Optimal Resource Partitioning in a Military Conflict based on Lanchester Attrition Models

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 in two different fronts. The Lanchester attrition model is used to develop the dynamical equations governing the variation in force strength. Three different allocation schemes - Time-Zero-Allocation (TZA), Allocate-Assess-Reallocate (AAR), and Continuous Constant Allocation (CCA) - are considered and the optimal solutions are obtained in each case. Numerical examples are given to support the analytical results.

Optimal Resource Partitioning in a Military Conflict based on Lanchester Attrition Models

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 in two different fronts. The Lanchester attrition model is used to develop the dynamical equations governing the variation in force strength. Three different allocation schemes - Time-Zero-Allocation (TZA), Allocate-Assess-Reallocate (AAR), and Continuous Constant Allocation (CCA) - are considered and the optimal solutions are obtained in each case. Numerical examples are given to support the analytical results.

A resource based game theoretical model for military conflicts

A resource interaction based game theoretical model for military conflicts is presented in this paper. The model includes both the spatial decision capability of adversaries (decision regarding movement and subsequent distribution of resources) as well as their temporal decision capability (decision regarding level of allocation of resources for conflict with adversary’s resources). Attrition is decided at present by simple deterministic models. An additional feature of this model is the inclusion of the possibility of a given resource interacting with several resources of the adversary.The decisions of the adversaries is determined by solving for the equilibrium Nash strategies given that the objectives of the adversaries may not be in direct conflict. Examples are given to show the applicability of these models and solution concepts.

Hydrogen and fluorine in crystal engineering: systematics from crystallographic studies of hydrogen bonded tartrate-amine complexes and fluoro-substituted coumarins, styrylcoumarins and butadienes

Three aspects of crystal engineering in molecular crystals are presented to emphasize the role of intermolecular interactions and factors influencing crystal packing. Hydrogen bonded tartrate-amine complexes have been analyzed with the propensity for formation of multidirectional hydrogen bonding as a key design element in the generation of materials for second harmonic generation (SHG). The invariance of the framework in DBT and its possible implications on SHG is outlined. The role of Fluorine in orienting molecules of coumarins, styrylcoumarins and butadienes for photodimerization is described with particular emphasis on its steering capability. Usage of coumarin as an design element for the generation of polymorphs of substituted styrylcoumarins is examined with specific examples.

Spatial Variability of the Depth of Weathered and Engineering Bedrock using Multichannel Analysis of Surface Wave Method

In this paper an attempt has been made to evaluate the spatial variability of the depth of weathered and engineering bedrock in Bangalore, south India using Multichannel Analysis of Surface Wave (MASW) survey. One-dimensional MASW survey has been carried out at 58 locations and shear-wave velocities are measured. Using velocity profiles, the depth of weathered rock and engineering rock surface levels has been determined. Based on the literature, shear-wave velocity of 330 ± 30 m/s for weathered rock or soft rock and 760 ± 60 m/s for engineering rock or hard rock has been considered. Depths corresponding to these velocity ranges are evaluated with respect to ground contour levels and top surface levels have been mapped with an interpolation technique using natural neighborhood. The depth of weathered rock varies from 1 m to about 21 m. In 58 testing locations, only 42 locations reached the depths which have a shear-wave velocity of more than 760 ± 60 m/s. The depth of engineering rock is evaluated from these data and it varies from 1 m to about 50 m. Further, these rock depths have been compared with a subsurface profile obtained from a two-dimensional (2-D) MASW survey at 20 locations and a few selected available bore logs from the deep geotechnical boreholes.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

A study in Crystal engineering: Solid-state photodimerization of chloro- and methyl-coumarins

Use of chloro and methyl substitution in crystal engineering and their interchangeability in terms of mode of packing have been examined in a series of substituted coumarins. Photoreactivity in the solid state lists been correlated with the crystallograhic structures of these coumarins. The packing of chloro-substituted aromatic compounds has been investigated by analysing the arrangement of 132 compounds. Results substantiate the use of the chloro group as a steering agent and show that the chloro and methyl groups are not always interchangeable.

A study on bullock carts. Part 1. Engineering analysis of the two-wheel bullock cart design

An engineering analysis of the design of two-wheel bullock carts has been carried out with the aid of a mathematical model. Non-dimensional expressions for the pull and the neck load have been developed. In the first instance, the cart is assumed to be cruising at constant velocity on a terrain with the effective coefficient of rolling friction varying over a wide range (0.001 to 0.5) and the gradient varying between +0.2 to −0.2. Subsequently, the effect of inertia force due to an acceleration parallel to the ground is studied. In the light of this analysis, two modifications to the design of the cart have been proposed and the relative merits of the current designs and the proposed designs are discussed.

Spectroscopic studies of micro-explosions

NONEL tube finds vast applications in civil and military because of its safe and confined explosion technique. Spectroscopic and chemical analysis of a NONEL tube with an uniform mixture of HMX and Al is reported here. Peak temperature obtained at the open end of the NONEL tube due to the detonation of the explosive has been calculated using Planck’s radiation law. The products of the chemical reaction taking place due to the ignition of HMX + Al are characterized using FTIR spectroscopy.

Milking Diatoms for Sustainable Energy: Biochemical Engineering versus Gasoline-Secreting Diatom Solar Panels

In the face of increasing CO2 emissions from conventional energy (gasoline), and the anticipated scarcity of Crude oil, a worldwide effort is underway for cost-effective renewable alternative energy sources. Here, we review a simple line of reasoning: (a) geologists claim that Much crude oil comes from diatoms; (b) diatoms do indeed make oil; (c) agriculturists Claim that diatoms could make 10-200 times as much oil per hectare as oil seeds; and (d) therefore, sustainable energy could be made from diatoms. In this communication, we propose ways of harvesting oil from diatoms, using biochemical engineering and also a new solar panel approach that utilizes genomically modifiable aspects of diatom biology, offering the prospect of ``milking'' diatoms for Sustainable energy by altering them to actively secrete oil products. Secretion by and milking of diatoms may provide a way around the puzzle of how to make algae that both grow quickly and have a very high oil content.

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.

Systematic study on crystal-contact engineering of diphthine synthase: influence of mutations at crystal-packing regions on X-ray diffraction quality

It is well known that protein crystallizability can be influenced by site-directed mutagenesis of residues on the molecular surface of proteins, indicating that the intermolecular interactions in crystal-packing regions may play a crucial role in the structural regularity at atomic resolution of protein crystals. Here, a systematic examination was made of the improvement in the diffraction resolution of protein crystals on introducing a single mutation of a crystal-packing residue in order to provide more favourable packing interactions, using diphthine synthase from Pyrococcus horikoshii OT3 as a model system. All of a total of 21 designed mutants at 13 different crystal-packing residues yielded almost isomorphous crystals from the same crystallization conditions as those used for the wild-type crystals, which diffracted X-rays to 2.1 angstrom resolution. Of the 21 mutants, eight provided crystals with an improved resolution of 1.8 angstrom or better. Thus, it has been clarified that crystal quality can be improved by introducing a suitable single mutation of a crystal-packing residue. In the improved crystals, more intimate crystal-packing interactions than those in the wild-type crystal are observed. Notably, the mutants K49R and T146R yielded crystals with outstandingly improved resolutions of 1.5 and 1.6 angstrom, respectively, in which a large-scale rearrangement of packing interactions was unexpectedly observed despite the retention of the same isomorphous crystal form. In contrast, the mutants that provided results that were in good agreement with the designed putative structures tended to achieve only moderate improvements in resolution of up to 1.75 angstrom. These results suggest a difficulty in the rational prediction of highly effective mutations in crystal engineering.