Charged-soliton excitations in statistical mechanics

A method is developed for demonstrating how solitons with some internal periodic motion may emerge as elementary excitations in the statistical mechanics of field systems. The procedure is demonstrated in the context of complex scalar fields which can, for appropriate choices of the Lagrangian, yield charge-carrying solitons with such internal motion. The derivation uses the techniques of the steepest-descent method for functional integrals. It is shown that, despite the constraint of some fixed total charge, a gaslike excitation of such charged solitons does emerge.

A parallel wilf algorithm for complex zeros of a polynomial

A global recursive bisection algorithm is described for computing the complex zeros of a polynomial. It has complexityO(n 3 p) wheren is the degree of the polynomial andp the bit precision requirement. Ifn processors are available, it can be realized in parallel with complexityO(n 2 p); also it can be implemented using exact arithmetic. A combined Wilf-Hansen algorithm is suggested for reduction in complexity.

Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

Note on the stability of parallel magnetic fields

The stability characteristics of parallel magnetic fields when fluid motions are present along the lines of force is studied. The stability criterion for both symmetric (m=0) and asymmetric (m=1) modes are discussed and the results obtained by Trehan and Singh (1978) are amended in the present study. The results obtained for the cylindrical geometry are shown to play an important role forka<4, wherek is the wave number,a is the radius of the cylinder, compared to the results obtained by Geronicolas (1977) for the slab geometry.

A unified approach to the solution of plane problems of Magneto-elasticity with special reference to a hole in a thin infinite conducting plate

Under certain specific assumption it has been observed that the basic equations of magneto-elasticity in the case of plane deformation lead to a biharmonic equation, as in the case of the classical plane theory of elasticity. The method of solving boundary value problems has been properly modified and a unified approach in solving such problems has been suggested with special reference to problems relating thin infinite plates with a hole. Closed form expressions have been obtained for the stresses due to a uniform magnetic field present in the plane of deformation of a thin infinite conducting plate with a circular hole, the plate being deformed by a tension acting parallel to the direction of the magnetic field.

Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported

Solutions of the exact characteristic equations for the title problem derived earlier by an extension of Bolotin's asymptotic method are considered. These solutions, which correspond to flexural modes with frequency factor, R, greater than unity, are expressed in convenient forms for all combinations of clamped, simply supported and free conditions at the remaining pair of parallel edges. As in the case of uniform beams, the eigenvalues in the CC case are found to be equal to those of elastic modes in the FF case provided that the Kirchoff's shear condition at a free edge is replaced by the condition. The flexural modes with frequency factor less than unity are also investigated in detail by introducing a suitable modification in the procedure. When Poisson's ratios are not zero, it is shown that the frequency factor corresponding to the first symmetric mode in the free-free case is less than unity for all values of side ratio and rigidity ratios. In the case of one edge clamped and the other free it is found that modes with frequency factor less than unity exist for certain dimensions of the plate—a fact hitherto unrecognized in the literature.

Novel Biginelli dihydropyrimidines with potential anticancer activity: A parallel synthesis and CoMSIA study

Novel Biginelli dihydropyrimidines of biological interest were prepared using p-toluene sulphonic acid as an efficient catalyst. All the thirty-two synthesised dihydropyrimidines were evaluated for their in vitro antioxidant activity using DPPH method. Only, compounds 28 and 29 exhibited reasonably good antioxidant activity. Furthermore, the synthesised Biginelli compounds were subjected for their in vitro anticancer activity against MCF-7 human breast cancer cells. The title compounds were tested at the concentration of 10 μg. Compounds exhibited activity ranging from weak to moderate and, from moderate to high in terms of percentage cytotoxicity. Among them, compounds 10 and 11 exhibited significant anticancer activity. In order to elucidate the three-dimensional structure–activity relationships (3D QSAR) towards their anticancer activity, we subjected them for comparative molecular similarity indices analysis (CoMSIA). Illustration regarding their synthesis, analysis, antioxidant activity, anticancer activity and 3D QSAR study is described.

Prediction of masonry compressive behaviour using a damage mechanics inspired modelling method

Masonry under compression is affected by the properties of its constituents and their interfaces. In spite of extensive investigations of the behaviour of masonry under compression, the information in the literature cannot be regarded as comprehensive due to ongoing inventions of new generation products – for example, polymer modified thin layer mortared masonry and drystack masonry. As comprehensive experimental studies are very expensive, an analytical model inspired by damage mechanics is developed and applied to the prediction of the compressive behaviour of masonry in this paper. The model incorporates a parabolic progressively softening stress-strain curve for the units and a progressively stiffening stress-strain curve until a threshold strain for the combined mortar and the unit-mortar interfaces is reached. The model simulates the mutual constraints imposed by each of these constituents through their respective tensile and compressive behaviour and volumetric changes. The advantage of the model is that it requires only the properties of the constituents and considers masonry as a continuum and computes the average properties of the composite masonry prisms/wallettes; it does not require discretisation of prism or wallette similar to the finite element methods. The capability of the model in capturing the phenomenological behaviour of masonry with appropriate elastic response, stiffness degradation and post peak softening is presented through numerical examples. The fitting of the experimental data to the model parameters is demonstrated through calibration of some selected test data on units and mortar from the literature; the calibrated model is shown to predict the responses of the experimentally determined masonry built using the corresponding units and mortar quite well. Through a series of sensitivity studies, the model is also shown to predict the masonry strength appropriately for changes to the properties of the units and mortar, the mortar joint thickness and the ratio of the height of unit to mortar joint thickness. The unit strength is shown to affect the masonry strength significantly. Although the mortar strength has only a marginal effect, reduction in mortar joint thickness is shown to have a profound effect on the masonry strength. The results obtained from the model are compared with the various provisions in the Australian Masonry Structures Standard AS3700 (2011) and Eurocode 6.

