n=1/4 domain-growth universality class: Crossover to the n=1/2 class

The kinetic domain-growth exponent is studied by Monte Carlo simulation as a function of temperature for a nonconserved order-parameter model. In the limit of zero temperature, the model belongs to the n=(1/4 slow-growth unversality class. This is indicative of a temporal pinning in the domain-boundary network of mixed-, zero-, and finite-curvature boundaries. At finite temperature the growth kinetics is found to cross over to the Allen-Cahn exponent n=(1/2. We obtain that the pinning time of the zero-curvature boundary decreases rapidly with increasing temperature.

Kerr measurements on single-domain SrRuO3 thin films

We report on the magneto-optical measurements of an epitaxial SrRuO3 film grown on SrTiO3 (0 0 1), which previously was determined to be single domain orientated by x-ray diffraction and Raman spectroscopy techniques. Our experiments reveal a large Kerr rotation, which reaches a maximum value of about 0.5° at low temperature. By measuring magnetic hysteresis loops at different temperatures, we determined the temperature dependence of the Kerr rotation in the polar configuration. Values of the anisotropic magnetoresistance ~ 20% have been measured. These values are remarkably higher than those of other metallic oxides such as manganites. This striking difference can be attributed to the strong spin-orbit interaction of the Ru 4d ion in the SrRuO3 compound.

Perturbations on domain walls and strings: A covariant theory

A covariant formalism is developed for describing perturbations on vacuum domain walls and strings. The treatment applies to arbitrary domain walls in (N+1)-dimensional flat spacetime, including the case of bubbles of a true vacuum nucleating in a false vacuum. Straight strings and planar walls in de Sitter space, as well as closed strings and walls nucleating during inflation, are also considered. Perturbations are represented by a scalar field defined on the unperturbed wall or string world sheet. In a number of interesting cases, this field has a tachyonic mass and a nonminimal coupling to the world-sheet curvature.

Quantum fluctuations on domain walls, strings, and vacuum bubbles

We develop a covariant quantum theory of fluctuations on vacuum domain walls and strings. The fluctuations are described by a scalar field defined on the classical world sheet of the defects. We consider the following cases: straight strings and planar walls in flat space, true vacuum bubbles nucleating in false vacuum, and strings and walls nucleating during inflation. The quantum state for the perturbations is constructed so that it respects the original symmetries of the classical solution. In particular, for the case of vacuum bubbles and nucleating strings and walls, the geometry of the world sheet is that of a lower-dimensional de Sitter space, and the problem reduces to the quantization of a scalar field of tachyonic mass in de Sitter space. In all cases, the root-mean-squared fluctuation is evaluated in detail, and the physical implications are briefly discussed.

Quantum tunneling of magnetization in single domain particles

We present a study of the magnetic relaxation of several ferrofluids composed of particles of about 40 Å in diameter (Fe3O4FeC, CoFe2O4). Our key observation is a nonthermal character of the relaxation below 3 K for the CoFe2O4 ferrofluid and below 1 K for the FeC ferrofluid. The crossover temperature from thermal to nonthermal (quantum) regime is in accordance with theoretical suggestions of macroscopic quantum tunneling of magnetization in single doma in particles

Quantum tunneling of domain walls in ferromagnets

We present a theoretical study of the quantum depinning of domain walls. Our approach extends earlier work by Stamp and confirms his suggestion that quantum tunneling of domain walls in ferromagnets may reveal itself at a macroscopic level in a manner similar to the Josephson effect in superconductors. The rate of tunneling of a domain wall through a barrier formed by a planar defect is calculated in terms of macroscopic parameters of the ferromagnet. A universal behavior of the WKB exponent in the limit of small barriers is demonstrated. The effect of dissipation on the tunneling rate is studied. It is argued that quantum diffusion of domain walls apparently explains a nonthermal magnetic relaxation observed in some materials at low temperatures.

Magnetic properties and domain-wall motion in single-crystal BaFe10.2Sn0.74Co0.66O19

The magnetic properties of BaFe12O19 and BaFe10.2Sn0.74Co0.66O19 single crystals have been investigated in the temperature range (1.8 to 320 K) with a varying field from -5 to +5 T applied parallel and perpendicular to the c axis. Low-temperature magnetic relaxation, which is ascribed to the domain-wall motion, was performed between 1.8 and 15 K. The relaxation of magnetization exhibits a linear dependence on logarithmic time. The magnetic viscosity extracted from the relaxation data, decreases linearly as temperature goes down, which may correspond to the thermal depinning of domain walls. Below 2.5 K, the viscosity begins to deviate from the linear dependence on temperature, tending to be temperature independent. The near temperature independence of viscosity suggests the existence of quantum tunneling of antiferromagnetic domain wall in this temperature range.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Hindleg muscle energy and substrate balances in cold-exposed rats

Rats chronically cannulated in the carotid artery and the muscular branch of the femoral vein were subjected to a cold (4 °C) environment for up to 2 h. The changes in blood flow (measured with 46Sc microspheres) and arterio-venous differences in the concentrations of glucose, lactate, triacylglycerols and amino acids allowed the estimation of substrate (and energy) balances across the hindleg. Mean glucose uptake was 0.28mmol min21, mean lactate release was 0.33mmol min21 and the free fatty acid basal release of 0.31mmol min21 was practically zero upon exposure to the cold; the initial uptake of triacylglycerols gave place to a massive release following exposure. The measurement of PO·, PCO· and pH also allowed the estimation of oxygen, CO2 and bicarbonate balances and respiratory quotient changes across the hindleg. The contribution of amino acids to the energy balance of the hindleg was assumed to be low. These data were used to determine the sources of energy used to maintain muscle shivering with time. Three distinct phases were observed in hindleg substrate utilization. (1) The onset of shivering, with the use of glucose/glycogen and an increase in lactate efflux. Lipid oxidation was practically zero (respiratory quotient near 1), but the uptake of triacylglycerols from the blood remained unchanged. (2) A substrate-energy shift, with drastically decreased use of glucose/glycogen, and of lactate efflux; utilization of triacylglycerol as practically the sole source of energy (respiratory quotient approximately 0.7); decreasing uptake of triacylglycerol and increased tissue lipid mobilization. (3) The onset of a new heat-homeostasis setting for prolonged cold-exposure, with maintenance of muscle energy and heat production based on triacylglycerol utilization and efflux from the hindleg (muscle plus skin and subcutaneous adipose masses) contributing energy to help sustain heat production by the core organs and surrounding brown adipose tissue.

Dynamics of transient domain structures in nematic liquid crystals: The splay Fréedericksz transition

We discuss the dynamics of the transient pattern formation process corresponding to the splay Fréedericksz transition. The emergence and subsequent evolution of the spatial periodicity is here described in terms of the temporal dependence of the wave numbers corresponding to the maxima of the structure factor. Situations of perpendicular as well as oblique field-induced stripes relative to the initial orientation of the director are both examined with explicit indications of the time scales needed for their appearance and posterior development.

Transient patterns in nematic liquid crystals: Domain-wall dynamics

We study the dynamics of the late stages of the Fréedericksz transition in which a periodic transient pattern decays to a final homogeneous state. A stability analysis of an unstable stationary pattern is presented, and equations for the evolution of the domain walls are obtained. Using results of previous theories, we analyze the effect that the specific dynamics of the problem, incorporating hydrodynamic couplings, has on the expected logarithmic domain growth law.