Shock wave focusing using geometrical shock dynamics

A finite-difference numerical method for geometrical shock dynamics has been developed based on the analogy between the nonlinear ray equations and the supersonic potential equation. The method has proven to be an efficient and inexpensive tool for approximately analyzing the focusing of weak shock waves, where complex nonlinear wave interactions occur over a large range of physical scales. The numerical results exhibit the qualitative behavior of strong, moderate, and weak shock focusing observed experimentally. The physical mechanisms that are influenced by aperture angle and shock strength are properly represented by geometrical shock dynamics. Comparison with experimental measurements of the location at which maximum shock pressure occurs shows good agreement, but the maximum pressure at focus is overestimated by about 60%. This error, though large, is acceptable when the speed and low cost of the method is taken into consideration. The error is primarily due to the under prediction of disturbance speed on weak shock fronts. Adequate resolution of the focal region proves to be particularly important to properly judge the validity of shock dynamics theory, under-resolution leading to overly optimistic conclusions

Variable-free exploration of stochastic models: a gene regulatory network example

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [13], we assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e, effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [9] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free coarse-grained, computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.Comment: 26 pages, 9 figure

Power-law decay of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state

The hydrodynamic part of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state has been calculated by using mode-coupling theory for a finite system with periodic boundary conditions. The existence of the shearing instability, leading to a divergent behavior of the velocity flow fluctuations, is taken into account. A time region in which the velocity autocorrelation function exhibits a power law decay, when time is measured by the number of collisions per particle, has been been identified. Also the explicit form of the exponential asymptotic long time decay has been obtained. The theoretical prediction for the power law decay is compared with molecular dynamics simulation results, and a good agreement is found, after taking into account finite size corrections. The effects of approaching the shearing instability are also explored

Dynamics of a viscous vesicle in linear flows

An analytical theory is developed to describe the dynamics of a closed lipid bilayer membrane (vesicle) freely suspended in a general linear flow. Considering a nearly spherical shape, the solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, incompressibility and resistance to bending. The constraint for a fixed total area leads to a non-linear shape evolution equation at leading order. As a result two regimes of vesicle behavior, tank-treading and tumbling, are predicted depending on the viscosity contrast between interior and exterior fluid. Below a critical viscosity contrast, which depends on the excess area, the vesicle deforms into a tank--treading ellipsoid, whose orientation angle with respect to the flow direction is independent of the membrane bending rigidity. In the tumbling regime, the vesicle exhibits periodic shape deformations with a frequency that increases with the viscosity contrast. Non-Newtonian rheology such as normal stresses is predicted for a dilute suspension of vesicles. The theory is in good agreement with published experimental data for vesicle behavior in simple shear flow

How corporate governance and globalization can run afoul of the law and good practices in business: The Enron's disgraceful affair.

The purpose of this paper is to set out the Enron’s demise into the perspective of Corporate and Global Governance. To accomplish this target, the incremental cash flow model is expanded to give room for governance issues, while a functional introduction to information sets is developed, including bounded rationality, asymmetric information, opportunistic behavior, transaction costs and agency problems. Then, corporate governance is linked to globalization by means of some recent approaches that go beyond a narrow economic mindset to encompass a far-reaching dynamics. Taking advantage of such background, the Enron’s story is tracked down over a span of fifteen years since its starting day to its bankruptcy filing. Leading events are explained from corporate and global governance viewpoints, while an in-depth analysis is worked out on Enron’s complex game of deception and breach of contracts: the outrageous affiliated limited partnerships, the lavish pay package to its executives, the involvement with global governance through the Indian affair and the Taliban connection. It is for the incremental cash flow model to explain malfeasance with cash flows from assets, and how cash flows to creditors were actually contrived. Furthermore, to highlight how cash flows were swindled from stockholders and, finally, how Enron made wheeling and dealing with cash flows on behalf of its managers.corporate governance, global governance, incremental cash flow model, globalization, information sets, good practices.