Search

This commentary addresses several issues raised in Charles Levin and Dawn Skorczewski’s probing and insightful paper (this issue) on the tragic story of Anne Sexton’s sexual relations with her anal...

This paper is devoted to the output-feedback stabilisation for a class of wave equations. Remarkably, only one boundary measurement corrupted by disturbance is available for feedback, and the bound...

In this paper, we study the classical problem of the first hitting time density to a moving boundary for a diffusion process, which satisfies the Cherkasov condition, and hence, can be reduced to a...

In this paper, a nonconforming finite element method (FEM) is proposed for the Neumann type boundary optimal control problems (OCPs) governed by elliptic equations. The state and adjoint state are ...

In this paper we present the development of numerical methods for two problems in chemical engineering: adsorption of carbon dioxide into phenyl glycidyl ether and diffusion and reaction processes in a porous catalyst. Both problems are modelled by systems of two coupled nonlinear ordinary differential equations. Dirichlet and Neumann type boundary conditions are considered. We develop the standard homotopy analysis method and the boundary-domain element method to solve for the unknown steady-state concentrations of reactants. The validity of the proposed methods is checked and demonstrated by numerical examples. Convergence rates are compared and the advantages and drawbacks of the proposed methods are discussed and compared to the Mathematica NDSOLVE solver. We show, that the proposed homotopy analysis method features exponential convergence rate and is highly accurate and efficient. As low as 6 terms are needed to reach error norms of Furthermore, the boundary-domain integral approach is also capable of solving the same problem very efficiently, using a very coarse computational mesh (21 nodes).

In this paper, we establish the asymptotic boundary of traveling waves (first-component) in a discrete diffusive epidemic model, whose existence is well-known. Meanwhile, we derive the nonexistence...

In this paper new stability theorems for Yee's Finite- Difference Time-Domain (FDTD) formulation are derived based on the energy method. A numerical energy expression is proposed. This numerical energy is dependent on the FDTD model's E and H field components. It is shown that if the numerical energy is bounded, then all the field components will also be bounded as the simulation proceeds. The theorems in this paper are inspired by similar results in nonlinear dynamical system. The new theorems are used to prove the stability of a FDTD model containing non-homogeneous dielectrics, perfect electric conductor (PEC) boundary, nonlinear dielectric and also linear/nonlinear lumped elements. The theorems are intended to complement the well-known Courant-Friedrich-Lewy (CFL) Criterion. Finally it is shown how the theorems can be used as a test, to determine if the formulation of new lumped element in FDTD is proper or not. A proper formulation will preserve the dynamical stability of the FDTD model. The finding reported in this paper will have implications in the manner stability analysis of FDTD algorithm is carried out in the future.

This paper develops a fault compensation scheme for a class of Euler–Bernoulli beam-ODE cascade systems to deal with certain boundary input faults, using a model transform-based backstepping contro...

In this paper, we consider the one-dimensional linear-KdV (Korteweg–de Vries) equation posed in bounded interval with delay boundary control acting on the left boundary by Dirichlet condition where...

In this paper, we consider a system of two viscoelastic equations with Dirichlet boundary conditions. Under suitable conditions, we establish a general decay result of solutions. Moreover, we prove...

In this paper we consider the interior inverse problem of identifying a rigid boundary of an annular infinitely long cylinder within which there is a stationary Oseen viscous fluid, by measuring various quantities such as the fluid velocity, fluid traction (stress force) and/or the pressure gradient on portions of the outer accessible boundary of the annular geometry. The inverse problems are nonlinear with respect to the variable polar radius parameterizing the unknown star-shaped obstacle. Although for the type of boundary data that we are considering the obstacle can be uniquely identified based on the principle of analytic continuation, its reconstruction is still unstable with respect to small errors in the measured data. In order to deal with this instability, the nonlinear Tikhonov regularization is employed. Obstacles of various shapes are numerically reconstructed using the method of fundamental solutions for approximating the fluid velocity and pressure combined with the MATLAB©© toolbox routine lsqnonlin for minimizing the nonlinear Tikhonov's regularization functional subject to simple bounds on the variables.

The boundary system of a firm is intended to set constraints to the behaviour of organisational participants and, by this, to affect decision-making in the direction of the firm’s overall objective. In growing firms, the boundary system is subject to a particular tension: balancing the search for new opportunities and innovation with behavioural constraints to deal with increasing size and intra-organisational complexity. Against this background, the paper studies the adaptation of the boundary system in growing firms. For this, an agent-based simulation based on the framework of NK fitness landscapes is employed which is a rather new approach in the domain of management control systems. The study controls for different levels of task complexity and for different styles in firms’ search for new opportunities in terms of exploitative, explorative or ambidextrous search strategies. The results suggest that the level of task complexity subtly interferes with the search strategy employed in respect of the emerging boundaries. In particular, results support the conjecture that growing task complexity leads to more coordination via hierarchy. However, the search strategy employed shapes the predominance of boundaries compared to less constraining modes of coordination granting higher levels of autonomy to subordinates.

