Optimal resource allocation in conflicts with the Lanchester linear law (2,1) model

This paper presents a detailed analysis of a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts in an area fire situation. Lanchester linear law attrition model is used to develop the dynamical equations governing the variation in force strength. Here we address a static resource allocation problem namely, Time-Zero-Allocation (TZA) where the resource allocation is done only at the initial time. Numerical examples are given to support the analytical results.

Gauss law commutator in the chirally gauged Wess-Zumino-Witten model

We evaluate the commutator of the Gauss law constraints starting from the chirally gauged Wess-Zumino-Witten action. The calculations are done at tree level, i.e. by evaluating corresponding Poisson brackets. The results are compared with commutators obtained by others directly from the gauged fermionic theory, and with Faddeev's results based on cohomology.

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile-target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law. (C) 2013 Elsevier B. V. All rights reserved.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

Heat transfer to power-law fluids in thermal entrance region with viscous dissipation for constant heat flux conditions

An analytical solution of the heat transfer problem with viscous dissipation for non-Newtonian fluids with power-law model in the thermal entrance region of a circular pipe and two parallel plates under constant heat flux conditions is obtained using eigenvalue approach by suitably replacing one of the boundary conditions by total energy balance equation. Analytical expressions for the wall and the bulk temperatures and the local Nusselt number are presented. The results are in close agreement with those obtained by implicit finite-difference scheme. It is found that the role of viscous dissipation on heat transfer is completely different for heating and cooling conditions at the wall. The results for the case of cooling at the wall are of interest in the design of the oil pipe line.

A Nonlinear Approach for Re-entry Guidance of Reusable Launch Vehicles Using Model Predictive Static Programming

A nonlinear suboptimal guidance scheme is developed for the reentry phase of the reusable launch vehicles. A recently developed methodology, named as model predictive static programming (MPSP), is implemented which combines the philosophies of nonlinear model predictive control theory and approximate dynamic programming. This technique provides a finite time nonlinear suboptimal guidance law which leads to a rapid solution of the guidance history update. It does not have to suffer from computational difficulties and can be implemented online. The system dynamics is propagated through the flight corridor to the end of the reentry phase considering energy as independent variable and angle of attack as the active control variable. All the terminal constraints are satisfied. Among the path constraints, the normal load is found to be very constrictive. Hence, an extra effort has been made to keep the normal load within a specified limit and monitoring its sensitivity to the perturbation.

Optimal resource partitioning in conflicts based on Lanchester (n, 1) attrition model

This paper develops a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary from n different fronts. The problem of optimally partitioning the defending forces against the attacking forces is addressed. The Lanchester square law model is used to develop the dynamical equations governing the variation in force strength. Two different allocation schemes-Time-ZeroAllocation (TZA) and Continuous Constant Allocation (CCA) are considered and the optimal solutions for both are obtained analytically. These results generalize other results available in the literature. Numerical examples are given to support the analytical results.

Fatigue crack propagation model for plain concrete - An analogy with population growth

In this work, an analytical model is proposed for fatigue crack propagation in plain concrete based on population growth exponential law and in conjunction with principles of dimensional analysis and self-similarity. This model takes into account parameters such as loading history, fracture toughness, crack length, loading ratio and structural size. The predicted results are compared with experimental crack growth data for constant and variable amplitude loading and are found to capture the size effect apart from showing a good agreement. Using this model, a sensitivity analysis is carried out to study the effect of various parameters that influence fatigue failure. (C) 2010 Elsevier Ltd. All rights reserved.

Physics-Based Thermal Conductivity Model for Metallic Single-Walled Carbon Nanotube Interconnects

In this letter, a closed-form analytical model for temperature-dependent longitudinal diffusive lattice thermal conductivity (kappa) of a metallic single-walled carbon nanotube (SWCNT) has been addressed. Based on the Debye theory, the second-order three-phonon Umklapp, mass difference (MD), and boundary scatterings have been incorporated to formulate. in both low-and high-temperature regimes. It is proposed that. at low temperature (T) follows the T-3 law and is independent of the second-order three-phonon Umklapp and MD scatterings. The form factor due to MD scattering also plays a key role in the significant variation of. in addition to the SWCNT length. The present diameter-independent model of. agrees well with the available experimental data on suspended intrinsic metallic SWCNTs over a wide range of temperature and can be carried forward for electrothermal analyses of CNT-based interconnects.

