Radially symmetric cavitation for hyperelastic materials
Randomly forced vibrations of a string
Rank 1 convex hulls of isotropic functions in dimension 2 by 2
Let be a rotationally invariant (with respect to the proper orthogonal group) function defined on the set of all by matrices. Based on conditions for the rank 1 convexity of in terms of signed invariants of (to be defined below), an iterative procedure is given for calculating the rank 1 convex hull of a rotationally invariant function. A special case in which the procedure terminates after the second step is determined and examples of the actual calculations are given.
Rank-one connections at infinity and quasiconvex hulls.
Rate independent Kurzweil processes
The Kurzweil integral technique is applied to a class of rate independent processes with convex energy and discontinuous inputs. We prove existence, uniqueness, and continuous data dependence of solutions in spaces. It is shown that in the context of elastoplasticity, the Kurzweil solutions coincide with natural limits of viscous regularizations when the viscosity coefficient tends to zero. The discontinuities produce an additional positive dissipation term, which is not homogeneous of degree...
Rayleigh wave scattering at the foot of a mountain.
Rayleigh waves in a thermoelastic granular medium under initial stress.
Rayleigh waves in a viscoelastic half-space under initial hydrostatic stress in the presence of the temperature field.
RBF Based Meshless Method for Large Scale Shallow Water Simulations: Experimental Validation
2D shallow water equations with depth-averaged k−ε model is considered. A meshless method based on multiquadric radial basis functions is described. This methods is based on the collocation formulation and does not require the generation of a grid and any integral evaluation. The application of this method to a flow in horizontal channel, taken as an experimental device, is presented. The results of computations are compared with experimental data...
Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping
We show that the set of nonnegative equilibrium-like states, namely, like of the semilinear vibrating string that can be reached from any non-zero initial state , by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace of . Our main results deal with nonlinear terms which admit at most the linear growth at infinity in and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.
Recent advancements in fractal geometric-based nonlinear time series solutions to the micro-quasistatic thermoviscoelastic creep for rough surfaces in contact.
Reconstruction of the parameters of a system of connected beams from dynamic boundary measurements.
Recovering a time- and space-dependent kernel in a hyperbolic integro-differential equation from a restricted Dirichlet-to-Neumann operator.
Rectangular thin elastic plate with edges “remaining straight‟ during the deformation
Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems
We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....
Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems
We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....
Reduction of boundary value problem to Possio integral equation in theoretical aeroelasticity.
Reflection and transmission of elastic waves at viscous liquid/micropolar elastic solid interface.
Reflection and transmission of seismic waves under initial stress at the earth's core-mantle boundary.
Regular Splittings and the Discrete Neumann Problem.