Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Using ground reaction force to predict knee kinetic asymmetry following anterior cruciate ligament reconstruction.

Asymmetries in sagittal plane knee kinetics have been identified as a risk factor for anterior cruciate ligament (ACL) re-injury. Clinical tools are needed to identify the asymmetries. This study examined the relationships between knee kinetic asymmetries and ground reaction force (GRF) asymmetries during athletic tasks in adolescent patients following ACL reconstruction (ACL-R). Kinematic and GRF data were collected during a stop-jump task and a side-cutting task for 23 patients. Asymmetry indices between the surgical and non-surgical limbs were calculated for GRF and knee kinetic variables. For the stop-jump task, knee kinetics asymmetry indices were correlated with all GRF asymmetry indices (P < 0.05), except for loading rate. Vertical GRF impulse asymmetry index predicted peak knee moment, average knee moment, and knee work (R(2)  ≥ 0.78, P < 0.01) asymmetry indices. For the side-cutting tasks, knee kinetic asymmetry indices were correlated with the peak propulsion vertical GRF and vertical GRF impulse asymmetry indices (P < 0.05). Vertical GRF impulse asymmetry index predicted peak knee moment, average knee moment, and knee work (R(2)  ≥ 0.55, P < 0.01) asymmetry indices. The vertical GRF asymmetries may be a viable surrogate for knee kinetic asymmetries and therefore may assist in optimizing rehabilitation outcomes and minimizing re-injury rates.

Visual Disobedience: The Geopolitics of Experimental Art in Central America, 1990-Present

This dissertation centers on the relationship between art and politics in postwar Central America as materialized in the specific issues of racial and gendered violence that derive from the region's geopolitical location and history. It argues that the decade of the 1990s marks a moment of change in the region's cultural infrastructure, both institutionally and conceptually, in which artists seek a new visual language of experimental art practices to articulate and conceptualize a critical understanding of place, experience and knowledge. It posits that visual and conceptual manifestations of violence in Central American performance, conceptual art and installation extend beyond a critique of the state, and beyond the scope of political parties in perpetuating violent circumstances in these countries. It argues that instead artists use experimental practices in art to locate manifestations of racial violence in an historical system of domination and as a legacy of colonialism still witnessed, lived, and learned by multiple subjectivities in the region. In this postwar period artists move beyond the cold-war rhetoric of the previous decades and instead root the current social and political injustices in what Aníbal Quijano calls the `coloniality of power.' Through an engagement of decolonial methodologies, this dissertation challenges the label "political art" in Central America and offers what I call "visual disobedience" as a response to the coloniality of seeing. I posit that visual colonization is yet another aspect of the coloniality of power and indispensable to projects of decolonization. It offers an analysis of various works to show how visual disobedience responds specifically to racial and gender violence and the equally violent colonization of visuality in Mesoamerica. Such geopolitical critiques through art unmask themes specific to life and identity in contemporary Central America, from indigenous genocide, femicide, transnational gangs, to mass imprisonments and a new wave of social cleansing. I propose that Central American artists--beyond an anti-colonial stance--are engaging in visual disobedience so as to construct decolonial epistemologies in art, through art, and as art as decolonial gestures for healing.

Local kinetic interpretation of entropy production through reversed diffusion.

The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching formula for the steady-state probability density function along with a geometric interpretation of the fluctuation-dissipation relation. Finally, the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties, and a stochastic differential equation for entropy production is obtained using the Girsanov theorem for reversed diffusion. The results are illustrated for the Ornstein-Uhlenbeck process.