Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell: Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc.

Renormalization of noncommutative quantum field theories

We report on a comprehensive analysis of the renormalization of noncommutative phi(4) scalar field theories on the Groenewold-Moyal plane. These scalar field theories are twisted Poincare invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and beta-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a comprehensive review of different approaches for the computation of the noncommutative S-matrix: noncommutative interaction picture and noncommutative Lehmann-Symanzik-Zimmermann formalism. DOI: 10.1103/PhysRevD.87.064014

Poincare invariant quantum field theories with twisted internal symmetries

Following up the work of 1] on deformed algebras, we present a class of Poincare invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can provide a natural-framework for the discussion of the marginal deformations (beta-deformations) of the N = 4 SUSY theories.

On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

Spontaneous Lorentz violation in gauge theories

Frohlich, Morchio and Strocchi long ago proved that the Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where the consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected ``Sky'' group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These Abelian considerations and model are extended to non-Abelian gauge symmetries. Basic issues regarding the observability of twisted non-Abelian gauge symmetries and of the asymptotic ADM symmetries of quantum gravity are raised.

Evaluating competing theories of street entrepreneurship

Conventionally, street entrepreneurs were either seen as a residue from a pre-modern era that is gradually disappearing (modernisation theory), or an endeavour into which marginalised populations are driven out of necessity in the absence of alternative ways of securing a livelihood (structuralist theory). In recent years, however, participa-tioninstreetentrepreneurshiphas beenre-read eitherasa rationaleconomicchoice(neo-liberal theory) or as conducted for cultural reasons (post-modern theory). The aim of this paper is to evaluate critically these competing explanations for participation in street entrepreneurship. To do this, face-to-face interviews were conducted with 871 street entrepreneurs in the Indian city of Bangalore during 2010 concerning their reasons for participation in street entrepreneurship. The finding is that no one explanation suffices. Some 12 % explain their participation in street entrepreneurship as necessity-driven, 15 % as traditional ancestral activity, 56 % as a rational economic choice and 17 % as pursued for social or lifestyle reasons. The outcome is a call to combine these previously rival explanations in order to develop a richer and more nuanced theorisation of the multifarious motives for street entrepreneurship in emerging market economies.

Hall viscosity to entropy ratio in higher derivative theories

In this paper based on the basic principles of gauge/gravity duality we compute the hall viscosity to entropy ratio in the presence of various higher derivative corrections to the dual gravitational description embedded in an asymptotically AdS(4) space time. As the first step of our analysis, considering the back reaction we impose higher derivative corrections to the abelian gauge sector of the theory where we notice that the ratio indeed gets corrected at the leading order in the coupling. Considering the probe limit as a special case we compute this leading order correction over the fixed background of the charged black brane solution. Finally we consider higher derivative (R-2) correction to the gravity sector of the theory where we notice that the above ratio might get corrected at the sixth derivative level.

On entanglement entropy functionals in higher-derivative gravity theories

In arXiv:1310.5713 1] and arXiv:1310.6659 2] a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926 3]. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the R-2 case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

Holographic charge transport in non commutative gauge theories

In this paper, based on the holographic techniques, we explore the hydrodynamics of charge diffusion phenomena in non commutative N = 4 SYM plasma at strong coupling. In our analysis, we compute the R charge diffusion rates both along commutative as well as the non commutative coordinates of the brane. It turns out that unlike the case for the shear viscosity, the DC conductivity along the non commutative direction of the brane differs significantly from that of its cousin corresponding to the commutative direction of the brane. Such a discrepancy however smoothly goes away in the limit of the vanishing non commutativity.

A Review of Theories and Models of Design

This paper intends to provide an overview of the rich legacy of models and theories that have emerged in the last fifty years of the relatively young discipline of design research, and identifies some of the major areas of further research. It addresses the following questions: What are the major theories and models of design? How are design theory and model defined, and what is their purpose? What are the criteria they must satisfy to be considered a design theory or model? How should a theory or model of design be evaluated or validated? What are the major directions for further research?

Comparison of Various Adhesion Contact Theories and the Influence of Dimensionless Load Parameter

Three models, JKR (Johnson, Kendall and Roberts), DMT (Derjaguin, Muller, and Toporov) andMD (Maugis-Dugdale),are compared with the Hertz model in dealing with nano-contact problems. It has been shown that both the dimensionless load parameter, P D P=.1/4

A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.

Validity ranges of interfacial wave theories in a two-layer fluid system

In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness d(1), and lower layer thickness d(2), instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehautes plot for free surface waves if water depth ratio r = d(1)/d(2) approaches to infinity and the upper layer water density rho(1) to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of sigma = (rho(2) - rho(1))/rho(2) -> 1.0 and r > 1.0. In the end, several figures of the validity ranges for various interfacial wave theories in the two-layer fluid are given and compared with the results for surface waves.