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Mathematical and numerical modelling of rapid transients at partially lifted sluice gates. (arXiv:2303.07396v1 [physics.flu-dyn]) arxiv.org/abs/2303.07396

Mathematical and numerical modelling of rapid transients at partially lifted sluice gates

The present paper deals with the modelling of rapid transients at partially lifted sluice gates from both a mathematical and numerical perspective in the context of the Shallow water Equations (SWE). First, an improved exact solution of the dam-break problem is presented, assuming (i) the dependence of the gate contraction coefficient on the upstream flow depth, and (ii) a physically congruent definition for the submerged flow equation. It is shown that a relevant solution always exists for any set of initial conditions, but there are also initial conditions for which the solution is multiple. In the last case, a novel disambiguation criterion based on the continuous dependence of the solution on the initial conditions is used to select the physically congruent one among the alternatives. Secondly, a one (1-d) and a two-dimensional (2-d) form of a SWE Finite Volume numerical model, equipped with an approximate Riemann solver for the sluice gate treatment at cells interfaces, are presented. It is shown that the numerical implementation of classic steady state gate equations (classic equilibrium approach) leads to unsatisfactory numerical results in the case of fast transients, while a novel relaxed version of these equations (non-equilibrium approach) supplies very satisfactory results both in the 1-d and 2-d case. In particular, the 1-d numerical model is tested against (i) the proposed novel exact solutions and (ii) recent dam-break laboratory results. The 2-d model is verified by means of a test in a realistic detention basin for flood regulation, demonstrating that the novel findings can be promptly applied in real-world cases.

arxiv.org

Near-exact solution to linear water and sound wave pathline equations: mathematical insights into Stokes drift. (arXiv:2303.07464v1 [physics.flu-dyn]) arxiv.org/abs/2303.07464

Near-exact solution to linear water and sound wave pathline equations: mathematical insights into Stokes drift

We undertake a fully Lagrangian approach and use asymptotic methods to accurately solve the respective pathline equation for linear sound and water waves. We show that the 2D pathline equations of water waves are reducible to a 1D equation when expressed in terms of particle phase. Contrary to the prevalent notion, the pathline for both kinds of \emph{linear waves} is an open trajectory, and a particle undergoes a net drift in the direction of wave propagation, which is nothing but Stokes drift. We argue that Stokes drift, although overwhelmingly studied and physically rationalized in the context of water waves, is a generic mechanism -- a consequence of the nonlinearity of the dynamical system represented by the pathline equation ensuing from linear wave theory. The fully Lagrangian approach enables us to accurately evaluate the elapsed time, displacement, and average horizontal velocity of a particle during the crest and trough segments of a phase cycle. We show that a particle spends more time and undergoes greater displacement, moving at a greater horizontal velocity, in the crest segment in comparison to the trough. These key characteristics of wave-induced particle motion cannot be obtained from the hybrid Eulerian-Lagrangian approach of \cite{stokes1847}, which is typically used for obtaining particle trajectories and evaluating Stokes drift.

arxiv.org

Enhanced beam shifts mediated by Bound States in Continuum. (arXiv:2303.06196v1 [physics.optics]) arxiv.org/abs/2303.06196

Enhanced beam shifts mediated by Bound States in Continuum

The interaction of light beams with resonant structures has led to the development of various optical platforms for sensing, particle manipulation, and strong light-matter interaction. In the current study, we investigate the manifestations of the bound states in continuum (BIC) on the in plane and out of plane shifts (referred to as Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts, respectively) of a finite beam with specific polarization incident at an arbitrary angle. Based on the angular spectrum decomposition, we develop a generic formalism for understanding the interaction of the finite beam with an arbitrary stratified medium with isotropic and homogeneous components. it is applied to the case of a Gaussian beam with p and circularly polarized light incident on a symmetric structure containing two polar dielectric layers separated by a spacer layer. For p-polarized plane wave incidence one of the coupled Berreman modes of the structure was recently shown to evolve to the bound state with infinite localization and diverging quality factor coexisting with the other mode with large radiation leakage (Remesh et al. Optics Communications, 498:127223, 2021). A small deviation from the ideal BIC resonance still offers resonances with very high quality factors and these are exploited in this study to report giant GH shifts. A notable enhancement in the IF shift for circularly polarized light is also shown. Moreover, the reflected beam is shown to undergo distortion leading to a satellite spot. The origin of such a splitting of the reflected beam is traced to a destructive interference due to the left and right halves of the corresponding spectra.

