Opposite Boundary Research Articles

Balanced truncation model reduction of a nonlinear cable-mass PDE system with interior damping

<p style='text-indent:20px;'>We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at one boundary. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the opposite boundary. We first prove that the linearized and nonlinear unforced systems are well-posed and exponentially stable under certain conditions on the damping parameters, and then consider a balanced truncation method to generate the reduced order model (ROM) of the nonlinear input-output system. Little is known about model reduction of nonlinear input-output systems, and so we present detailed numerical experiments concerning the performance of the nonlinear ROM. We find that the ROM is accurate for many different combinations of model parameters.

Filling of a Plane Slit Volume with a Glow Discharge in a Transverse Magnetic Field and Its Effect on the Discharge Contraction

We consider a dc glow discharge in a plane slit volume with electrodes in the slit plane in a magnetic field transverse to the current, which has been studied experimentally. As in the experiment, the discharge is artificially confined at one of the dielectric boundaries of the volume and propagates to the opposite dielectric boundary until it is stabilized. It is shown using a 2D calculation of the nonstationary process that the discharge in a magnetic field occupies a noticeably larger volume (with a lower current density at the electrodes) than in zero magnetic field. The effect of the magnetic field is also manifested in that it hampers the contraction of the discharge, substantially elevating the threshold current of the diffuse discharge. The discharge contraction is calculated in the approximation of a homogeneous positive column along the current right to the attainment of the stationary state. In calculations with a magnetic field, hysteresis appears in transitions from the diffuse to the contracted state and back.

A mechanism for differential sorting of the planar cell polarity proteins Frizzled6 and Vangl2 at the trans-Golgi network

In planar cell polarity (PCP), the epithelial cells are polarized along the plane of the cell surface perpendicular to the classical apical-basal axis, a process mediated by several conserved signaling receptors. Two PCP-signaling proteins, VANGL planar cell polarity protein 2 (Vangl2) and Frizzled6 (Fzd6), are located asymmetrically on opposite boundaries of the cell. Examining sorting of these two proteins at the trans-Golgi network (TGN), we demonstrated previously that the GTP-binding protein ADP-ribosylation factor-related protein 1 (Arfrp1) and the clathrin-associated adaptor protein complex 1 (AP-1) are required for Vangl2 transport from the TGN. In contrast, TGN export of Frizzled6 does not depend on Arfrp1 or AP-1. Here, to further investigate the TGN sorting process in mammalian cells, we reconstituted release of Vangl2 and Frizzled6 from the TGN into vesicles in vitro Immunoblotting of released vesicles indicated that Vangl2 and Frizzled6 exit the TGN in separate compartments. Knockdown analysis revealed that a clathrin adaptor, epsinR, regulates TGN export of Frizzled6 but not of Vangl2. Protein interaction analysis suggested that epsinR forms a stable complex with clathrin and that this complex interacts with a conserved polybasic motif in the Frizzled6 cytosolic domain to package Frizzled6 into transport vesicles. Moreover, we found that Frizzled6-epsinR binding dissociates epsinR from AP-1, which may separate these two cargo adaptors from each other to perform distinct cargo-sorting functions. Our results suggest that Vangl2 and Frizzled6 are packaged into separate vesicles that are regulated by different clathrin adaptors at the TGN, which may contribute to their asymmetric localizations.

Numerical study of turbulent separation bubbles with varying pressure gradient and Reynolds number.