Mechanics of transition in an axisymmetric laminar boundary layer on a circular cylinder

Measurements of the growth of artificially generated turbulent spots and intermittency distribution in the transition region on a circular cylinder in axial flow show that the instability Reynolds number of 11,000 has a marked effect on the properties. In particular, it is found that the spot production in the initial region when a single turbulent spot has not yet wrapped around the cylinder and the propagation is essentially two-dimensional, is significantly altered. But the transition in the downstream or latter region, where most of the turbulent spots propagate onedimensionally (like the turbulent plugs in a pipe), is not affected. When the radius Reynolds number is more than 11,000, the intermittency law in the initial region is essentially the same as in twodimensional flow on a flat plate and in the latter region it is the one-dimensional flow in a pipe, the demarcation between the two regions being quite sharp.

Development of a transient gradient enhanced non local continuum damage mechanics model for masonry

Due to the advent of varied types of masonry systems a comprehensive failure mechanism of masonry essential for the understanding of its behaviour is impossible to be determined from experimental testing. As masonry is predominantly used in wall structures a biaxial stress state dominates its failure mechanism. Biaxial testing will therefore be necessary for each type of masonry, which is expensive and time consuming. A computational method would be advantageous; however masonry is complex to model which requires advanced computational modelling methods. This thesis has formulated a damage mechanics inspired modelling method and has shown that the method effectively determines the failure mechanisms and deformation characteristics of masonry under biaxial states of loading.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Inflammation-driven bone formation in a mouse model of ankylosing spondylitis: Sequential not parallel processes

Background Ankylosing spondylitis (AS) is an immune-mediated arthritis particularly targeting the spine and pelvis and is characterised by inflammation, osteoproliferation and frequently ankylosis. Current treatments that predominately target inflammatory pathways have disappointing efficacy in slowing disease progression. Thus, a better understanding of the causal association and pathological progression from inflammation to bone formation, particularly whether inflammation directly initiates osteoproliferation, is required. Methods The proteoglycan-induced spondylitis (PGISp) mouse model of AS was used to histopathologically map the progressive axial disease events, assess molecular changes during disease progression and define disease progression using unbiased clustering of semi-quantitative histology. PGISp mice were followed over a 24-week time course. Spinal disease was assessed using a novel semi-quantitative histological scoring system that independently evaluated the breadth of pathological features associated with PGISp axial disease, including inflammation, joint destruction and excessive tissue formation (osteoproliferation). Matrix components were identified using immunohistochemistry. Results Disease initiated with inflammation at the periphery of the intervertebral disc (IVD) adjacent to the longitudinal ligament, reminiscent of enthesitis, and was associated with upregulated tumor necrosis factor and metalloproteinases. After a lag phase, established inflammation was temporospatially associated with destruction of IVDs, cartilage and bone. At later time points, advanced disease was characterised by substantially reduced inflammation, excessive tissue formation and ectopic chondrocyte expansion. These distinct features differentiated affected mice into early, intermediate and advanced disease stages. Excessive tissue formation was observed in vertebral joints only if the IVD was destroyed as a consequence of the early inflammation. Ectopic excessive tissue was predominantly chondroidal with chondrocyte-like cells embedded within collagen type II- and X-rich matrix. This corresponded with upregulation of mRNA for cartilage markers Col2a1, sox9 and Comp. Osteophytes, though infrequent, were more prevalent in later disease. Conclusions The inflammation-driven IVD destruction was shown to be a prerequisite for axial disease progression to osteoproliferation in the PGISp mouse. Osteoproliferation led to vertebral body deformity and fusion but was never seen concurrent with persistent inflammation, suggesting a sequential process. The findings support that early intervention with anti-inflammatory therapies will be needed to limit destructive processes and consequently prevent progression of AS.

Observation of a mixed antiparallel and parallel beta-sheet motif in the crystal structure of Boc-Ala-Ile-Aib-OMe

A diastereomeric mixture of the tripeptide Boc-Ala-Ile-Aib-OMe crystallized in the space group P1 from CH3OH/H2O. The unit cell parameters are a = 10.593(2) A, b = 14.377(3) A, c = 17.872(4) A, alpha = 104.41(2) degrees, beta = 90.55(2) degrees, gamma = 106.91(2) degrees, V = 2512.4 A3, Z = 4. X-Ray crystallographic studies show the presence of four molecules in the asymmetric unit consisting of two pairs of diastereomeric peptides, Boc-L-Ala-L-Ile-Aib-OMe and Boc-L-Ala-D-Ile-Aib-OMe. The four molecules in the asymmetric unit form a rarely found mixed antiparallel and parallel beta-sheet hydrogen bond motif. The Ala and (L,D)-Ile residues in all the four molecules adopt the extended conformations, while the phi, psi values of the Aib residues are in the right-handed helical region. In one of the molecules the Ile sidechain adopts the unusual gauche conformation about the C beta-C gamma bond.

Commodity taxation and parallel imports

We examine the interaction between commodity taxes and parallel imports in a two-country model with imperfect competition. While governments determine non-cooperatively their commodity tax rate, the volume of parallel imports is determined endogenously by the retailing sector. We compare the positive and normative implications of having commodity taxes based on destination or origin principle. We show that, as the volume of parallel imports increases, non-cooperative origin taxes converge, while destination taxes diverge. Moreover, origin taxes are more similar and lead to higher aggregate welfare levels than destination taxes.