The $$SO(3,1) \times U(1)$$-gauge invariant approach to charged bosons in relativistic magnetars

Using a perturbative method, we investigate solutions of the Klein–Gordon equations for a charged massive field in the background of a magnetar, both in the interior solution and outside the star. A special attention is given to cases where the variables can be separated and the wave function is expressed in terms of the Heun’s general or confluent functions. By imposing various conditions on the parameters, one gets the energy quantization law and simple polynomial forms of the Heun’s functions, which can be used in computing first-order transition amplitudes.     

Ion-implantation induced phase transitions: Order-disorder and amorphous-crystal transformations (CEMS studies)

The implantation induced disordering of intermetallic compounds is studied using the CEMS technique. The results mainly concern a magnetic transition in Fe−Al 40%at. and the crystallization process in⁵⁷Fe implanted Ni−Ti 50%at.     

A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations

In dimension n?3, we define a generalization of the classical two-dimensional partial Legendre transform, that reduces interior regularity of the generalized Monge-Ampère equation to regularity of a divergence form quasilinear system of special form. This is then used to obtain smoothness of C^2,1 solutions, having n-1 nonvanishing principal curvatures, to certain subelliptic Monge-Ampère equations in dimension n?3. A corollary is that if k?0 vanishes only at nondegenerate critical points, then a C^2,1 convex solution u is smooth if and only if the symmetric function of degree n-1 of the principal curvatures of u is positive, and moreover, u fails to be when not smooth.     

The Rubin–Stark Conjecture for imaginary abelian fields of odd prime power conductor

We build upon ideas developed in [9], as well as results of Greither on a strong form of Brumers Conjecture ([2]–[4]), and prove Rubins integral version of Starks Conjecture for imaginary abelian extensions of Q of odd prime power conductor.Mathematics Subject Classification (1991): 11R42, 11R58, 11R27Research on this project was partially supported by NSF grants DMS–9801267 and DMS–0196340Revised version: 11 October 2002     

Structural influence of erbium centers on silicon nanocrystal phase transitions

Two different types of erbium-doped silicon nanocrystals, along with undoped, oxide-capped Si dots, are employed to probe the impact of the impurity center location on phase transition pressure. Using a combination of high pressure optical absorption, micro-Raman, and x-ray diffraction measurements in a diamond anvil cell, it is demonstrated that the magnitude of this phase transition elevation is strongly dictated by the average spatial location of impurity centers introduced into the nanocrystal along with the interfacial quality of the surrounding oxide.     

Surface and bulk spin ordering of antiferromagnetic materials: NiO(111)

We present a study of the prototypical NiO(111) antiferromagnet by nonresonant surface x-ray magnetic scattering. Direct access to the antiferromagnetic surface and bulk spin ordering is demonstrated. Our data support a first order antiferromagnetic to paramagnetic transition. A quantitative determination of the magnetization profile is proposed. It is shown that the NiO(111) surface spins remain ordered at higher temperatures than in the bulk and that the blocking temperature in exchange coupled ferromagnetic-NiO interfaces is most likely related to an S-domain structure loss occurring 25 K below the Ne el temperature.     

The Dirichlet problem and nondivergence harmonic measure

We consider the Dirichlet problem

for two second-order elliptic operators , , in a bounded Lipschitz domain . The coefficients belong to the space of bounded mean oscillation with a suitable small modulus. We assume that is regular in for some , , that is, for all continuous boundary data . Here is the surface measure on and is the nontangential maximal operator. The aim of this paper is to establish sufficient conditions on the difference of the coefficients that will assure the perturbed operator to be regular in for some , .

     

Regularity of weak solutions to the Monge-Ampère equation

We study the properties of generalized solutions to the Monge-Ampère equation , where the Borel measure satisfies a condition, introduced by Jerison, that is weaker than the doubling property. When , this condition, which we call , admits the possibility of vanishing or becoming infinite. Our analysis extends the regularity theory (due to Caffarelli) available when , which implies that is doubling. The main difference between the case and the case when is bounded between two positive constants is the need to use a variant of the Aleksandrov maximum principle (due to Jerison) and some tools from convex geometry, in particular the Hausdorff metric.

     

Deterministic automata simulation, universality and minimality

Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/ extrinsic perception (see, for instance [3, 6, 18–21]). These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, consequently, a discrete model of Heisenberg uncertainty has been suggested. For this aim the classical theory of finite automata — which considers automata with initial states — is not adequate, and a new approach is necessary. A study of finite deterministic automata without initial states is exactly the aim of this paper. We will define and investigate the complexity of various types of simulations between automata. Minimal automata will be constructed and proven to be unique up to an isomorphism. We will build our results on an extension of Myhill-Nerode technique; all constructions will make use of “automata responses” to simple experiments only, i.e., no information about the internal machinery will be considered available.