Fatigue crack propagation model and size effect in concrete using dimensional analysis

It is well known that fatigue in concrete causes excessive deformations and cracking leading to structural failures. Due to quasi-brittle nature of concrete and formation of a fracture process zone, the rate of fatigue crack growth depends on a number of parameters, such as, the tensile strength, fracture toughness, loading ratio and most importantly the structural size. In this work, an analytical model is proposed for estimating the fatigue crack growth in concrete by using the concepts of dimensional analysis and including the above parameters. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between different parameters involved. It is shown that the proposed fatigue law is able to capture the size effect in plain concrete and agrees well with different experimental results. Through a sensitivity analysis, it is shown that the structural size plays a dominant role followed by loading ratio and the initial crack length in fatigue crack propagation. (C) 2010 Elsevier Ltd. All rights reserved.

Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ''relaxation'' behavior of the dynamic order parameter has been observed and the ''relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ''specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.

Nonequilibrium phase transition in the kinetic Ising model: Divergences of fluctuations and responses near the transition point

The nonequilibrium dynamic phase transition in the kinetic Ising model in the presence of an oscillating magnetic field is studied by Monte Carlo simulation. The fluctuation of the dynamic older parameter is studied as a function of temperature near the dynamic transition point. The temperature variation of appropriately defined ''susceptibility'' is also studied near the dynamic transition point. Similarly, the fluctuation of energy and appropriately defined ''specific heat'' is studied as a function of temperature near the dynamic transition point. In both cases, the fluctuations (of dynamic order parameter and energy) and the corresponding responses diverge (in power law fashion) near the dynamic transition point with similar critical behavior (with identical exponent values).

Chaotic and power law states in the Portevin-Le Chatelier effect

Recent studies on the Portevin-Le Chatelier effect report an intriguing crossover phenomenon from low-dimensional chaotic to an infinite-dimensional scale-invariant power law regime in experiments on CuAl single crystals and AlMg polycrystals, as function of strain rate. We devise fully dynamical model which reproduces these results. At low and medium strain rates, the model is chaotic with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, power law statistics for the magnitudes and durations of the stress drops emerge as in experiments and concomitantly, the largest Lyapunov exponent is zero.

Phase diagram of a two-species lattice model with a linear instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy (Phys. Rev. Lett., 79, 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case,, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.

A numerical model of a liquid-feed solid polymer electrolyte DMFC and its experimental validation

A one-dimensional, biphasic, multicomponent steady-state model based on phenomenological transport equations for the catalyst layer, diffusion layer, and polymeric electrolyte membrane has been developed for a liquid-feed solid polymer electrolyte direct methanol fuel cell (SPE- DMFC). The model employs three important requisites: (i) implementation of analytical treatment of nonlinear terms to obtain a faster numerical solution as also to render the iterative scheme easier to converge, (ii) an appropriate description of two-phase transport phenomena in the diffusive region of the cell to account for flooding and water condensation/evaporation effects, and (iii) treatment of polarization effects due to methanol crossover. An improved numerical solution has been achieved by coupling analytical integration of kinetics and transport equations in the reaction layer, which explicitly include the effect of concentration and pressure gradient on cell polarization within the bulk catalyst layer. In particular, the integrated kinetic treatment explicitly accounts for the nonhomogeneous porous structure of the catalyst layer and the diffusion of reactants within and between the pores in the cathode. At the anode, the analytical integration of electrode kinetics has been obtained within the assumption of macrohomogeneous electrode porous structure, because methanol transport in a liquid-feed SPE- DMFC is essentially a single-phase process because of the high miscibility of methanol with water and its higher concentration in relation to gaseous reactants. A simple empirical model accounts for the effect of capillary forces on liquid-phase saturation in the diffusion layer. Consequently, diffusive and convective flow equations, comprising Nernst-Plank relation for solutes, Darcy law for liquid water, and Stefan-Maxwell equation for gaseous species, have been modified to include the capillary flow contribution to transport. To understand fully the role of model parameters in simulating the performance of the DMCF, we have carried out its parametric study. An experimental validation of model has also been carried out. (C) 2003 The Electrochemical Society.