A family of cases each containing a small separation bubble is treated by direct numerical simulation (DNS), varying two parameters: the severity of the pressure gradients, generated by suction and blowing across the opposite boundary, and the Reynolds number. Each flow contains a well-developed entry region with essentially zero pressure gradient, and all are adjusted to have the same value for the momentum thickness, extrapolated from the entry region to the centre of the separation bubble. Combined with fully defined boundary conditions this will make comparisons with other simulations and turbulence models rigorous; we present results for a set of eight Reynolds-averaged Navier-Stokes turbulence models. Even though the largest Reynolds number is approximately 5.5 times higher than in a similar DNS study we presented in 1997, the models have difficulties matching the DNS skin friction very closely even in the zero pressure gradient, which complicates their assessment. In the rest of the domain, the separation location per se is not particularly difficult to predict, and the most definite disagreement between DNS and models is near reattachment. Curiously, the better models tend to cluster together in their predictions of pressure and skin friction even when they deviate from the DNS, although their eddy-viscosity levels are widely different in the outer region near the bubble (or they do not rely on an eddy viscosity). Stratford's square-root law is satisfied by the velocity profiles, both at separation and reattachment. The Reynolds-number range covers a factor of two, with the Reynolds number based on the extrapolated momentum thickness equal to approximately 1500 and 3000. This allows tentative estimates of the improvements that even higher values will bring to the model comparisons. The solutions are used to assess models through pressure, skin friction and other measures; the flow fields are also used to produce effective eddy-viscosity targets for the models, thus guiding turbulence-modelling work in each region of the flow.

Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions.

We experimentally characterize the impact response of concentrated suspensions consisting of cornstarch and water. We observe that the suspensions support a large normal stress-on the order of MPa-with a delay after the impactor hits the suspension surface. We show that neither the delay nor the magnitude of the stress can yet be explained by either standard rheological models of shear thickening in terms of steady-state viscosities, or impact models based on added mass or other inertial effects. The stress increase occurs when a dynamically jammed region of the suspension in front of the impactor propagates to the opposite boundary of the container, which can support large stresses when it spans between solid boundaries. We present a constitutive relation for impact rheology to relate the force on the impactor to its displacement. This can be described in terms of an effective modulus but only after the delay required for the dynamically jammed region to span between solid boundaries. Both the modulus and the delay are reported as a function of impact velocity, fluid height, and weight fraction. We report in a companion paper the structure of the dynamically jammed region when it spans between the impactor and the opposite boundary [Allen et al., Phys. Rev. E 97, 052603 (2018)10.1103/PhysRevE.97.052603]. In a direct follow-up paper, we show that this constitutive model can be used to quantitatively predict, for example, the trajectory and penetration depth of the foot of a person walking or running on cornstarch and water [Mukhopadhyay et al., Phys. Rev. E 97, 052604 (2018)10.1103/PhysRevE.97.052604].

Submerged turbulent twin jets interacting with a free surface and a solid wall

The mean flow properties and turbulence characteristics of submerged twin jets interacting with a free surface or a solid wall are investigated using particle image velocimetry. The experiments were performed with two parallel round nozzles of transverse separation ratio, G/d = 2, where d is the nozzle diameter, and jet exit Reynolds number, Re = 5000. The effects of offset ratio and boundary condition were investigated by positioning one of the jets closer to a free surface or a solid wall at offset heights of 1d, 2d and 4d, while the other jet is sufficiently far from the opposite boundary. The results indicate that the decay rate of the jet closer to the boundary decreased with offset ratio but was independent of boundary condition. The effects of the boundary condition on the mean velocities and Reynolds stresses were confined to the immediate vicinity of the boundary. In this region, the transverse turbulence intensity and Reynolds shear stress were reduced, but the reduction was more dramatic near the wall than the free surface. Unlike the solid wall, the relaxation of the no-slip condition at the free surface and the reduction in transverse turbulence intensity gave rise to high streamwise turbulence intensity at the free surface. As offset ratio decreased, the surface mean velocities and turbulence intensities beyond the attachment point increased considerably. Two-point auto-correlations of the velocity fluctuations demonstrated that the spatial coherence of the turbulence structures increases with increasing offset ratio and the extents of the transverse auto-correlation, Rvv are reduced in the far field near the solid wall compared to the free surface cases.

