Experiments are reported that involved spatial judgments of planar surfaces that had contradictory stereo and monocular information. Tasks included comparing the relative depths of two points on the depicted surface and judging the surface's apparent spatial orientation. It was found that for planar surfaces the 3D perception was dominated by the monocular interpretation, despite the strongly c...

The absorption of compressional and shear waves in many viscoelastic solids has been experimentally shown to follow a frequency power law. It is now well established that this type of loss behavior can be modeled using fractional derivatives. However, previous fractional constitutive equations for viscoelastic media are based on temporal fractional derivatives. These operators are non-local in ...

In order to reconstruct spatial curves from discrete electronic sensor data, two alternative C Pythagorean–hodograph (PH) quintic spline formulations are proposed, interpolating given spatial data subject to prescribed contraints on the arc length of each spline segment. The first approach is concerned with the interpolation of a sequence of points, while the second addresses the interpolation ...

We report the analysis of the statistics of the phase fluctuations in the coda of earthquakes recorded during a temporary experiment deployed at Pinyon Flats Observatory, California. The observed distributions of the spatial derivatives of the phase in the seismic coda exhibit universal power-law decays whose exponents agree accurately with circular Gaussian statistics. The correlation function...

This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by time-dependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differential-algebraic equations (DAEs) with a package for large-scale optimization based on sequential quadratic programming (SQP). DASOPT is intended fo...

In this paper, the identification of a class of multiscale spatio-temporal dynamical systems, which incorporate multiple spatial scales, from observations is studied. The proposed approach is a combination of Adams integration and an orthogonal least squares algorithm, in which the multiscale operators are expanded, using polynomials as basis functions, and the spatial derivatives are estimated...

In this paper, a discrete singular convolution (DSC) algorithm is introduced to solve Fisher’s equation, to which obtaining an accurate and reliable traveling wave solution is a challenging numerical problem. Two novel numerical treatments, a moving frame scheme and a new asymptotic scheme, are designed to overcome the subtle difficulties involved in the numerical solution of Fisher’s equation....

This paper presents a nonstationary structural spatial model that explicitly sets the data to evolve across a rectangular lattice constrained by secondorder smoothing restrictions. The model exemplifies the concept of model-based spatial smoothing and, in particular, it provides a rationale for the popular discrete thin-plate smoothing method. We show how to use a frequency-domain approach in o...

We propose a new extension of Kalman filtering for continuous-discrete systems with nonlinear state-space models that we name as the level set filter (LSKF). The LSKF assumes probability distribution can be approximated Gaussian and updates through time-update step measurement-update step. improves compared to existing methods, such cubature (CD-CKF), by reformulating underlying Fokker-Planck e...

We consider non degenerate Brownian SDEs with Hölder continuous in space diffusion coefficient and unbounded drift linear growth. derive two sided bounds for the associated density pointwise controls of its derivatives up to order under some additional spatial continuity assumptions on drift. Importantly, estimates reflect transport initial condition by through an auxiliary, possibly regularize...