124 research outputs found
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 âbackward movieâ 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
Microwave sintering of complex shapes: From multiphysics simulation to improvements of process scalability
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
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