Optimization of the graph model of the water conduit network, based on the approach of search space reducing

In this paper we present a heuristic approach, improving the efficiency of methods, used for creation of efficient architecture of water distribution networks. The essence of the approach is a procedure of search space reduction the by limiting the range of available pipe diameters that can be used for each edge of the network graph. In order to proceed the reduction, two opposite boundary scenarios for the distribution of flows are analysed, after which the resulting range is further narrowed by applying a flow rate limitation for each edge of the network. The first boundary scenario provides the most uniform distribution of the flow in the network, the opposite scenario created the net with the highest possible flow level. The parameters of both distributions are calculated by optimizing systems of quadratic functions in a confined space, which can be effectively performed with small time costs. This approach was used to modify the genetic algorithm (GA). The proposed GA provides a variable number of variants of each gene, according to the number of diameters in list, taking into account flow restrictions. The proposed approach was implemented to the evaluation of a well-known test network - the Hanoi water distribution network [1], the results of research were compared with a classical GA with an unlimited search space. On the test data, the proposed trip significantly reduced the search space and provided faster and more obvious convergence in comparison with the classical version of GA.

Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators

Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect within recently proposed Brillouin-Wigner perturbation theory that allows us to map a time-dependent problem into a stationary one. Our analysis reveals that both the gap and the components of the group velocity of the surface states can be tuned in a controllable fashion by adjusting the intensity of the driving field within an experimentally accessible range and demonstrate the effect of light-induced band inversion in the spectrum of the surface states for high enough values of the pump.

Long-Range Correlations Between Transmitted and Reected Fluxes of Electromagnetic Waves

We study the long-range spatial correlations between intensity fluctuations in speckles formed by multiply scattered light. The correlation function between intensity fluctuations at the opposite boundaries of the slab are analyzed under the conditions of circular polarization memory. It shown that, until the scattered light is depolarized completely, the polarization and scalar contributions to the correlation function are of the same order of magnitude. As the slab thickness increases, their ratio falls off in inverse proportion to the thickness.

The Relevance of Grain Dissection for Grain Size Reduction in Polar Ice: Insights from Numerical Models and Ice Core Microstructure Analysis

The flow of ice depends on the properties of the aggregate of individual ice crystals, such as grain size or lattice orientation distributions. Therefore, an understanding of the processes controlling ice micro-dynamics is needed to ultimately develop a physically based macroscopic ice flow law. We investigated the relevance of the process of grain dissection as a grain-size-modifying process in natural ice. For that purpose, we performed numerical multi-process microstructure modelling and analysed microstructure and crystallographic orientation maps from natural deep ice-core samples from the North Greenland Eemian Ice Drilling (NEEM) project. Full crystallographic orientations measured by electron backscatter diffraction (EBSD) have been used together with c-axis orientations using an optical technique (Fabric Analyser). Grain dissection is a feature of strain-induced grain boundary migration. During grain dissection, grain boundaries bulge into a neighbouring grain in an area of high dislocation energy and merge with the opposite grain boundary. This splits the high dislocation-energy grain into two parts, effectively decreasing the local grain size. Currently, grain size reduction in ice is thought to be achieved by either the progressive transformation from dislocation walls into new high-angle grain boundaries, called subgrain rotation or polygonisation, or bulging nucleation that is assisted by subgrain rotation. Both our time-resolved numerical modelling and NEEM ice core samples show that grain dissection is a common mechanism during ice deformation and can provide an efficient process to reduce grain sizes and counter-act dynamic grain-growth in addition to polygonisation or bulging nucleation. Thus, our results show that solely strain-induced boundary migration, in absence of subgrain rotation, can reduce grain sizes in polar ice, in particular if strain energy gradients are high. We describe the microstructural characteristics that can be used to identify grain dissection in natural microstructures.

Refined models of contact interaction of a thin plate with positioned on both sides deformable foundations

We consider a rectangular plate connected along the outer contour with an absolutely rigid and fixed support through a low tough elastic support elements included in the class of transversely soft foundations. It is assumed that the contact interaction of plate at its points of faces of the connection to the support elements there is no relative slip and separation, and the opposite boundary surfaces of the support elements are fixed. Deformation of plate’s mid-surface is described by geometrically nonlinear relationships of the classical plate theory based on the hypothesis of the Kirchhoff–Love (the first option), and refined Timoshenko model taking into account the transverse shear compression (second version). The mechanics of support elements is described by the linearized equations of three-dimensional theory of elasticity, which have been simplified in the framework of transversely soft layer model. By integrating the latter equations along the transverse coordinate and satisfying to the conditions of the kinematic coupling of plate to the support elements at their initial compression in the thickness direction, two-dimensional geometrical nonlinear equations and their corresponding boundary conditions have been introduced, which describe the contact interaction of elements of the concerned deformable system. Simplification of derived relationships for the case when foundations have a symmetrical layer structure is carried out.

