Four generations: SUSY and SUSY breaking

We revisit four generations within the context of supersymmetry. Wecompute the perturbativity limits for the fourth generation Yukawa couplings and show that if the masses of the fourth generation lie within reasonable limits of their present experimental lower bounds, it is possible to have perturbativity only up to scales around 1000 TeV. Such low scales are ideally suited to incorporate gauge mediated supersymmetry breaking, where the mediation scale can be as low as 10-20 TeV. The minimal messenger model, however, is highly constrained. While lack of electroweak symmetry breaking rules out a large part of the parameter space, a small region exists, where the fourth generation stau is tachyonic. General gauge mediation with its broader set of boundary conditions is better suited to accommodate the fourth generation.

Raman effect of corundum

The Raman effect of corundum (sapphire) was measured with an Ar+ laser source. The seven expected Raman active phonons were found and their symmetry characters determined. Assignment of the internal and external vibrations of the crystals was made and the effect of birefringence in the Raman selection rules is discussed.

On the conformation of cyclohexane-1,4-dione and its derivatives—I : Infrared and raman spectra of cyclohexane 1,4-dione and infrared spectrum of its octadeutero analogue

Raman spectra of cyclohexane 1,4-dione (I), in chloroform, benzene and water solutions have been recorded. Temperature effect on the spectrum has been studied. The IR spectra of I and its octadeutero analogue in the solid state have also been studied. The spectra have been found on the basis of selection rules applicable for Raman and IR spectra, to be consistent with a single conformer of C2 symmetry. Plausible causes of conformational preference have been discussed.

Raman spectra of alkali halides

In this article, we present a comparative study of the Raman spectra of alkali halides in relation to the lattice dynamics ofBorn andRaman. It is shown that the experimentally observed limit of the second-order spectra in almost all the cases can be explained well by the Lyddane-Sachs-Teller relation. It is also seen, while, an explanation of the second-order Raman spectrum of a crystal of diamond or zinc blende structure requires the frequencies from the critical points,W, Gamma, X andL inBorn's analysis, the frequencies fromGamma, X andL alone are sufficient and necessary for an interpretation of the same onRaman's model. Some similarities in the determination of the long wave properties of crystals like elastic constants and limiting frequencies of the lattice vibrations in the symmetry directions in both the models are pointed out.

Raman spectrum of crystalline aminosulphonic acid

The Raman spectrum of a single crystal of sulphamic acid has been recorded withλ 2537 excitation. Thirty-eight lines have been observed, of which twenty-nine have been recorded for the first time. Seven Raman lines with shifts in the region 50–155 cm.−1 have been assigned to the lattice oscillations, two at 177 and 240 cm.−1 have been attributed to the low-frequency hydrogen bond vibrations.. The splitting of the degenerate modes and the appearance of N-H....O bonded stretching vibrations are consistent with the structural data which expect the presence of the free molecule as a Zwitter ion with only slight distortion from C3v symmetry.

Dipole patterns in the structures of some ferroelectrics and antiferroelectrics

The dipole patterns in the ferroelectric and antiferroelectric structures are drawn according to experimentally determined symmetry changes in the ferroelectrics and antiferroelectrics. For the ferroelectrics the dipoles of the unit cells for one domain are oriented in parallel and the directions of the polarisation in the adjacent domains are at definite angles to each other. It is assumed for the antiferroelectrics, that the superstructural unit cell is formed by the adjacent cells of the paraelectrical modification; the subcells having the antiparallel directions of the polarisation. It is these superstructural cells of the antiferroelectrics that are determined during the experimental investigations of the antiferroelectrics. The superstructural cells of the adjacent domains are different. In one case, the difference is that in the adjacent domains, the directions of the polarisation in the subcells form an angle (e.g., in PbZrO3). In other cases the superstructural cells have not only different directions of the polarisation in the subcells but different signs of the enantiomorphism (e.g., NH4H2PO4). In the third case, the only difference is that the superstructural unit cells in the adjacent domains are turned by an angle to each other round the direction of the subcell polarisation [e.g., (NH4)2H3IO6], etc.

Diphenyl sulphox1de complexes of thorium(IV)

Thorium(IV) is known to form high coordination-number complexes. An attempt has therefore been made to determine the effect of anions on the coordination complexes of diphenyl sulphoxide (DPSO) with thorium(IV). The complexes formed have the formulae [Th(DPSO)6](ClO4)4, [Th(DPSO)4Cl4], [Th(DPSO)4Br4], [Th(DPSO)6I2]I2, [Th(DPSO)4(NCS)4]and [Th(DPSO)3(NO3)4]. In all the complexes, DPSO is coordinated to the metal ion through its oxygen. The electrical conductances in nitrobenzene and in nitromethane, and ebullioscopic molecular weights in acetonitrile, show that the perchlorate and iodide complexes behave as 1:4 and 1:2 electrolytes, respectively; while the other complexes are monomeric and non-electrolytes. The infrared spectra of the solid complexes indicate the ionic nature of the perchlorate, the bidentate nature of the nitrate and the coordination of the thiocyanate through its nitrogen. [Th(DPSO)4Cl4], [Th(DPSO)4Br4]and [Th-(DPSO)3 (NO3)4]decompose endothermically while [Th(DPSO)6](ClO4)4 and [Th(DPSO)4(NCS)4]decompose exothermically, both in air and in nitrogen. The perchlorate complex has octahedral symmetry around the thorium, the halo- and the thiocyanato complexes are 8-coordinate, probably with square antiprismatic structures, while the nitrate complex is 11-coordinate

