Information obtained from multiple sensory modalities, such as vision and touch, is integrated to yield a holistic percept. As a haptic approach usually involves cross-modal sensory experiences, it is necessary to develop an apparatus that can characterize how a biological system integrates visual-tactile sensory information as well as how a robotic device infers object information emanating from both vision and touch. In the present study, we develop a novel visual-tactile cross-modal integration stimulator that consists of an LED panel to present visual stimuli and a tactile stimulator with three degrees of freedom that can present tactile motion stimuli with arbitrary motion direction, speed, and indentation depth in the skin. The apparatus can present cross-modal stimuli in which the spatial locations of visual and tactile stimulations are perfectly aligned. We presented visual-tactile stimuli in which the visual and tactile directions were either congruent or incongruent, and human observers reported the perceived visual direction of motion. Results showed that perceived direction of visual motion can be biased by the direction of tactile motion when visual signals are weakened. The results also showed that the visual-tactile motion integration follows the rule of temporal congruency of multi-modal inputs, a fundamental property known for cross-modal integration.

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Abstract. In this paper we investigate the initial and initial-boundary value problems for strictly hyperbolic balance laws with time-evolution of flux and source. Such nonlinear balance laws arise in, for instance, gas dynamics equations in time-dependent ducts and nozzles, shallow water equations, lanes-changing model in traffic flow and Einstein's field equations in a spherically symmetric spacetime. To account for the time dependence of flux and source, we introduce the perturbed Riemann and boundary Riemann problems. Such Riemann problems have unique solutions within elementary waves and an additional family of waves. Based on the work of [12,13], a new version of Glimm scheme is introduced and its stability is established by modified interaction estimates. Finally, the existence of global entropy solutions is achieved by showing the consistency of scheme, the weak convergence of source term and the entropy inequalities.

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In this paper, we study the initial-boundary value problem of compressible Euler equations with friction and heating that model the combined Fanno-Rayleigh flows through symmetric variable area nozzles, in particular, the case of contracting nozzles is considered. A new version of a generalized Glimm scheme (GGS) is presented for establishing the global existence of transonic entropy solutions. Modified Riemann and boundary Riemann solutions are applied to design this GGS which obtained by the contraction matrices acting on the homogeneous Riemann (or boundary-Riemann) solutions. The extended Glimm-Goodman wave interaction estimates are investigated for ensuring the stability of the scheme and the positivity of gas velocity that leads to the existence of the weak solution. The limit of approximation solutions serves as an entropy solution. Moreover, a quantitative relation between the shape of the nozzle, the friction, and the heat is proposed. Under this relation, the global existence of weak solution for contracting nozzle is achieved. Simulations of contraction-expansion and expansion-contraction nozzles are presented to illustrate the relevant theoretical results.