非线性科学学术速递[1.10]
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nlin非线性科学，共计10篇
【1】 Polynomial Dynamical Systems and Differentiation of Genus 4 Hyperelliptic Functions
标题：多项式动力系统与亏格4的超椭圆函数的微分
链接：https://arxiv.org/abs/2201.02462
摘要：We give an explicit solution to the problem of differentiation of
hyperelliptic functions in genus 4 case. We describe explicitly the polynomial
Lie algebras and polynomial dynamical systems connected to this problem.
【2】 General rogue wave solutions to the discrete nonlinear Schrödinger equation
标题：离散非线性薛定谔方程的一般流氓波解
链接：https://arxiv.org/abs/2201.02359
备注：16 pages, 4 figures
摘要：In the present paper, we attempt to construct both the general rogue wave
solutions to the fully discrete nonlinear Schr\"odinger (fd-NLS) equation via
the KP-Toda reduction method. First, we deduce the general breather solution of
the fd-NLS equation starting from a pair of bilinear equations. We then derive
the general rogue wave solution by taking a limit to the breather solution.
【3】 Schwarzian derivative, Painlevé XXV-Ermakov equation and Bäcklund transformations
标题：Schwarzian导数、PainlevéXXV-Ermakov方程和Bäcklund变换
链接：https://arxiv.org/abs/2201.02267
备注：21 pages
摘要：The role of Schwarzian derivative in the study of nonlinear ordinary
differential equations is revisited. Solutions and invariances admitted by
Painlev\'e XXV-Ermakov equation, Ermakov equation and third order linear
equation in a normal form are shown to be based on solutions of the Schwarzian
equation. Starting from the Riccati equation and the second order element of
the Riccati chian as the simplest examples of linearizable equations, by
introducing a suitable change of variables, it is shown how the Schwarzian
derivative represents a key tool in the construction of solutions. Two families
of B\"acklund transformations which link the linear and nonlinear equations
under investigation are obtained. Some examples with relevant applications are
given and discussed.
【4】 Loschmidt echo and Poincaré recurrences of entanglement
标题：Loschmidt回波与纠缠的Poincaré重现
链接：https://arxiv.org/abs/2201.02600
备注：28 pages, 20 figures and 4 pages with 4 figures Supplementary Material
摘要：We study numerically the properties of entanglement of two interacting, or
noninteracting, particles evolving in a regime of quantum chaos in the quantum
Chirikov standard map. Such pairs can be viewed as interacting, on
noninteracting, Einstein-Podolsky-Rosen pairs in a regime of quantum chaos. The
analysis is done with such tools as the Loschmidt echo of entanglement and the
Poincar\'e recurrences of entanglement in presence of absorption. The obtained
results show unusual features of the entropy of entanglement and the spectrum
of Schmidt decomposition with their dependence on interactions at different
quantum chaos regimes.
【5】 Effects of vaccination efficacy on wealth distributionin kinetic epidemic models
标题：动态流行病模型中疫苗接种效果对财富分配的影响
链接：https://arxiv.org/abs/2201.02553
备注：22 pages, 20 figures
摘要：The spreading of Covid-19 pandemic has highlighted the close link between
economics and health in the context of emergency management. A widespread
vaccination campaign is considered the main tool to contain the economic
consequences. This paper will focus, at the level of wealth distribution
modelling, on the economic improvements induced by the vaccination campaign in
terms of its effectiveness rate. The economic trend during the pandemic is
evaluated resorting to a mathematical model joining a classical compartmental
model including vaccinated individuals with a kinetic model of wealth
distribution based on binary wealth exchanges. The interplay between wealth
exchanges and the progress of the infectious disease is realized by assuming on
the one hand that individuals in different compartments act differently in the
economic process and on the other hand that the epidemic affects risk in
economic transactions. Using the mathematical tools of kinetic theory, it is
possible to identify the equilibrium states of the system and the formation of
inequalities due to the pandemic in the wealth distribution of the population.
Numerical experiments highlight the importance of the vaccination campaign and
its positive effects in reducing economic inequalities in the multi-agent
society.
【6】 Frozen dynamics of a breather induced by an adiabatic invariant
标题：绝热不变量诱导的呼吸器冻结动力学
链接：https://arxiv.org/abs/2201.02529
备注：23 pages
摘要：The Discrete Nonlinear Schr\"odinger (DNLS) equation is a Hamiltonian model
displaying frozen dynamics when breathers appear in the system. We study
breather relaxation in the thermal region, $T < +\infty$, in a unidirectional
version of the DNLS equation, where the rest of the system does not feel the
breather. Breather dynamics is governed by a time-dependent one-dimensional
Hamiltonian with two distinct time scales, and we show that the stability of
the breather is related to the existence of an adiabatic invariant (AI).
