34,971 research outputs found

### Mathematical models of martensitic microstructure

Martensitic microstructures are studied using variational models based on nonlinear elasticity. Some relevant mathematical tools from nonlinear analysis are described, and applications given to austenite-martensite interfaces and related topics

### B->gamma e nu Transitions from QCD Sum Rules

B->gamma e nu transitions have recently been studied in the framework of QCD
factorization. The attractiveness of this channel for such an analysis lies in
the fact that, at least in the heavy quark limit, the only hadron involved is
the B meson itself, so one expects a very simple description of the form factor
in terms of a convolution of the B meson distribution amplitude with a
perturbative kernel. This description, however, does not include contributions
suppressed by powers of the b quark mass. In this letter, we calculate
corrections to the factorized expression which are induced by the ``soft''
hadronic component of the photon. We demonstrate that the power-suppression of
these terms is numerically not effective for physical values of the $b$ quark
mass and that they increase the form factor by about 30% at zero momentum
transfer. We also derive a sum rule for lambda_B, the first negative moment of
the B meson distribution amplitude, and find lambda_B = 0.6 GeV (to leading
order in QCD).Comment: 13 pages, 5 figure

### Ben Bernanke and the Zero Bound

From 2000 to 2003, when Ben Bernanke was a professor and then a Fed Governor, he wrote extensively about monetary policy at the zero bound on interest rates. He advocated aggressive stimulus policies, such as a money-financed tax cut and an inflation target of 3-4%. Yet, since U.S. interest rates hit zero in 2008, the Fed under Chairman Bernanke has taken more cautious actions. This paper asks when and why Bernanke changed his mind about zero-bound policy. The answer, at one level, is that he was influenced by analysis from the Fed staff that was presented at the FOMC meeting of June 2003. This answer raises another question: why did the staff's views influence Bernanke so strongly? I seek answers to this question in the social psychology literature on group decision-making.

### Partial regularity and smooth topology-preserving approximations of rough domains

For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$,
the properties are studied of fields of `good directions', that is the
directions with respect to which $\partial\Omega$ can be locally represented as
the graph of a continuous function. For any such domain there is a canonical
smooth field of good directions defined in a suitable neighbourhood of
$\partial\Omega$, in terms of which a corresponding flow can be defined. Using
this flow it is shown that $\Omega$ can be approximated from the inside and the
outside by diffeomorphic domains of class $C^\infty$. Whether or not the image
of a general continuous field of good directions (pseudonormals) defined on
$\partial\Omega$ is the whole of $\mathbb{S}^{m-1}$ is shown to depend on the
topology of $\Omega$. These considerations are used to prove that if $m=2,3$,
or if $\Omega$ has nonzero Euler characteristic, there is a point
$P\in\partial\Omega$ in the neighbourhood of which $\partial\Omega$ is
Lipschitz. The results provide new information even for more regular domains,
with Lipschitz or smooth boundaries.Comment: Final version appeared in Calc. Var PDE 56, Issue 1, 201

### Nematic liquid crystals : from Maier-Saupe to a continuum theory

We define a continuum energy functional in terms of the mean-field Maier-Saupe free energy, that describes both spatially homogeneous and inhomogeneous systems. The Maier-Saupe theory defines the main macroscopic variable, the Q-tensor order parameter, in terms of the second moment of a probability distribution function. This definition requires the eigenvalues of Q to be bounded both from below and above. We define a thermotropic bulk potential which blows up whenever the eigenvalues tend to these lower and upper bounds. This is in contrast to the Landau-de Gennes theory which has no such penalization. We study the asymptotics of this bulk potential in different regimes and discuss phase transitions predicted by this model

### Quasistatic nonlinear viscoelasticity and gradient flows

We consider the equation of motion for one-dimensional nonlinear
viscoelasticity of strain-rate type under the assumption that the stored-energy
function is $\lambda$-convex, which allows for solid phase transformations. We
formulate this problem as a gradient flow, leading to existence and uniqueness
of solutions. By approximating general initial data by those in which the
deformation gradient takes only finitely many values, we show that under
suitable hypotheses on the stored-energy function the deformation gradient is
instantaneously bounded and bounded away from zero. Finally, we discuss the
open problem of showing that every solution converges to an equilibrium state
as time $t \to \infty$ and prove convergence to equilibrium under a
nondegeneracy condition. We show that this condition is satisfied in particular
for any real analytic cubic-like stress-strain function.Comment: 40 pages, 1 figur

### Handbook of Higher Twist Distribution Amplitudes of Vector Mesons in QCD

We give a summary of existing results on higher twist distribution amplitudes
of vector mesons in QCD. Special attention is payed to meson mass corrections
which turn out to be large. A ``shopping list'' is presented of most important
nonperturbative parameters which enter distribution amplitudes.Comment: Talk presented by V.M. Braun at 3rd workshop ``Continuous Advances in
QCD'', Minneapolis, MN, USA, April 16--19, 1998; 17 pages, 2 figures,
requires sprocl.sty (included

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