arxiv.org

Finite Elasticity of the Vertex Model and its Role in Rigidity of Curved Cellular Tissues. (arXiv:2303.06224v1 [cond-mat.soft]) arxiv.org/abs/2303.06224

Finite Elasticity of the Vertex Model and its Role in Rigidity of Curved Cellular Tissues

Using a mean field approach and simulation, we study the non-linear mechanical response of the vertex model (VM) of biological tissue under compression and dilation. The VM is known to exhibit a transition between rigid and fluid-like, or floppy, states driven by geometric incompatibility. Target perimeter and area set a target shape which may not be geometrically achievable, thereby engendering frustration. Previously, an asymmetry in the linear elastic response was identified at the rigidity transition between compression and dilation. Here we show and characterize how the asymmetry extends away from the transition point for finite strains. Under finite compression, an initially solid VM can totally relax perimeter tension, and thereby have reduced bulk and shear modulus. Conversely, an initially floppy VM under dilation can rigidify and have a higher bulk and shear modulus. These observations imply that re-scaling of cell area shifts the transition between rigid and floppy states. Based on this insight, we calculate the re-scaling of cell area engendered by intrinsic curvature and write a prediction for the rigidity transition in the presence of curvature. The shift of the rigidity transition in the presence of curvature for the VM provides a new metric for predicting tissue rigidity from image data for curved tissues in a manner analogous to the flat case.

arxiv.org

Second And Third-Order Structure Functions Of An 'Engineered' Random Field And Emergence Of The Kolmogorov 4/5 And 2/3-Scaling Laws Of Turbulence. (arXiv:2303.06248v1 [physics.flu-dyn]) arxiv.org/abs/2303.06248

Second And Third-Order Structure Functions Of An 'Engineered' Random Field And Emergence Of The Kolmogorov 4/5 And 2/3-Scaling Laws Of Turbulence

The 4/5 and 2/3 laws of turbulence can emerge from a theory of 'engineered' random vector fields $\mathcal{X}_{i}(x,t) =X_{i}(x,t)+\tfracθ{\sqrt{d(d+2)}} X_{i}(x,t)ψ(x)$ existing within $\mathbf{D}\subset\mathbf{R}^{d}$. Here, $X_{i}(x,t)$ is a smooth deterministic vector field obeying a nonlinear PDE for all $(x,t)\in\mathbf{D}\times\mathbf{R}^{+}$, and $θ$ is a small parameter. The field $ψ(x)$ is a regulated and differentiable Gaussian random field with expectation $\mathbb{E}[ψ(x)]=0$, but having an antisymmetric covariance kernel $\mathscr{K}(x,y)=\mathbb{E}[ψ(x)ψ(y)]=f(x,y)K(\|x-y\|;λ)$ with $f(x,y)=-f(y,x)=1,f(x,x)=f(y,y)=0$ and with $K(\|x-y\|;λ)$ a standard stationary symmetric kernel. For $0\le\ell\le λ<L$ with $X_{i}(x,t)=X_{i}=(0,0,X)$ and $θ=1$ then for $d=3$, the third-order structure function is \begin{align} S_{3}[\ell]=\mathbb{E}\left[|\mathcal{X}_{i}(x+\ell,t)-\mathcal{X}(x,t)|^{3}\right]=-\frac{4}{5}\|X_{i}\|^{3}=-\frac{4}{5}X^{3}\nonumber \end{align} and $S_{2}[\ell]=CX^{2}$. The classical 4/5 and 2/3-scaling laws then emerge if one identifies the random field $\mathcal{X}_{i}(x,t)$ with a turbulent fluid flow $\mathcal{U}_{i}(x,t)$ or velocity, with mean flow $\mathbb{E}[\mathcal{U}_{i}(x,t)]=U_{i}(x,t)=U_{i}$ being a trivial solution of Burger's equation. Assuming constant dissipation rate $ε$, small constant viscosity $ν$, corresponding to high Reynolds number, and the standard energy balance law, then for a range $η\le\ell\ll λ<L$ \begin{align} S_{3}[\ell]=\mathbb{E}\left[|\mathcal{U}_{i}(x+\ell,t)-\mathcal{U}(x,t)|^{3}\right]=-\frac{4}{5}ε\ell\nonumber \end{align} where $η=(ν^{3/4}ε)^{-1/4}$. For the second-order structure function, the 2/3-law emerges as $S_{2}[\ell]=Cε^{2/3}\ell^{2/3}$.

