Periodic Klein–Gordon Chains with Three Particles in 1:2:2 Resonance

Journal of Dynamics and Differential Equations - In this paper, we deal with the three degrees of freedom Hamiltonian systems describing the Klein–Gordon chains with three particles of equal...     

Numerical study on Fermi–Pasta–Ulam–Tsingou problem for 1D shallow-water waves

Beginning with the first mode as the initial condition, long-term evolutions of gravity waves in shallow water are simulated based on the full nonlinear Boussinesq model. Evident recurrence is observed in long basins with appropriate initial amplitudes. Equipartition can be obtained in the case of a long basin, large initial amplitude or a long evolution time. Well-defined solitary waves are present during the recurrence stage and completely lost at the equipartition stage. The transition from regular to chaotic motion is conjectured to be related to the ratio of the dispersion and nonlinearity of the initial condition. For short basins with small initial amplitudes, nonlinearity is much smaller than dispersion, energy transfer is weak, and no recurrence can be observed. If dispersion and nonlinearity are chosen to be the same order in the initial condition, recurrence clearly emerges. However, if nonlinearity is chosen to be larger than dispersion, recurrence is absent and the system reaches equipartition rapidly.     

Correspondence between de Saint-Venant and Boussinesq. 1: Birth of the Shallow–Water Equations

The Shallow–Water Equations (SWEs), also referred to as the de Saint-Venant equations, constitute the current governing mathematical tool for free-surface water flows. These include, e.g., flood flows in rivers and in urban zones, flows across hydraulic structures as dams or wastewater facilities, flows in the environmental fields, glaciology, or meteorology. Despite this attractiveness, the system of two partial differential equations has an exact mathematical solution only for a limited number of problems of practical relevance.This historical work on the SWEs is based on a correspondence between two 19th-century scientists, de Saint-Venant and Boussinesq. Their well-known papers are thus commented from the point of development of their theory; the input of both scientists is evidenced by their writings, and comments of both to each other that led to what is commonly known as the SWEs. Given the age difference of the two of 45 years, the experienced engineer de Saint-Venant, and the mathematician Boussinesq, two eminent researchers, met to discuss not only problems in hydraulics, but in physics generally. In addition, their correspondence embraced also questions in ethics, religion, history of sciences, and personal news.The results of the SWEs cease to hold if streamline curvature effects dominate; this includes breaking waves, solitary and cnoidal waves, or non-linear waves in general. In most other cases, however, the SWEs perfectly apply to typical flows in engineering practice; they are considered the fundamental system of equations describing open channel flows. This work thus provides a background to its birth, including lots of comments as to its improvement, physical meanings, methods of solution, and a discussion of the results. This paper also deals with the steady flow equations, gives a short account on the main persons mentioned in the Correspondence, and provides a summary of further developments of the SWEs until 1920.     

Chapman–Jouguet hypothesis 1899–1999: One century between myth and reality

The 20th century saw the rapid development of quantum mechanics and micro-scales physics. However, classical mechanics did not lose any interest, and did not cease setting severe enigmas. Among them lies detonation, observed and measured since Berthelot (1881), but whose modeling required nearly hundred years of effort. Following the fashion of celebrations, we could say that the publication by Chapman in 1899 is a reason for rewriting, in modern terms, the main facts of past century: enhancing the few brilliant steps and also mentioning their sluggish diffusion, which arises from linguistic and national fractures within the scientific world and also reflects scientists' great reluctancy to recognize and overcome the intrinsic uncertainties of modeling. Received 19 April 1999 / Accepted 27 May 1999     

The Horton–Rogers–Lapwood Problem Revisited: The Effect of Pressure Work

The problem of the onset of convective roll instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures, well known as the Horton–Rogers–Lapwood problem, is revisited including the effect of pressure work and viscous dissipation in the local energy balance. A linear stability analysis of rolls disturbances is performed. The analysis shows that, while the contribution of viscous dissipation is ineffective, the contribution of the pressure work may be important. The condition of marginal stability is investigated by adopting two solution procedures: method of weighted residuals and explicit Runge–Kutta method. The pressure work term in the energy balance yields an increase of the value of the Darcy–Rayleigh number at marginal stability. In other words, the effect of pressure work is a stabilizing one. Furthermore, while the critical value of the Darcy– Rayleigh number may be considerably affected by the pressure work contribution, the critical value of the wave number is affected only in rather extreme cases, i.e. for very high values of the Gebhart number. A nonlinear stability analysis is also performed pointing out that the joint effects of viscous dissipation and pressure work result in a reduction of the excess Nusselt number due to convection, when the Darcy–Rayleigh number is replaced by the superadiabatic Darcy–Rayleigh number.     