Optical properties of magnetic crystals

From symmetry considerations and using generalized Onsager relations, it is shown that 66 of the 90 magnetic classes, consisting of 29 single colour and 37 double colour ones, can exhibit what may be called the strain gyrotropic rotation. Similarly, 69 of the 90 magnetic classes, consisting of 21 single colour and 48 double colour ones, can exhibit what may be called the strain gyrotropic birefringence. A crystal in the class m3 or m3 m is interesting as it can exhibit strain gyrotropic rotation despite its being cubic and incapable of exhibiting gyrotropic rotation in the unstressed state. Similarly, a crystal in the class m3 m, is interesting as it can exhibit strain gyrotropic birefringence despite its being cubic and incapable of exhibiting gyrotropic birefringence in the unstressed state.

Raman spectrum of strontium titanate

The Raman spectrum of strontium titanate has been recorded using λ 4358 of mercury as exciter. The observed spectrum consists of 7 Raman lines, one of which is of low frequency, as expected from the recent theory of Cochran. 6 of these Raman lines have been interpreted as the first order spectrum arising from a small deviation of the cubic strontium titanate from its idealized symmetry. It has been shown that one normal mode of SrTiO3 neglected by J.T. Last, will be really active in infrared absorption in the region of 440 cm-1 and that it has to be taken into account in the interpretation of the infrared spectra of titanates. The four vibrational modes of the unit cell of SrTiO3 correspond to frequencies of 90, 335, 441 and 620 cm-1 observed in Raman effect. The large width of the Raman lines and the additional lines at 256 cm-1 and 726 cm-1 have been attributed to a splitting of the longitudinal and transverse optical modes. With the observed frequencies it has been found possible to account for in a satisfactory manner the specific heat of SrTiO3 in the range 54·84° K to 1800° K.

Elastic behaviour of matter under very high pressures - Uniform compression

In order to study the elastic behaviour of matter when subjected to very large pressures, such as occur for example in the interior of the earth, and to provide an explanation for phenomena like earthquakes, it is essential to be able to calculate the values of the elastic constants of a substance under a state of large initial stress in terms of the elastic constants of a natural or stress-free state. An attempt has been made in this paper to derive expressions for these quantities for a substance of cubic symmetry on the basis of non-linear theory of elasticity and including up to cubic powers of the strain components in the strain energy function. A simple method of deriving them directly from the energy function itself has been indicated for any general case and the same has been applied to the case of hydrostatic compression. The notion of an effective elastic energy-the energy require to effect an infinitesimal deformation over a state of finite strain-has been introduced, the coefficients in this expression being the effective elastic constants. A separation of this effective energy function into normal co-ordinates has been given for the particular case of cubic symmetry and it has been pointed out, that when any of such coefficients in this normal form becomes negative, elastic instability will set in, with associated release of energy.

Optimal non-linear reinforcement schemes for stochastic automata

Two optimal non-linear reinforcement schemes—the Reward-Inaction and the Penalty-Inaction—for the two-state automaton functioning in a stationary random environment are considered. Very simple conditions of symmetry of the non-linear function figuring in the reinforcement scheme are shown to be necessary and sufficient for optimality. General expressions for the variance and rate of learning are derived. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning.

Dynamics of capacitively coupled double quantum dots

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong-coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime, and then towards and through the quantum phase transition to a charge-ordered ( CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.

Type I seesaw mechanism for quasi-degenerate neutrinos

We discuss symmetries and scenarios leading to quasi-degenerate neutrinos in type I seesaw models. The existence of degeneracy in the present approach is not linked to any specific structure for the Dirac neutrino Yukawa coupling matrix y(D) and holds in general. Basic input is the application of the minimal flavour violation principle to the leptonic sector. Generalizing this principle, we assume that the structure of the right-handed neutrino mass matrix is determined by y(D) and the charged lepton Yukawa coupling matrix y(l) in an effective theory invariant under specific groups G(F) contained in the full symmetry group of the kinetic energy terms. G(F) invariance also leads to specific structure for the departure from degeneracy. The neutrino mass matrix (with degenerate mass m(0)) resulting after seesaw mechanism has a simple form Mv approximate to m(0)(I - py(l)y(l)(T)) in one particular scenario based on supersymmetry. This form is shown tolead to correct description of neutrino masses and mixing angles. The thermal leptogenesis after inclusion of flavour effects can account for the observed baryon asymmetry of the universe within the present scenario. Rates for lepton flavour violating processes can occur at observable levels in the supersymmetric version of the scenario. (c) 2010 Elsevier B.V. All rights reserved.

New Solid State Forms of the Anti-HIV Drug Efavirenz. Conformational Flexibility and High Z ` Issues

Structural information on the solid forms of efavirenz, a non-nucleoside reverse transcriptase inhibitor, is limited, although various polymorphic forms of this drug have been patented. We report here structural studies of four new crystal forms a pure form, a cyclohexane solvate, and cocrystals with 1,4-cyclohexanedione and 4,4'-bipyridine. Temperature dependent single-crystal to single-crystal phase transitions are observed for the pure form and for the cyclohexane solvate with an increase in the number of symmetry independent molecules, Z', upon a lowering of temperature. Other issues related to these solid forms, such as thermal stability, conformational flexibility, and high Z' occurrences, are addressed by using a combined experimental and computational approach.

Undamped Oscillations of Collisionless Stellar Systems: Spheres,Spheroids and Discs.

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed.