A model of gravitation with global U(1)-symmetry

It is shown that an embedding of the general relativity $4-$space into a flat $12-$space gives a model of gravitation with the global $U(1)-$symmetry and the discrete $D_{1}-$one. The last one may be transformed into the $SU(2)-$symmetry of the unified model, and the demand of independence of $U(1)-$ and $SU(2)-$transformations leads to the estimate $\sin^{2}\theta_{min}=0,20$ where $\theta_{min}$ is an analog of the Weinberg angle of the standard model.Comment: 7 page

Do metals exist in two dimensions? A study of many-body localisation in low density electron gas

Using a combination of ground state quantum Monte-Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localisation length of a disordered two-dimensional electron gas. We find that correlations delocalise the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalisation is much more dramatic in the presence of valley degeneracy (as in Si MOSFETSs) where the localization length increases drastically. Our results suggest that a rather simple mechanism can account for the main features of the metallic behaviour observed in high mobility Si MOSFETs. Our findings support the claim that this behaviour is indeed a genuine effect of the presence of electron-electron interactions, yet that the system is not a ``true'' metal in the thermodynamic sense.Comment: 5 pages 4 figure

On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.Comment: 13 pages, to appear in J. Phys. A: Math. Ge

Perceived health and quality of life: the effect of exposure to atmospheric pollution

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Solution polymerization of methyl methacrylate at high conversion in a recycle tubular reactor

The kinetics of the soln. polymn. of Me methacrylate is characterized by a strong increase of viscosity of ?6 orders of magnitude and autoacceleration of the reaction rate due to the gel effect. This can lead to thermal and kinetic reactor instabilities. The kinetics is detd. sep. using DSC and described with a modified published model. The model predictions are verified in pilot plant expts. at 130-170 Deg. [on SciFinder (R)

Theory of Non-Reciprocal Optical Effects in Antiferromagnets: The Case Cr_2O_3

A microscopic model of non-reciprocal optical effects in antiferromagnets is developed by considering the case of Cr_2O_3 where such effects have been observed. These effects are due to a direct coupling between light and the antiferromagnetic order parameter. This coupling is mediated by the spin-orbit interaction and involves an interplay between the breaking of inversion symmetry due to the antiferromagnetic order parameter and the trigonal field contribution to the ligand field at the magnetic ion. We evaluate the matrix elements relevant for the non-reciprocal second harmonic generation and gyrotropic birefringence.Comment: accepted for publication in Phys. Rev.

Strong disorder renormalization group study of aperiodic quantum Ising chains

We employ an adaptation of a strong-disorder renormalization-group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation-length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method

Vectorial Control of Magnetization by Light

Coherent light-matter interactions have recently extended their applications to the ultrafast control of magnetization in solids. An important but unrealized technique is the manipulation of magnetization vector motion to make it follow an arbitrarily designed multi-dimensional trajectory. Furthermore, for its realization, the phase and amplitude of degenerate modes need to be steered independently. A promising method is to employ Raman-type nonlinear optical processes induced by femtosecond laser pulses, where magnetic oscillations are induced impulsively with a controlled initial phase and an azimuthal angle that follows well defined selection rules determined by the materials' symmetries. Here, we emphasize the fact that temporal variation of the polarization angle of the laser pulses enables us to distinguish between the two degenerate modes. A full manipulation of two-dimensional magnetic oscillations is demonstrated in antiferromagnetic NiO by employing a pair of polarization-twisted optical pulses. These results have lead to a new concept of vectorial control of magnetization by light

Biharmonic pattern selection

A new model to describe fractal growth is discussed which includes effects due to long-range coupling between displacements $u$. The model is based on the biharmonic equation $\nabla^{4}u =0$ in two-dimensional isotropic defect-free media as follows from the Kuramoto-Sivashinsky equation for pattern formation -or, alternatively, from the theory of elasticity. As a difference with Laplacian and Poisson growth models, in the new model the Laplacian of $u$ is neither zero nor proportional to $u$. Its discretization allows to reproduce a transition from dense to multibranched growth at a point in which the growth velocity exhibits a minimum similarly to what occurs within Poisson growth in planar geometry. Furthermore, in circular geometry the transition point is estimated for the simplest case from the relation $r_{\ell}\approx L/e^{1/2}$ such that the trajectories become stable at the growing surfaces in a continuous limit. Hence, within the biharmonic growth model, this transition depends only on the system size $L$ and occurs approximately at a distance $60 \%$ far from a central seed particle. The influence of biharmonic patterns on the growth probability for each lattice site is also analysed.Comment: To appear in Phys. Rev. E. Copies upon request to [email protected]