High-order synchronization of stick–slip process: experiments on spring–slider system

In the last years it has been shown that the synchronization and triggering of dynamic events by weak external forcing is ubiquitous and is observed in biological systems, lasers, electronic networks, etc. In the present paper, new experimental data on the phase synchronization in frictional system induced by a weak electromagnetic or mechanical periodic forcing are analyzed. For quantitative analysis of stick–slip time series, modern tools of nonlinear dynamics were used. Stick–slip events were identified by recording acoustic emissions, which accompany slip displacements. The spring–slider system in stick–slip regime is considered as a proxy of active tectonic fault, generating earthquakes. The effect of high-order synchronization of stick–slip events by weak electromagnetic or mechanical periodic forcing, as well as the phenomenon of phase time delay of the synchronized slip events behind the forcing phase, was discovered. These findings can help to find new regularities in seismic time series.     

Interlayer shear of nanomaterials:Graphene–graphene,boron nitride–boron nitride and graphene–boron nitride

In this paper, the interlayer sliding between graphene and boron nitride(h-BN) is studied by molecular dynamics simulations. The interlayer shear force between h-BN/h-BN is found to be six times higher than that of graphene/graphene, while the interlayer shear between graphene/h-BN is approximate to that of graphene/graphene. The graphene/hBN heterostructure shows several anomalous interlayer shear characteristics compared to its bilayer counterparts. For graphene/graphene and h-BN/h-BN, interlayer shears only exit along the sliding direction while interlayer shear for graphene/h-BN is observed along both the translocation and perpendicular directions. Our results provide significant insight into the interlayer shear characteristics of 2D nanomaterials.     

充液挠性航天器俯仰运动 1:1:1 内共振动力学分析

采用已推导的俯仰运动矩形贮箱受控刚-液-弹耦合系统在外力矩作用下的耦合动力 学模型,在刚体上加入控制项,详细分析了系统固有频率的精确解与近似解. 应用多尺 度法对耦合系统1:1:1内共振进行解析分析,与数值解比较验证解析解的正确性. 通过近 似解析分析得到刚-液-弹之间的耦合作用机理：1) 液深影响整个系统的软硬特性,当液体发 生软硬特性转化时,处于液体原多值频率区域的刚体和弹性体幅频曲线分支峰值会减弱,且 具有相同的特性转化趋势;处于液体新多值频率区域的刚体和弹性体幅频曲线分支峰值会增 强,且具有相反的特性转化趋势. 2) 刚体和弹性体幅频曲线的峰值均在以受控刚体和弹性体 为主的耦合系统固有频率处,以液体为主固有频率激励,刚体和弹性体振幅较小.     

Non-linear electromechanical response of 1–3 type piezocomposites

Domain switching in piezoelectric materials is caused by external loads such as electric field and stress that leads to non-linear behaviour. A study is carried out to compare the non-linear behaviour of 1–3 piezocomposites with different volume fractions and bulk piezoceramics. Experiments are conducted to measure the electrical displacement and strain on piezocomposites and bulk ceramics under high cyclic electrical loading and constant compressive prestress. A thermodynamically consistent uni-axial framework is developed to predict the nonlinear behaviour by combining the phenomenological and micromechanical techniques. Volume fractions of three distinct uni-axial variants (instead of six variants) are used as internal variables to describe the microscopic state of the material. In this model, the grain boundary effects are taken into account by introducing the back fields (electric field and stress) as non-linear kinematic hardening functions. An analytical model based on equivalent layered approach is used to calculate effective properties such as elastic, piezoelectric, and dielectric constants for different volume fractions of piezocomposites. The predicted effective properties are incorporated in the proposed uni-axial model and the dielectric hysteresis (electrical displacement versus electric field) as well as butterfly curves (strain versus electric field) are simulated. Comparison between the experiments and simulations show that this model can reproduce the characteristics of non-linear response. It is observed that the variation in fiber volume fraction and compressive stress has a significant influence on the response of the 1–3 piezocomposites.     

Correction to: Darcy–Brinkman–Forchheimer Model for Film Boiling in Porous Media

Transport in Porous Media - A correction to this paper has been published: https://doi.org/10.1007/s11242-021-01631-0     

The effect of surfactants on air–water annular and churn flow in vertical pipes. Part 1: Morphology of the air–water interface

In this work, the influence of surfactants on air–water flow was studied by performing experiments in a 12 metre long, 50 mm inner diameter, vertical pipe at ambient conditions. High-speed visualisation of the flow shows that the morphology of the air–water interface determines the formation of foam. The foam subsequently alters the flow morphology significantly. In annular flow, the foam suppresses the roll waves, and a foamy crest is formed on the ripple waves. In the churn flow regime, the flooding waves and the downwards motion of the liquid film are suppressed by the foam. The foam is transported in foam waves moving upwards superposed on an almost stagnant foam substrate at the pipe wall. Foam thus effectively reduces the superficial gas velocity at which the transition from annular to churn flow occurs. These experiments make more clear how surfactants can postpone liquid loading in vertical pipes, such as in gas wells.     