This paper is devoted to $C^2$ a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments, existence results in space forms are established for prescribed Gauss curvature equation under the assumption of a strictly locally convex subsolution., Comment: 30 pages, final accepted version with many updates

In this paper, we study the general decay rate of a nonlinear Bresse system with memory conditions on part of the boundary. Without imposing u0=v0=w0=0 on Γ1, an explicit general decay rate results...

In this paper, we prove convexity of super-level sets of a semi-linear PDE with a non-monotone right-hand side, and with a free boundary (1) Δu=χ{0

In this paper, we study the existence of positive solutions to a nonlinear elliptic inclusion problem driven by an elliptic differential operator with Dirichlet boundary and a multivalued term depe...

This paper examines {101¯2} twin nucleation and growth under uniaxial tension at the prismatic/basal boundary through both molecular dynamics simulations and continuum mechanics modelling. Our resu...

In this paper, we present dynamics analysis and vibration control for a nanoscale beam. The nanobeam is modelled based on the modified couple stress theory which incorporates small length scale eff...

This paper considers the fault-tolerant control (FTC) problem for switched systems described by linear hyperbolic partial differential equations with the process and boundary faults. The effect of ...

In this paper, we study the inverse problem of reconstructing an interior interface appearing in an elliptic equation in a bounded domain Ω from the knowledge of the boundary measurements. This pro...

In this paper, the boundary control problem of stochastic reaction-diffusion systems (SRDSs) is studied. First, a distribution controller is designed, and a sufficient condition is established to a...

In this paper, it is proposed an efficient GUI for the treatment of two-dimensional physical geometric models and the generation of mixed meshes of boundary and finite elements, respectively, BEM a...

In this paper we investigate the existence of nodal solutions to elliptic problem involving the GJMS operators on Riemannian manifold with boundary, Comment: 13 pages

In this paper, we consider a Timoshenko system subject to viscoelastic damping acting on a part of the boundary. We use a general assumption on the relaxation function and establish explicit energy...

It is well known that typical Hamiltonian systems have divided phase space consisting of regions with regular dynamics on KAM tori and region(s) with chaotic dynamics called chaotic sea(s). This complex structure makes rigorous analysis of such systems virtually impossible and significantly complicates numerical exploration of their dynamical properties. In this paper we outline a new approach for the analysis of Hamiltonian systems with divided phase space. These systems are approximated by a sequence of Hamiltonian systems having an increasing (but finite) number of KAM islands. The islands in the approximating systems are sub-islands of the islands in the initial system with an infinite number of KAM-islands. We apply this approach to two-dimensional billiards and demonstrate that it works. In particular the statistical characteristics of the approximating systems tend to the ones for the whole system when the number of islands in the approximating systems grows. Therefore our approach opens up a new way for numerical and analytical studies of the dynamics of Hamiltonian systems with divided phase space., Comment: 8 pages (RevTex), 9 figures; version as accepted by Experimental Mathematics

In this paper, we study a parameter identification problem for elliptic partial differential equations. We reconstruct the coefficient with additional boundary measurements, including both Dirichle...

In this paper, lattice Boltzmann method is used for the simulation of two-dimensional flow over an immersed solid body using external boundary force. Fluid simulation is performed using the Euleria...

Approximate analytical solution of point source diffraction from a strip satisfying a recently introduced boundary condition is presented in this paper. Both separated and interacted fields are com...

In this paper, vibration reduction of a viscoelastic flexible beam conveying fluid with variable velocity is studied. A control is designed at the top boundary of the beam based on original infinit...

Building edge or boundary extraction is always one of the most important issues for remote sensing application. In order to accurately extract the edges or boundary of a building, there are usually two problems. Firstly, strong interference edges from backgrounds such as road, trees and others cannot be avoided. Secondly, it is more difficult for the lower contrast building edges to be detected. In order to address these two problems to a certain extent, a Robust Building Boundary Extraction method (DS-RBBE) is proposed in this paper, which is based on dual-scale sparse SVM classification and decision fusion. First, training samples are automatically selected by employing prior knowledge of main direction and linearity information. Next, a sparse SVM classifier is trained using the dual-scale local edge features of the training samples. And then, the trained sparse SVM is employed to classify all extracted edges. Finally, a dual-scale decision fusion strategy is performed for final building bounda...

In this paper, we are concerned with boundary output feedback stabilisation of two parallel coupled string equations with matched external disturbance. By the method proposed by Feng and Guo in IEE...

In the recent paper [E. C. Balreira, S. Elaydi, and R. Luis, J. Differ. Equ. Appl. 23 (2017), pp. 2037-2071], Balreira, Elaydi and Luis established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luis' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.

The paper reports the experimental investigation of free surface turbulent flow under control laboratory flume conditions over a bed artificially roughened by cubes arranged periodically and symmet...