arxiv.org

Dynamics of spheroids in pressure driven flows of shear thinning fluids. (arXiv:2303.06251v1 [physics.flu-dyn]) arxiv.org/abs/2303.06251

Dynamics of spheroids in pressure driven flows of shear thinning fluids

Particles in inertialess flows of shear thinning fluids are a model representation for several systems in biology, ecology, and micro-fluidics.In this paper, we analyze the motion of a spheroid in a pressure driven flow of a shear thinning fluid.The shear thinning rheology is characterized by the Carreau model.We use a combination of perturbative techniques and the reciprocal theorem to delineate the kinematics of prolate and oblate spheroids.There are two perturbative strategies adopted, one near the zero shear Newtonian plateau and the other near the infinite shear Newtonian plateau.In both limits, we find that a reduction in effective viscosity decreases the spheroid's rotational time period in pressure driven flows.The extent to which shear thinning alters the kinematics is a function of the particle shape.For a prolate particle, the effect of shear thinning is most prominent when the spheroid projector is aligned in the direction of the velocity gradient, while for an oblate particle the effect is most prominent when the projector is aligned along the flow direction.Lastly, we compare the tumbling behavior of spheroids in pressure driven flow to those in simple shear flow.While the time period decreases monotonically with Carreau number for pressure driven flows, the trend is non monotonic for shear flows where time period first increases at low Carreau number and then decreases at high Carreau numbers.Shear thinning does not resolve the degeneracy of Jefferey's orbits.

arxiv.org

A Tensor Formulation of Second-Order Brillouin-Wigner Perturbation Theory with a Size-Consistent Correlation Energy. (arXiv:2303.06271v1 [physics.chem-ph]) arxiv.org/abs/2303.06271

A Tensor Formulation of Second-Order Brillouin-Wigner Perturbation Theory with a Size-Consistent Correlation Energy

Second-order Moller-Plesset perturbation theory (MP2) often breaks down catastrophically in small-gap systems, leaving much to be desired in its performance for myriad chemical applications such as noncovalent interactions, thermochemistry, and dative bonding in transition metal complexes. This divergence problem has reignited interest in Brillouin-Wigner perturbation theory (BWPT), which is regular at all orders but lacks size-consistency and extensivity, severely limiting its application to chemistry. In this work, we propose a generalized tensor formulation of second-order BWPT that recasts the energy denominator as a sum of energy-gap and regularizer tensors, where the regularizer is taken (by ansatz) to be the correlation contribution to the ionization energy of a given occupied orbital. This choice of regularizer leads to a Brillouin-Wigner correlation energy expression that is size-extensive, size-consistent, and invariant to unitary transformations among the occupied or virtual orbitals. Our size-consistent second-order Brillouin-Wigner (scBW2) approach is capable of describing the exact dissociation limit of H2 in a minimal basis set regardless of the spin-polarization of the reference orbitals. More broadly, we find that scBW2 offers improvements relative to MP2 for covalent bond breaking, noncovalent interaction energies, and metal/organic reaction energies, while rivaling coupled-cluster with single and double substitutions (CCSD) for thermochemical properties. Not only does scBW2 offer improvements in transferability relative to empirical energy-gap dependent regularizers, but the ab initio framework that we propose can be used as a guidepost for developments of future Brillouin-Wigner functionals.

arxiv.org

Generative Adversarial Networks for Scintillation Signal Simulation in EXO-200. (arXiv:2303.06311v1 [hep-ex]) arxiv.org/abs/2303.06311

Generative Adversarial Networks for Scintillation Signal Simulation in EXO-200

Generative Adversarial Networks trained on samples of simulated or actual events have been proposed as a way of generating large simulated datasets at a reduced computational cost. In this work, a novel approach to perform the simulation of photodetector signals from the time projection chamber of the EXO-200 experiment is demonstrated. The method is based on a Wasserstein Generative Adversarial Network - a deep learning technique allowing for implicit non-parametric estimation of the population distribution for a given set of objects. Our network is trained on real calibration data using raw scintillation waveforms as input. We find that it is able to produce high-quality simulated waveforms an order of magnitude faster than the traditional simulation approach and, importantly, generalize from the training sample and discern salient high-level features of the data. In particular, the network correctly deduces position dependency of scintillation light response in the detector and correctly recognizes dead photodetector channels. The network output is then integrated into the EXO-200 analysis framework to show that the standard EXO-200 reconstruction routine processes the simulated waveforms to produce energy distributions comparable to that of real waveforms. Finally, the remaining discrepancies and potential ways to improve the approach further are highlighted.

arxiv.org
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