Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr\"odinger Equation with Saturable Nonlinearity

We show that the two-dimensional, nonlinear Schr\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero

Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition

We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrodinger (NLS) equation, the $\lambda \phi^4$ model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure for generating solutions is successful as a consequence of some powerful, recently discovered, cyclic identities satisfied by the Jacobi elliptic functions.Comment: 19 pages, 4 figure

Spontaneous Symmetry Breaking and the Renormalization of the Chern-Simons Term

We calculate the one-loop perturbative correction to the coefficient of the \cs term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual $U(1)$ symmetry, radiative corrections do not change the coefficient of the \cs term. In the case of an unbroken non-abelian subgroup, the coefficient of the relevant \cs term (suitably normalized) attains an integral correction, as required for consistency of the quantum theory. Interestingly, this coefficient arises purely from the unbroken non-abelian sector in question; the orthogonal sector makes no contribution. This implies that the coefficient of the \cs term is a discontinuous function over the phase diagram of the theory.Comment: Version to be published in Phys Lett B., minor additional change

Linear Superposition in Nonlinear Equations

Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by virtue of some remarkable new identities satisfied by the elliptic functions.Comment: 7 pages, 1 figur

Angular separations of the lensed QSO images

We have analyzed the observed image separations of the gravitationally lensed images of QSOs for a possible correlation with the source redshift. Contrary to the previously noted anti-correlation based on a smaller data set, no correlation is found for the currently available data. We have calculated the average image separations of the lensed QSOs as a function of source redshifts, for isothermal spheres with cores in a flat universe, taking into account the amplification bias caused by lensing. The shape of the distribution of average image separation as a function of redshift is very robust and is insensitive to most model parameters. Observations are found to be roughly consistent with the theoretical results for models which assume the lens distribution to be (i) Schechter luminosity function which, however, can not produce images with large separation and (ii) the mass condensations in a cold dark matter universe, as given by the Press-Schechter theory if an upper limit of 1-7$\times 10^{13}$ M$\odot$ is assumed on the mass of the condensations.Comment: 20 pages, 7 postscript figures, accepted for publication in The Astrophysical Journa

Performance of Large Storage Tank in Bhuj Earthquake

The 2001 Bhuj earthquake of magnitude 7.7 caused a widespread damage in the state of Gujarat, India. This paper presents a case study of phosphoric acid storage tank weighing 100,000 kN and measuring 30 m in diameter built for a fertilizer plant in Kandla, Gujarat. The post earthquake performance assessment was carried out by exhuming the nearby piles and non-destructive testing of piles. The storage tanks supported on piles, installed in a ground treated with stone columns, showed no failure and have performed well during the earthquake. The design philosophy used to resist axial and lateral loads is explained

Bogomol'nyi Equations of Maxwell-Chern-Simons vortices from a generalized Abelian Higgs Model

We consider a generalization of the abelian Higgs model with a Chern-Simons term by modifying two terms of the usual Lagrangian. We multiply a dielectric function with the Maxwell kinetic energy term and incorporate nonminimal interaction by considering generalized covariant derivative. We show that for a particular choice of the dielectric function this model admits both topological as well as nontopological charged vortices satisfying Bogomol'nyi bound for which the magnetic flux, charge and angular momentum are not quantized. However the energy for the topolgical vortices is quantized and in each sector these topological vortex solutions are infinitely degenerate. In the nonrelativistic limit, this model admits static self-dual soliton solutions with nonzero finite energy configuration. For the whole class of dielectric function for which the nontopological vortices exists in the relativistic theory, the charge density satisfies the same Liouville equation in the nonrelativistic limit.Comment: 30 pages(4 figures not included), RevTeX, IP/BBSR/93-6

Strategy for Smart City Development

Initiatives to set up 100 smart cities in the country by 2022 are underway and being implemented at a very faster pace. With the aim to strengthen and revitalize the urban local bodies the government has introduces a city challenge system for selecting smart cities on the basis of urban amenities, demographic profile and financial situation. India is the third largest Economy in the world in terms of purchasing power parity (PPP) with a 6.4% share of worldwide gross domestic product (GDP) on a PPP basis. The country also ranks second in terms of population, with more than 1.2 billion people, out of which, nearly one-third are urban dwellers. The urban population in the country has increased from 17.3 % in 1951 to 31.2% in 2011.Over the last decade Indian cities have witnessed a high rate of Urbanization with Delhi leading the race, registering a growth rate of 4.1%, followed by Mumbai and Kolkata with growth rates of 3.1 % and 2.1 % respectively (2). The new Indian government has taken cognizance of this accelerating expansion. Investments required to stabilize, augment as well as build a robust infrastructure are at the forefront of the governments agenda. The objective of this Knowledge paper is to provide an overview of the opportunity landscape for smart cities in India as well as facilitate Global solution providers to take stock of the current situation and support the Indian government’s Smart city initiative. A strong and stable democratic government coupled with the relatively free play of market forces today makes India the most Attractive Investment destination. It would also be imperative to have smart leadership not only at the national level but also at the local municipal level who can take bold decisions in every urban area and more importantly , smart people who are willing to support smart leaders for bringing the necessary change and to implement the plans

Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Order One and Two

Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lame polynomials of order one and two. Some of the models discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik model, (iii) coupled saturated discrete nonlinear Schrodinger equation, (iv) coupled phi4 model, and (v) coupled phi6 model. Furthermore, we show that most of these coupled models in fact also possess an even broader class of exact solutions.Comment: 31 pages, to appear in Pramana (Journal of Physics) 201

New Approach of Inter-Cross: An Efficient Multilevel Cache Management Policy

Cache performance has been critical for large scale systems. Until now, many multilevel cache management policies LRU-K, PROMOTE, DEMOTE have been developed but still there is performance issue. Many approaches have been proposed to reduce the gap between different levels such as hint-based multilevel cache. Some approaches like demote or promote are based on the latest cache history information, which is inadequate for applications where there are regular demote and promote operations occur. The major drawback of these policies is selecting a victim. In this paper, the new multilevel cache replacement policy called Inter-cross is implemented to improve the cache performance of a system. The decision of promotion and demotion is based on the block\u27s previous N-step promotion or demotion history and the size and resident time of the block in the cache. Comparative study between inter-cross and existing multilevel policies shows that, existing keeps track on last K references of the block within a last cache level, while inter-cross keeps track of the information of the last K movements of blocks among all the cache levels. Inter-cross algorithms are designed that can efficiently describe the activeness of any blocks in any cache level. Experimental results show that inter-cross achieves better performance compared to existing multilevel cache replacement policies such as LRU-K, PROMOTE, and DEMOTE under different workloads