Effect of texture and grain size on the residual stress of nanocrystalline thin films

Residual stresses develop in thin film interconnects mainly as a result of deposition conditions and multiple thermal loading cycles during the manufacturing flow. Understanding the relation between the distribution of residual stress and the interconnect microstructure is of key importance to manage the nucleation and growth of defects that can lead to failure under reliability testing and use conditions. Dislocation dynamics simulations are performed in nanocrystalline copper subjected to cyclic loading to quantify the distribution of residual stresses as a function of grain misorientation and grain size distribution. The outcomes of this work help to evaluate the effect of microstructure in thin films failure by identifying potential voiding sites. Furthermore, the simulations show how dislocation structures are influenced by texture and grain size distribution that affect the residual stress. For example, when dislocation loops reach the opposite grain boundary during loading, these dislocations remain locked during unloading.

Intrinsic spin Hall conductivity in three-dimensional topological insulator/normal insulator heterostructures

In the framework of an effective functional approach based on the k · p method, we study the combined effect of an interface potential and a thickness of a three-dimensional (3D) topological insulator (TI) thin film on the spin Hall conductivity in layered heterostructures comprising TI and normal insulator (NI) materials. We derive an effective two-dimensional (2D) Hamiltonian of a 3D TI thin film sandwiched between two NI slabs and define the applicability limits of approximations used. The energy gap and mass dispersion in the 2D Hamiltonian, originated from the hybridization between TI/NI interfacial bound electron states at the opposite boundaries of a TI film, are demonstrated to change sign with the TI film thickness and the interface potential strength. Finally, we argue that the spin Hall conductivity can efficiently be tuned varying the interface potential characteristics and TI film thickness.

The influence of an external electric field on the propagation of light waves in cholesteric liquid crystal cells

The specific features of light transmission in a cholesteric liquid crystal (LC) cell with a director rotated by 90° have been investigated. In this structure, where a light wave is incident at a large angle with respect to the LC surface, the light is reflected (refracted) in the LC layer near the opposite boundary. It is shown that the application of an electric field changes the character of extraordinary wave refraction, as a result of which light starts passing through a cell. The transmission threshold voltage is determined, and its dependence on the angle of incidence of light is obtained. The dependence of the transmitted-light intensity on the voltage across the cell is obtained as well. The same dependences are also derived by numerical calculations with allowance for the turning points and extinction.

An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient

Abstract The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.

Exotic topological states with Raman-induced spin-orbit coupling

We propose a simple experimental scheme to realize simultaneously the one-dimensional spin-orbit coupling and the staggered spin-flip in ultracold pseudospin-$1/2$ atomic Fermi gases trapped in square optical lattices. In the absence of interspecies interactions, the system supports gapped Chern insulators and gapless topological semimetal states. By turning on the $s$-wave interactions, a rich variety of gapped and gapless inhomogeneous topological superfluids can emerge. In particular, a gapped topological Fulde-Ferrell superfluid, in which the chiral edge states at opposite boundaries possess the same chirality, is predicted.

