Search

Existing techniques for the cost optimization of water distribution networks either employ meta-heuristics, or try to develop problem-specific optimization techniques. Instead, we exploit recent advances in generic NLP solvers and explore a rich set of model refinement techniques. The networks that we study contain a single source and multiple demand nodes with residual pressure constraints. Indeterminism of flow values and flow direction in the network leads to non-linearity in these constraints making the optimization problem non-convex. While the physical network is cyclic, flow through the network is necessarily acyclic and thus enforces an acyclic orientation. We devise different strategies of finding acyclic orientations and explore the benefit of enforcing such orientations explicitly as a constraint. Finally, we propose a parallel link formulation that models flow in each link as two separate flows with opposing directions. This allows us to tackle numerical difficulties in optimization when flow in a link is near zero. We find that all our proposed formulations give results at par with least cost solutions obtained in the literature on benchmark networks. We also introduce a suite of large test networks since existing benchmark networks are small in size, and find that the parallel link approach outperforms all other approaches on these bigger networks, resulting in a more tractable technique of cost optimization., Comment: 14 pages, 2 figures

We propose an epidemic model SIPHERD in which three categories of infection carriers Symptomatic, Purely Asymptomatic, and Exposed are considered with different rates of transmission of infection that are taken dependent on the lockdown and social distancing. The rate of detection of the infected carriers is taken dependent on the tests done per day. The model is applied for the COVID outbreak in Germany and South Korea to validate its predictive capabilities and then applied to India and the United States for the prediction of its spread with different lockdown situations and testing in the coming months., Comment: 6 pages, 11 figures

We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a certain way. This description does not introduce any new variables, but consists of exponentially many inequalities. An extended formulation with a few extra variables and much smaller number of constraints is presented. We also derive a linear time separation algorithm for finding the facet defining inequalities of this convex hull. We study the effectiveness of the new inequalities and the extended formulation using some examples.

We observe critical phenomena in spherically symmetric gravitational collapse of Einstein Cluster. We show analytically that the collapse evolution ends either in formation of a black hole or in dispersal depending on the values of initial parameters which characterize initial density and angular momentum of the collapsing cloud. Near the threshold of black hole formation, we obtain scaling relation for the mass of the black hole and find the critical exponent value to be 3/2. We numerically confirm that there exist wide ranges of initial parameter values around the critical configuration for which the model remains shell-crossing free., Comment: Accepted for publication in Prog. Theor. Phys

Dynamical Einstein cluster is a spherical self-gravitating system of counterrotating particles, which may expand, oscillate and collapse. This system exhibits critical behaviour in its collapse at the threshold of black hole formation. It appears when the specific angular momentum of particles is tuned finely to the critical value. We find the unique exact self-similar solution at the threshold. This solution begins with a regular surface, involves timelike naked singularity formation and asymptotically approaches a static self-similar cluster., Comment: 4 pages, 3 figures, accepted for publication in General Relativity and Gravitation, typos corrected

We examine spherical gravitational collapse of a matter model with vanishing radial pressure and non-zero tangential pressure. It is seen analytically that the collapsing cloud either forms a black hole or disperses depending on values of the initial parameters which are initial density, tangential pressure and velocity profile of the cloud. A threshold of black hole formation is observed near which a scaling relation is obtained for the mass of black hole, assuming initial profiles to be smooth. The similarities in the behaviour of this model at the onset of black hole formation with that of numerical critical behaviour in other collapse models are indicated., Comment: 15 pages, To be published in Gen.Rel.Grav

Generalizing earlier results on dust collapse in higher dimensions, we show here that cosmic censorship can be restored in gravitational collapse with tangential pressure present if we take the spacetime dimension to be $N\ge6$. This is under conditions to be motivated physically, such as the smoothness of initial data from which the collapse develops. The models considered here incorporating a non-zero tangential pressure include the Einstein cluster spacetime., Comment: 7 pages,1 figure,revtex4

We study here the spherical gravitational collapse assuming initial data to be necessarily smooth, as motivated by the requirements based on physical reasonableness. A tangential pressure model is constructed and analyzed in order to understand the final fate of collapse explicitly in terms of the density and pressure parameters at the initial epoch from which the collapsedevelops. It is seen that both black holes and naked singularities are produced as collapse end states even when the initial data is smooth. We show that the outcome is decided entirely in terms of the initial data, as given by density, pressure and velocity profiles at the initial epoch, from which the collapse evolves., Comment: 10 pages,3 figures,revtex4,Revised Version