Zero inertia limit of incompressible Qian–Sheng model

The Qian–Sheng model is a system describing the hydrodynamics of nematic liquid crystals in the Q-tensor framework. When the inertial effect is included, it is a hyperbolic-type system involving a second-order material derivative coupling with forced incompressible Navier–Stokes equations. If formally letting the inertial constant [Formula: see text] go to zero, the resulting system is the corresponding parabolic model. We provide the result on the rigorous justification of this limit in [Formula: see text] with small initial data, which validates mathematically the parabolic Qian–Sheng model. To achieve this, an initial layer is introduced to not only overcome the disparity of the initial conditions between the hyperbolic and parabolic models, but also make the convergence rate optimal. Moreover, a novel [Formula: see text]-dependent energy norm is carefully designed, which is non-negative only when [Formula: see text] is small enough, and handles the difficulty brought by the second-order material derivative.

3D pressure field reconstruction from time-resolved stereoscopic PIV measurements by relaxation of Taylor's hypothesis

This work presents reconstructions of 3D pressure fields starting from 2D3C stereoscopic-PIV (SPIV) measurements. In Fratantonio et al. (2021), we presented a new reconstruction algorithm, the “Instantaneous convection” method, capable of producing 3D velocity fields from time-resolved SPIV measurements. For reconstructions in flows with strong shear layers and high turbulence intensity, this method is able to provide time-resolved 3D velocity volumes that are more accurate than those that can be obtained from the more frequently employed reconstruction method based on the Taylor’s hypothesis and on the use of a mean convective field. Here we investigate the possibility of reconstructing the 3D pressure field from the timeresolved series of reconstructed 3D velocity data. A pseudo-tracking method is employed for computing the velocity material derivative, and the pressure field is then reconstructed by solving the 3D Poisson equation. The velocity and pressure reconstructions are validated on the Direct Numerical Simulation data of the turbulent channel flow taken from the John Hopkins Turbulence Database (JHTDB), and an application to experimental SPIV measurements of an air jet flow in coflow carried out at the Turbulent Mixing Tunnel (TMT) facility at Los Alamos National Laboratory is presented.

On a Generalization of One-Dimensional Kinetics

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

Nonlinear Phenomena in Axially Moving Beams with Speed-Dependent Tension and Tension-Dependent Speed

This paper investigates some nonlinear dynamical behaviors about domains of attraction, bifurcations, and chaos in an axially accelerating viscoelastic beam under a time-dependent tension and a time-dependent speed. The axial speed and the axial tension are coupled to each other on the basis of a harmonic variation over constant initial values. The transverse motion of the moving beam is governed by nonlinear integro-partial-differential equations with the rheological model of the Kelvin–Voigt energy dissipation mechanism, in which the material derivative is applied to the viscoelastic constitutive relation. The fourth-order Galerkin truncation is employed to transform the governing equation to a set of nonlinear ordinary differential equations. The nonlinear phenomena of the system are numerically determined by applying the fourth-order Runge–Kutta algorithm. The tristable and bistable domains of attraction on the stable steady state solution with a three-to-one internal resonance are analyzed emphatically by means of the fourth-order Galerkin truncation and the differential quadrature method, respectively. The system parameters on the bifurcation diagrams and the maximum Lyapunov exponent diagram are demonstrated by some numerical results of the displacement and speed of the moving beam. Furthermore, chaotic motion is identified in the forms of time histories, phase-plane portraits, fast Fourier transforms, and Poincaré sections.

A Pressure-Invariant Neutral Density Variable for the World's Oceans

We present a new method to calculate the neutral density of an arbitrary water parcel. Using this method, the value of neutral density depends only on the parcel’s salinity, temperature, latitude, and longitude and is independent of the pressure (or depth) of the parcel, and is therefore independent of heave in observations or high-resolution models. In this method we move the parcel adiabatically and isentropically like a submesoscale coherent vortex (SCV) to its level of neutral buoyancy on four nearby water columns of a climatological atlas. The parcel’s neutral density γSCV is interpolated from prelabeled neutral density values at these four reference locations in the climatological atlas. This method is similar to the neutral density variable γn of Jackett and McDougall: their discretization of the neutral relationship equated the potential density of two parcels referenced to their average pressure, whereas our discretization equates the parcels’ potential density referenced to the pressure of the climatological parcel. We calculate the numerical differences between γSCV and γn, and we find similar variations of γn and γSCV on the ω surfaces of Klocker, McDougall, and Jackett. We also find that isosurfaces of γn and γSCV deviate from the neutral tangent plane by similar amounts. We compare the material derivative of γSCV with that of γn, finding their total material derivatives are of a similar magnitude.

A Novel Spatio-Temporal Violence Classification Framework Based on Material Derivative and LSTM Neural Network

In the current era, the implementation of automated security video surveillance systems is particularly needy in terms of human violence recognition. Nevertheless, the latter encounters various interlinked difficulties which require efficient solutions as well as feasible methods that provide a relevant distinction between normal human actions and abnormal ones. In this paper, we present an overview of these issues and a literature review of the related works and current research on-going efforts on this field and suggests a novel prediction model for violence recognition, based on a preliminary spatio-temporal features extraction using the material derivative which describes the rate of change of a particle while in motion with respect to time. The classification algorithm is then carried out using a deep learning LSTM technique to classify generated features into eight specified violent and non-violent categories and a prediction value for each class of action is calculated. The whole model is trained on a public dataset and its classification capacity is evaluated on a confusion matrix which assembles all the predictions made by the system with their actual labels. The obtained results are promising and show that the proposed model can be potentially useful for detecting human violence.

Correct Expression of the Material Derivative in Continuum Physics

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}+(\bm v\cdot \bm \nabla)$, used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt}=\frac{\partial }{\partial t}(:)+\bm v\cdot [\bm \nabla (:)]$ is formulated. The solution existence condition of Navier-Stokes equation has been proposed from its form-solution, the conclusion is that "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

Correct Expression of the Material Derivative in Continuum Physics

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}+(\bm v\cdot \bm \nabla)$, used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt}=\frac{\partial }{\partial t}(:)+\bm v\cdot [\bm \nabla (:)]$ is formulated. The solution existence condition of Navier-Stokes equation has been proposed from its form-solution, the conclusion is that "\emph{The Navier-Stokes equation has solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

Correct Expression of the Material Derivative in Continuum Physics

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}$+ (v • ∇), used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt} = \frac{\partial }{\partial t}$(:) + v · [∇(:)] is formulated.