arXiv subjects

Joshua E. S. Socolar

Publications and source records attributed to Joshua E. S. Socolar.

42 records · Page 3Linked to original sources

arXiv1998

Force distribution in a scalar model for non-cohesive granular material

We study a scalar lattice model for inter-grain forces in static, non-cohesive, granular materials, obtaining two primary results. (i) The applied stress as a function of overall strain shows a power law dependence with a nontrivial exponent, which moreover varies with system geometry. (ii) Probability distributions for forces on individual grains appear Gaussian at all stages of compression, showing no evidence of exponential tails. With regard to both results, we identify correlations responsible for deviations from previously suggested theories.

cond-mat.soft↗

arXiv1997

Failure of linear control in noisy coupled map lattices

We study a 1D ring of diffusively coupled logistic maps in the vicinity of an unstable, spatially homogeneous fixed point. The failure of linear controllers due to additive noise is discussed with the aim of clarifying the failure mechanism. A criterion is suggested for estimating the noise level that can be tolerated by the given controller. The criterion implies the loss of control for surprisingly low noise levels in certain cases of interest, and accurately accounts for the results of numerical experiments over a broad range of parameter values. Previous results of Grigoriev, et al (Phys. Rev. Lett., 79, 2795) are reviewed and compared with our numerical and analytical results.

chao-dyn↗

arXiv1997

Average stresses and force fluctuations in non-cohesive granular materials

A lattice model is presented for investigating the fluctuations in static granular materials under gravitationally induced stress. The model is similar in spirit to the scalar q-model of Coppersmith et al., but ensures balance of all components of forces and torques at each site. The geometric randomness in real granular materials is modeled by choosing random variables at each site, consistent with the assumption of cohesionless grains. Configurations of the model can be generated rapidly, allowing the statistical study of relatively large systems. For a 2D system with rough walls, the model generates configurations consistent with continuum theories for the average stresses (unlike the q-model) without requiring the assumption of a constitutive relation. For a 2D system with periodic boundary conditions, the model generates single-grain force distributions similar to those obtained from the q-model with a singular distribution of q's.

cond-mat↗

arXiv1996

Controlling extended systems with spatially filtered, time-delayed feedback

We investigate a control technique for spatially extended systems combining spatial filtering with a previously studied form of time-delay feedback. The scheme is naturally suited to real-time control of optical systems. We apply the control scheme to a model of a transversely extended semiconductor laser in which a desirable, coherent traveling wave state exists, but is a member of a nowhere stable family. Our scheme stabilizes this state, and directs the system towards it from realistic, distant and noisy initial conditions. As confirmed by numerical simulation, a linear stability analysis about the controlled state accurately predicts when the scheme is successful, and illustrates some key features of the control including the individual merit of, and interplay between, the spatial and temporal degrees of freedom in the control.

chao-dyn↗

arXiv1996

Controlling spatiotemporal dynamics with time-delay feedback

We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external generation of an ideal reference state and can suppress both absolute and convective instabilities. As an example, we analyze the complex Ginzburg-Landau equation in one dimension, showing how the time-delay feedback enlarges the stability domain for travelling waves.

chao-dyn↗

arXiv1995

Stability of periodic orbits controlled by time-delay feedback

Extended time-delay auto-synchronization (ETDAS) is a promising technique for stabilizing unstable periodic orbits in low-dimensional dynamical systems. The technique involves continuous feedback of signals delayed by multiples of the orbit's period in a manner that is especially well-suited for fast systems and optical implementation. We show how to analyze the stability of a given implementation of ETDAS without explicit integration of time-delay equations. To illustrate the method and point out some nontrivial features of ETDAS, we obtain the domain of control for a period-one orbit of the driven, damped pendulum.

chao-dyn↗