The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine representation formula for eternal solutions of Smoluchowski's equation (Adv. Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on the scaling attractor, revealing these dynamics to be conjugate to a continuous dilation, and chaotic in a classical sense. Furthermore, our study of scaling limits explains how Smoluchowski dynamics ``compactifies'' in a natural way that accounts for clusters of zero and infinite size (dust and gel)

Design of a Secure Architecture for Last Mile Communication in Smart Grid Systems

AbstractEver increasing need of electricity has paved the need for Smart Grids. Smart Meters, digitalized networks and fault tolerant systems are the basic infrastructure which supports Smart Grid. Security in Smart Grid has become a major concern in the present scenario. In this paper we have proposed security architecture at the last mile distribution in Home Area Networks. A Secure communication architecture has been modeled which focuses on secure data transmission between the Smart Meters at home and Central Gateway at the utility centre. Hybrid Encryption algorithms and Digital Signature has been used to provide data integrity. The strength of the model has been verified with the help of an attacker and the model is found to resist attacks. The Encryption time and Decryption time of the cyptostack is lower when compared with other encryption algorithms

Applicability of a Representation for the Martin's Real-Part Formula in Model-Independent Analyses

Using a novel representation for the Martin's real-part formula without the full scaling property, an almost model-independent description of the proton-proton differential cross section data at high energies (19.4 GeV - 62.5 GeV) is obtained. In the impact parameter and eikonal frameworks, the extracted inelastic overlap function presents a peripheral effect (tail) above 2 fm and the extracted opacity function is characterized by a zero (change of sign) in the momentum transfer space, confirming results from previous model-independent analyses. Analytical parametrization for these empirical results are introduced and discussed. The importance of investigations on the inverse problems in high-energy elastic hadron scattering is stressed and the relevance of the proposed representation is commented. A short critical review on the use of Martin's formula is also presented.Comment: Two comments and one reference added at the end of Subsec. 3.3; 23 pages, 9 figures; to be published in Int. J. Mod. Phys.

Limits on monopole fluxes from KFG experiment

The nucleon decay experiment at KGF at a depth of 2.3 Km is eminently suited for the search of Grand Unified theory (GUT) monopoles, whose velocities at the present epoch are predicted to be around 0.001C. At this depth the cosmic ray background is at a level 2/day in the detector of size 4m x 6m x 3.7m and one can look for monopoles traversing the detector in all directions, using three methods, i.e., (1) dE/dx (ionization); (2) time of flight and (3) catalysis of nucleon decay. The detector is composed of 34 layers of proportional counters arranged in horizontal planes one above the other in an orthogonal maxtrix. Each of the 1594 counters are instrumented to measure ionization in the gas (90% Argon + 10% Methane) as well as the time of arrival of particles

Settlement pattern of the larvae of Hydroides elegans (Polychaeta) in the presence of petroleum hydrocarbon compounds

Polyaromatic hydrocarbons (PAHs) have been recognised as the main toxic components of crude oil polluting the manne environment. The larvae of invertebrates, including polychaetes, are more susceptible to toxicants in the environment. The effect of different concentrations of water accommodated hydrocarbons on survival and settlement of Hydroides elegans (Haswell) was studied in the laboratory. A parallel study of the settlement pattern In the field were conducted using terra-cotta tiles. The dissolved / dispersed hydrocarbon concentration in the chosen area of Cochin harbour was mOnItored dunng the study period. The presence of PAHs in high concentrations was observed to have an adverse effect on the settlement of the larvae of Hydroides elegans

A quantitative evaluation of metallic conduction in conjugated polymers

As the periodicity in crystalline materials creates the optimal condition for electronic delocalization, one might expect that in partially crystalline conjugated polymers delocalization is impeded by intergrain transport. However, for the best conducting polymers this presumption fails. Delocalization is obstructed by interchain rather than intergrain charge transfer and we propose a model of weakly coupled disordered chains to describe the physics near the metal-insulator transition. Our quantitative calculations match the outcome of recent broad-band optical experiments and provide a consistent explanation of metallic conduction in polymers.Comment: 4 pages incl. 3 figure

Results on nucleon life-time from the Kolar gold field experiment

The KGF nucleon decay experiment has been in operation since October 1980 with a 140 ton calorimetric detector at a depth of 2.3 Km underground. The detector comprises 34 layers of proportional counters arranged in an orthogonal geometry with 12 mm thick iron plates in between successive layers. The proportional counters are made up of square (10 x 10 square centimeters) iron plates of wall thickness 2.3 mm. Each of the 1600 counters is instrumented to provide data on ionization, DE/dx and arrival time. The visible energy of a particle is determined to an accuracy of approximately 20% from the ionization and range of its track. The end point ionization of a stopping track provides the direction of motion as well as the nature of the particle (mu/pi,k,p). Decay of mu is recorded with an overall efficiency of only 20% in view of the thickness of 13 g/square centimeters between successive layers

Data acquisition system for phase-2 KGF proton decay experiment

Phase-2 of KGF proton decay experiment using 4000 proportional counters will start operating from middle of 1985. The detection systems, in addition to measuring the time information to an accuracy of 200 n see, also records ionization in the hit counters. It also monitors different characteristics of the counters like pulse height spectrum, pulse width spectrum and counting rate. The acquisition system is discussed