Fabrication of Net-Shape Functionally Graded Composites by Electrophoretic Deposition and Sintering: Modeling and Experimentation

It is shown that electrophoretic deposition (EPD) sintering is a technological sequence that is capable of producing net-shape bulk functionally graded materials (FGM). By controlling the shape of the deposition electrode, components of complex shapes can be obtained. To enable sintering net-shape capabilities, a novel optimization algorithm and procedure for the fabrication of net-shape functionally graded composites by EPD and sintering has been developed. The initial shape of the green specimen produced by EPD is designed in such a way that the required final shape is achieved after sintering-imposed distortions. The optimization is based on a special innovative iteration procedure that is derived from the solution of the inverse sintering problem: the sintering process is modeled in the “backward movie” regime using the continuum theory of sintering incorporated into a finite-element code. The experiments verifying the modeling approach include the synthesis by EPD of Al2O3/ZrO2 3-D (FGM) structures. In order to consolidate green parts shaped by EPD, post-EPD sintering is used. The fabricated deposits are characterized by optical and scanning electron microscopy. The experimentally observed shape change of the FGM specimen obtained by EPD and sintering is compared with theoretical predictions

Quantum field theory on manifolds with a boundary

We discuss quantum theory of fields \phi defined on (d+1)-dimensional manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which is a bilinear form in \phi defines the Gaussian measure with a covariance (Green function) {\cal G}. We discuss a relation between the quantum field theory with a fixed boundary condition \Phi and the theory defined by the Green function {\cal G}. It is shown that the latter results by an average over \Phi of the first. The QFT in (anti)de Sitter space is treated as an example. It is shown that quantum fields on the boundary are more regular than the ones on (anti) de Sitter space.Comment: The version to appear in Journal of Physics A, a discussion on the relation to other works in the field is adde

Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field

We obtain lower and upper bounds on the heat kernel and Green functions of the Schroedinger operator in a random Gaussian magnetic field and a fixed scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic upper bounds and the Jensen inequality for the lower bound. We show that if the covariance of the electromagnetic (vector) potential is increasing at large distances then the lower bound is decreasing exponentially fast for large distances and a large time.Comment: some technical improvements, new references, to appear in Journ.Phys.

Hyperentangled States

We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any quantum theory, they are dense in its state space. We also give prescriptions for constructing hyperentangled states that involve an arbitrarily large collection of systems.Comment: 23 pages, LaTeX, Submitted to Physical Review

The Enskog Process

The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the system at each fixed time is shown to be unique. The existence of a probability density for the time-marginals of the velocity is verified in the case where the initial condition is Gaussian, and is shown to be the density of an invariant measure.Comment: 38 page

Deformation aspects of anisotropic-porous bodies sintering

No abstract availabl

Optimal consumption and investment with liquid and illiquid assets

I consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio that consists of one bond, one liquid risky asset (no transaction costs), and one illiquid risky asset (proportional transaction costs). I fully characterize the optimal consumption and trading strategies in terms of the solution of the free boundary ordinary differential equation (ODE) with an integral constraint. I find an explicit characterization of model parameters for the well-posedness of the problem, and show that the problem is well posed if and only if there exists a shadow price process. Finally, I describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset