional chaotic systems.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Christian Klein, Goksu Oruc
Summary: A numerical study on the fractional Camassa-Holm equations is conducted to construct smooth solitary waves and investigate their stability. The long-time behavior of solutions for general localized initial data from the Schwartz class of rapidly decreasing functions is also studied. Additionally, the appearance of dispersive shock waves is explored.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper extends the standard action principle and the first Noether theorem to consider the general form of nonlocality in time and describes dissipative and non-Lagrangian nonlinear systems. The general fractional calculus is used to handle a wide class of nonlocalities in time compared to the usual fractional calculus. The nonlocality is described by a pair of operator kernels belonging to the Luchko set. The non-holonomic variation equations of the Sedov type are used to describe the motion equations of a wide class of dissipative and non-Lagrangian systems. Additionally, the equations of motion are considered not only with general fractional derivatives but also with general fractional integrals. An application example is presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)