Heat flow visualization during mixed convection within entrapped porous triangular cavities with moving horizontal walls via heatline analysis

This paper analyzes the fluid and heat flow within entrapped porous triangular cavities involving various thermal boundary conditions (case 1: hot horizontal walls and cold inclined walls; case 2: cold horizontal walls and hot inclined walls). Finite element based numerical study has been performed for various values of Prandtl number (Prm=0.026 and 7.2), Darcy number (Dam=10-4-10-2), Reynolds number (Re=1-1000) at a high value of Grashof number (Gr=105). The upper cavity for the case 1 and the lower cavity for the case 2 show almost similar trends and vice versa based on the exact opposite thermal boundary conditions. Heat transfer is conduction dominant at Dam=10-4 involving both Prm whereas, convection heat transfer dominates at Dam=10-2 especially for Prm=7.2. Although the motion of the horizontal walls significantly influences the fluid flow field within the cavities, due to the decoupling between the fluid and thermal fields at the low Pem (Pem=0.026,0.26 and 2.6), conduction dominant heat transfer occurs. At the high Dam and Prm=7.2, a pair of symmetric streamline or heatline cells are seen for Re≤1 whereas, a bigger primary streamline or heatline cell is accompanied by a secondary streamline or heatline cell for 1⩽Re≤100. At 500⩽Re⩽1000, the single larger streamlines or heatline cells are seen especially for Prm=7.2 involving Dam=10-2. At Prm=0.026, the average heat transfer rates (Nut‾,Nub‾, Nul‾ and Nur‾) are almost constant with Re and Dam. At Prm=7.2, the larger magnitudes ofNut‾ and Nul‾ are observed for Re≤10 compared to those for Re=100 involving Dam⩾10-3 whereas, the magnitudes of Nur‾ are almost similar for all Re involving all Dam in the upper cavity (case 1) within Re⩽100. In the lower cavity (case 1), the magnitudes of Nub‾ and Nur‾ are larger for Re=100 whereas, the magnitudes of Nul‾ are larger for Re≤1 for almost entire range of Dam within Re≤100 involving Prm=7.2. The average Nusselt numbers are significantly larger at the high Re (Re=500 and 1000) involving all Dam (except for the horizontal walls involving Dam⩽8×10-4) in the cases 1 and 2 at Prm=7.2.

Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control

We solve a disturbance rejection problem for a general class of heterodirectional 1-D linear hyperbolic partial differential equations (PDEs). The disturbance enters at one boundary, while sensing and actuation is limited to the opposite boundary. We do this by combining a separately designed controller and observer into an output feedback controller, and proving stability of the overall closed loop system and exponential regulation of the control objective to zero. The theory is demonstrated in a simulation.

Time-independent wormholes

We study two-sided static wormholes with an exact Killing symmetry that translates both mouths of the wormhole toward the future. This differs from the familiar Kruskal wormhole whose time translation is future-directed only in one asymptotic region and is instead past-directed in the other. Our spacetimes are solutions to Einstein-Hilbert gravity sourced by scalar domain walls. Explicit examples are found in the thin wall approximation. More generally, we show that such spacetimes can arise in the presence of scalar fields with potentials that are $C^1$ but not $C^2$ and find examples numerically. However, solutions with an exact such Killing symmetry are forbidden when the scalar potential is smooth. Finally, we consider the mutual information of boundary regions associated with such wormholes in AdS/CFT. Although the interior of our solutions are unstable, we find that even mutual informations between opposite boundaries are already thermalized at any finite $t$ in the sense that they agree with the $t\rightarrow \infty$ limit of results from the familiar AdS-Kruskal solution.

Signal transmissibility in marginal granular materials

We examine the ‘transmissibility’ of a simulated two-dimensional pack of frictionless disks formed by confining dilute disks in a shrinking, periodic box to the point of mechanical stability. Two opposite boundaries are then removed, thus allowing a set of free motions. Small free displacements on one boundary then induce proportional displacements on the opposite boundary. Transmissibility is the ability to distinguish different perturbations by their distant responses. We assess transmissibility by successively identifying free orthonormal modes of motion that have the smallest distant responses. The last modes to be identified in this ‘pessimistic’ basis are the most transmissive. The transmitted amplitudes of these most transmissive modes fall off exponentially with mode number. Similar exponential falloff is seen in a simple elastic medium, though the responsible modes differ greatly in structure in the two systems. Thus the marginal pack’s transmissibility is qualitatively similar to that of a simple elastic medium. We compare our results with recent findings based on the projection of the space of free motion onto interior sites.