Jordan–Cattaneo waves: Analogues of compressible flow

We review work of Jordan on a hyperbolic variant of the Fisher–KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee–Infante equation. Extension of Jordan’s ideas to a model for traffic flow are also mentioned. We also examine a diffusive susceptible–infected (SI) model, and generalizations of diffusive Lotka–Volterra equations, including a Lotka–Volterra–Bass competition model with diffusion. For all cases we show how a Jordan–Cattaneo wave may be analysed and we indicate how to find the wavespeeds and the amplitudes. Finally we present details of a fully nonlinear analysis of acceleration waves in a Cattaneo–Christov poroacoustic model.     

Poisson–Nernst–Planck Systems for Ion Flow with Density Functional Theory for Hard-Sphere Potential: I–V Relations and Critical Potentials. Part I: Analysis

In this work, we analyze a one-dimensional steady-state Poisson–Nernst–Planck type model for ionic flow through a membrane channel including ionic interactions modeled from the Density Functional Theory in a simple setting: Two oppositely charged ion species are involved with electroneutrality boundary conditions and with zero permanent charge, and only the hard sphere component of the excess (beyond the ideal) electrochemical potential is included. The model can be viewed as a singularly perturbed integro-differential system with a parameter resulting from a dimensionless scaling of the problem as the singular parameter. Our analysis is a combination of geometric singular perturbation theory and functional analysis. The existence of a solution of the model problem for small ion sizes is established and, treating the sizes as small parameters, we also derive an approximation of the I–V (current–voltage) relation. For this relatively simple situation, it is found that the ion size effect on the I–V relation can go either way—enhance or reduce the current. More precisely, there is a critical potential value V _c so that, if V > V _c , then the ion size enhances the current; if V < V _c , it reduces the current. There is another critical potential value V ^c so that, if V > V ^c , the current is increasing with respect to λ =? r ₂/r ₁ where r ₁ and r ₂ are, respectively, the radii of the positively and negatively charged ions; if V < V ^c , the current is decreasing in λ. To our knowledge, the existence of these two critical values for the potential was not previously identified.     

Aerosol–cloud–precipitation interactions: A challenging problem in regional environment and climate research

Aerosols affect clouds in two broad ways: (i) presence of more number of aerosols leads to formation of more smaller droplets, and reduces coalescence, resulting in brighter clouds that reflect more solar energy back to space, hence they contribute to cooling of the Earth's surface and (ii) numerous smaller cloud droplets tend to reduce precipitation and change the extent of cloud cover and increase cloud lifetime and albedo. One of our recent studies on aerosols over the Indo-Gangetic Plains (IGP) relative to the pristine oceans to the south of Indian Ocean showed that highly absorbing aerosols could potentially lead to the revival of active condition preceded by long break. The absorption of solar radiation by aerosols such as black carbon and desert dust produces surface cooling and local stabilization of lower atmosphere. This stability effect is overcome by the enhanced moisture convergence due to the meridional gradient of aerosol-induced heating. In some other studies, we showed association between cloud thickness and cloud to sub-cloud ratio (SCR), aerosol variability (in terms of aerosol optical depth and aerosol index) and monsoon precipitation and climate over regional scale. This paper provides an overview of some salient results that have been obtained from the studies conducted, using the ground- and space-based active and passive remote sensing techniques, at the Indian Institute of Tropical Meteorology (IITM), Pune, India in the recent decade.     

Predictions of the excess pressure drop of Boger fluids through a 2:1:2 contraction–expansion geometry using non-equilibrium molecular dynamics

Non-equilibrium molecular dynamics are used to generate the flow of polymer solutions, specifically of Boger fluids, through a planar 2:1:2 contraction–expansion geometry. The solvent molecules are represented by Lennard–Jones particles, while linear molecules are described by spring-monomers with a finite extensible non-linear elastic spring potential. The equations for Poiseuille flow are solved using a multiple time-scale algorithm extended to non-equilibrium situations. Simulations are performed at constant temperature using Nose–Hoover dynamics. At simulation conditions, changes in concentration show no significant effect on molecular conformation, velocity profiles, and stress fields, while variations in the Deborah number have a strong influence on fluid response. Increasing the magnitude of the Deborah number (De), larger deformation rates are developed in the flow region. For a Deborah number of one, the non-dimensional pressure drop presents values lower than the correspondent Newtonian case. However, for large Deborah numbers, the pressure drop increases above the Newtonian reference. An effective excess pressure drop above the Newtonian value is predicted for Boger fluids along this geometry.     

Global Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System in 1D

In this paper, we investigate a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids. We prove the existence and uniqueness of global classical solution, the existence of weak solutions and the existence of unique strong solution of the Navier–Stokes/Allen–Cahn system in 1D for initial data ρ ₀ without vacuum states.