This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified u...

The paper, ‘Microwave generation by excitation of a plasma-filled slow-wave structure’ written by Wu et al. in 1996, analysed the configuration as shown in figure 1. In this paper, equation (26) is the boundary condition of boundary 1 shown in figure 1, and equation (35) is the boundary condition of boundary 2 shown in figure 1. The above two equations are all derived from

The paper establishes the asymptotic distribution of the conditional maximum likelihood estimator for integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) processes of co...

An out-of-plane coordinate transformation can avoid singular materials in a two-dimensional electromagnetic cloak. Based on numerical simulations of elliptical cylinders, in this paper we show that...

In this paper, the gas dynamics within the pipelines is written as a wave repetitive process, and modified in a way that the dynamics is driven by the boundary conditions. We study controllability of the system through boundary control and every agent, as well as observability of the system being steered by initial and boundary data. Next, we obtain sufficient criteria for the existence and uniqueness of boundary equilibrium controls. From the point of view of some applications, e.g. in high pressure gas pipeline management, it seems to make sense to consider boundary data controls. The same problem is then extended to its infinite counterpart since it may run infinitely and, in this case, we become interested in studying its stabilisation.

The problem of light scattering by a homogeneous sphere above a plane boundary is considered in this paper. Hankel transformation and Erdelyi's formula are used to satisfy the boundary conditions o...

In this paper, we give a theoretical and numerical analysis of a model for small vertical vibrations of an elastic membrane coupled with a heat equation and subject to linear mixed boundary...

This paper studies the well-posedness and exponential stability of two-dimensional vibration model of a curved beam with tip mass under linear boundary control. The control task is to stabilise the...

In the paper we consider a stationary diffusion problem described by the Poisson equation. The problem is considered in a model domain, chosen as a half disk. Classical Dirichlet boundary condition...

In this paper, an optimal boundary control problem for a distributed elliptic system on Lipschitz domains with boundary homogeneous Dirichlet conditions and independently with Neumann conditions is analysed. The necessary and sufficient optimality conditions for such problems with the quadratic cost functionals are obtained. A Jacobi spectral Galerkin method is introduced to develop a direct solution technique for the numerical solution of elliptic problems subject to Dirichlet and Neumann conditions in one and two dimensions. The numerical examples are included to demonstrate the validity and applicability of the techniques and comparison is made with the existing results. The method is easy to implement and yields very accurate results.

In this paper, the stabilization problem of one-dimensional Schrodinger equation with boundary disturbance is concerned. The variable structure control technique is adopted to design the no...

This paper studies the low-speed manoeuvring problem for autono-mous ground vehicles operating in complex static environments. Making use of the intrinsic property of a fluid to naturally find its way to an outflow destination, a novel guidance method is proposed. In this approach, a reference flow field is calculated numerically through Computational Fluid Dynamics, based on which both the reference path topology and the steering reference to achieve the path are derived in a single process. Steering control considers three constraints: obstacle and boundary avoidance, rigidity of the vehicle, plus the non-holonomic velocity constraints due to the steering system. The influences of the parameters used during the flow field simulation and the control algorithm are discussed through numerical cases. A divergency field is defined to evaluate the quality of the flow field in guiding the vehicle. This is used to identify any problematic branching features of the flow, and control is adapted in the neighbourhood of such branching features to resolve possible ambiguities in the control reference. Results demonstrate the effectiveness of the method in finding smooth and feasible motion paths, even in complex environments

The stochastic-alpha-beta-rho (SABR) model is widely used in fixed income and foreign exchange markets as a benchmark. The underlying process may hit zero with a positive probability and therefore an absorbing boundary at zero should be specified to avoid arbitrage opportunities. However, a variety of numerical methods choose to ignore the boundary condition to maintain the tractability. This paper develops a new principle of not feeling the boundary to quantify the impact of this boundary condition to the distribution of underlying prices. It shows that the probability of the SABR hitting zero decays to 0 exponentially as the time horizon shrinks. Applying this principle, we further show that conditional on the volatility process, the distribution of the underlying process can be approximated by that of a time-changed Bessel process with an exponentially negligible error. This discovery provides a theoretical justification for many almost exact simulation algorithms for the SABR model in the literature. Numerical experiments are also presented to support our results.

This paper discusses grasping and orientation control of an object by dual one-link Timoshenko arms. The control objective is to control the grasping force and the orientation of the object, and to...

Describing phenomena of interest as a system is valuable because system science methodologies are applicable for the analysis. This paper presents a model to describe and analyze phenomena which pr...

This paper deals with the design of a boundary optimal controller for a general model of parabolic–hyperbolic PDEs coupled with an ODE. The augmented infinite-dimensional state-space representation...

In this paper, numerical boundary stabilisation of a non-uniform hyperbolic system of balance laws is studied. For the numerical discretisation of the balance laws, a first order explicit upwind sc...