Approximate expressions for the AI are obtained both by implementing a
canonical perturbation theory and a more phenomenological approach based on the
estimate of the energy flux. The close correspondence with the original model
allows excluding that breather destabilization is induced by the formation of
localized bound states such as dimers. Finally, the AI dynamics reveals an
unexpected similarity with Levy processes, which deserves further
investigations.
【7】 Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model
标题：形式化求解$O(N)$非线性Sigma模型的辅助系统
链接：https://arxiv.org/abs/2201.02493
备注：5 pages
摘要：We show that the integrability of the $SO(N)/SO(N-1)$ Principal Chiral Model
(PCM) originates from the Pohlmeyer reduction of the $O(N)$ Non Linear Sigma
Model (NLSM). In particular, we show that the Lax pair of the PCM is related
upon redefinitions and identification of parameters to the zero curvature
condition, which is a consequence of the flatness of the enhanced space used in
the Pohlmeyer reduction. This identification provides the solution of the
auxiliary system that corresponds to an arbitrary NLSM/PCM solution.
【8】 Mitigation of thermoacoustic instability in a turbulent combustor via self-coupling
标题：湍流燃烧室中热声不稳定性的自耦合缓解
链接：https://arxiv.org/abs/2201.02328
备注：17 pages, 6 figures, Preprint under review in Proceedings of The Combustion Institute
摘要：In this paper, we report the first observation of complete mitigation of
thermoacoustic instability in a bluff-body stabilized turbulent combustor
through the method of self-coupling. Self-coupling is achieved by coupling the
acoustic field of the combustor to itself through a coupling tube. We
characterize the effects of such acoustic self-feedback on the thermoacoustic
instability of the system by varying the length and diameter of the coupling
tube. We observe that the amplitude and the dominant frequency of the acoustic
pressure fluctuations gradually decrease as the length of the coupling tube is
increased. A complete suppression of thermoacoustic instability is observed
when the coupling tube length is nearly 1.5 times the combustor length.
Meanwhile, as we approach the suppression of thermoacoustic instability, the
dynamical behavior of acoustic pressure changes from the state of limit cycle
oscillations to low amplitude aperiodic oscillations via intermittency. We also
study the coupling between the acoustic field and the unsteady flame dynamics
for different conditions of self-coupling in the combustor. As the combustor
approaches the state of complete suppression, the temporal synchrony between
the acoustic pressure and the global heat release rate signals changes from the
state of synchronized periodicity to desynchronized aperiodicity through
intermittent synchronization. From the spatiotemporal analysis of the combustor
flow field, we find complete disruption of the coherent spatial structures of
acoustic energy production observed during the state of thermoacoustic
instability when the combustor is self-coupled with a tube of optimized size.
Thus, we anticipate self-coupling to be a viable option to mitigate high
amplitude thermoacoustic oscillations in turbulent combustion systems present
in gas turbines and rocket engines.
【9】 Long time and large crowd dynamics of discrete Cucker-Smale alignment models
标题：离散Cucker-Smer线形模型的长时间大人群动力学
链接：https://arxiv.org/abs/2201.02281
摘要：We provide a bird's eye view on developments in analyzing the long time,
large crowd behavior of Cucker-Smale alignment dynamics. We consider a class of
(fully-)discrete models, paying particular attention to general alignment
protocols in which agents, with possibly time-dependent masses, are driven by a
large class of heavy-tailed communication kernels. The presence of
time-dependent masses allows, in particular, non-symmetric communication. While
revisiting known results in the literature, we also shed new light of various
aspects on the long time flocking/swarming behavior, driven by the decay of
energy fluctuations and heavy-tailed connectivity. We also discuss the large
crowd dynamics in terms of the hydrodynamic description of Euler alignment
models.
【10】 Inferring Turbulent Parameters via Machine Learning
标题：基于机器学习的湍流参数推断
链接：https://arxiv.org/abs/2201.00732
摘要：We design a machine learning technique to solve the general problem of
inferring physical parameters from the observation of turbulent flows, a
relevant exercise in many theoretical and applied fields, from engineering to
earth observation and astrophysics. Our approach is to train the machine
learning system to regress the rotation frequency of the flow's reference
frame, from the observation of the flow's velocity amplitude on a 2d plane
extracted from the 3d domain. The machine learning approach consists of a Deep
Convolutional Neural Network (DCNN) of the same kind developed in computer
vision. The training and validation datasets are produced by means of fully
resolved direct numerical simulations. This study shows interesting results
from two different points of view. From the machine learning point of view it
shows the potential of DCNN, reaching good results on such a particularly
complex problem that goes well outside the limits of human vision. Second, from
the physics point of view, it provides an example on how machine learning can
be exploited in data analysis to infer information that would be inaccessible
otherwise. Indeed, by comparing DCNN with the other possible Bayesian
approaches, we find that DCNN yields to a much higher inference accuracy in all
the examined cases.
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