Fractional Differential Equations

The science and technology of ultracapacitors are reviewed for a number of electrode materials, including carbon, mixed metal oxides, and conducting polymers. More work has been done using microporous carbons than with the other materials and most of the commercially available devices use carbon electrodes and an organic electrolytes. The energy density of these devices is 3¯5 Wh/kg with a power density of 300¯500 W/kg for high efficiency (90¯95%) charge/discharges. Projections of future developments using carbon indicate that energy densities of 10 Wh/kg or higher are likely with power densities of 1¯2 kW/kg. A key problem in the fabrication of these advanced devices is the bonding of the thin electrodes to a current collector such the contact resistance is less than 0.1 cm2. Special attention is given in the paper to comparing the power density characteristics of ultracapacitors and batteries. The comparisons should be made at the same charge/discharge efficiency.

Ultracapacitors: Why, How, and Where is the Technology

http://ieeexplore.ieee.org/iel5/5610941/5624686/05624745.pdf

Power electronics

System Identification I

Consider the function defined for $\alpha _{1},\ \alpha _{2} \in \mathbb{R}$ (α 1 2 +α 2 2 ≠ 0) and $\beta _{1},\beta _{2} \in \mathbb{C}$ by the series 

$$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \in \mathbb{C}). }$$

(6.1.1)

Such a function with positive α 1 > 0, α 2 > 0 and real $\beta _{1},\beta _{2} \in \mathbb{R}$ was introduced by Dzherbashian [Dzh60].

Multi-index Mittag-Leffler Functions

Starch solutions, which are strongly non-Newtonian, show a surface instability, when subjected to a load. A droplet of the fluid is sandwiched between two glass plates and a weight varying from 1 to 5 kgs. is placed on the top plate. The area of contact between the fluid and plate increases in an oscillatory manner, unlike Newtonian fluids in a similar situation. The periphery moreover, develops a viscous fingering like instability, which is not expected under compression. We attempt to model the non-Newtonian nature of the fluid through a visco-elastic model incorporating generalized calculus. This is shown to exhibit a qualitatively similar oscillatory variation in the surface strain.

Oscillatory Spreading and Surface Instability of a Non-Newtonian Fluid under Compression

The graph bisection problem asks to partition the n vertices of a graph into two sets of equal size so that the number of edges across the cut is minimum. We study finite, connected subgraphs of the infinite twodimensional grid that do not have holes. Since bisection is an intricate problem, our interest is in the tradeoff between runtime and solution quality that we get by limiting ourselves to a special type of cut, namely cuts with at most one bend each (corner cuts). We prove that optimum corner cuts get us arbitrarily close to equal sized parts, and that this limitation makes us lose only a constant factor in the quality of the solution. We obtain our result by a thorough study of cuts in polygons and the effect of limiting these to corner cuts. 1 Comparing Optimal with Restricted Cuts We consider the bisection problem: partition the vertex set of a given graph into two (almost) equal sized subsets such that the number of edges with an endpoint in each partition is minimised. The problem has been studied extensively, due to its utility in divide-and-conquer algorithms. It is NP-hard in general [5] and the best approximation algorithm known for general graphs [9] guarantees an approximation ratio of O(log n). For planar graphs a PTAS [2] has been found, while for trees an optimum solution can be computed in O(n) time [6, 7]. Our motivation to study the bisection problem comes from the need to parallelise a finite element computation of a human bone structure model in order to diagnose osteoporosis [1]. In such an application the aim is to distribute the data, modelled by the vertices (of a graph G), evenly onto a given number p ∗We gratefully acknowledge discussions with Peter Arbenz who introduced the human bone simulation problem to us, and the support of this work through the Swiss National Science Foundation under Grant No. 200021 125201/1. †An extended abstract of this report appeared at the 37th International Workshop on Graph-Theoretic Concepts in Computer Science [4]

A proof via polygons

In this work gelatinized potato starch is shown to retain the memory of past loading history. It exhibits a visco-elastic response which does not depend solely on instantaneous conditions. A simple squeeze flow experiment is performed, where loading is done in two steps with a time lag $\tau \sim$ seconds between the steps. The effect on the strain, of varying $\tau$ is reproduced by a three element visco-elastic solid model. Non-linearity is introduced through a generalized calculus approach by incorporating a non-integer order time derivative in the viscosity equation. A strain hardening proportional to the time lag between the two loading steps is also incorporated. 
This model reproduces the three salient features observed in the experiment, namely - the memory effect, slight initial oscillations in the strain as well as the long-time solid-like response. Dynamic visco-elasticity of the sample is also reported.

Squeeze flow of potato starch gel: effect of loading history on visco-elastic properties

This paper presents the simulation and its based characterization of five negative permeability inclusion plasmonic structures named as SRR (Split Ring Resonator), SSRR (Square Split Ring Resonator), TTSR (Two Turn Spiral Resonator), NBSR (Non Bi-anisotropic Spiral Resonator) and LR (Labyrinth Resonator) used in metamaterials. These structures are designed and simulated using commercial FEM (Finite Element Method) solver at X-band (8-12 GHz). Using simulation results, a standard scattering-parameter based retrieval method is applied to characterize theses structures. All the results have been compared for performance comparison.

http://ieeexplore.ieee.org/iel7/6653326/6661709/06661813.pdf

Simulation based characterization of negative permeability plasmonic structures at X band

In this work, machinability study during turning of Al-Mg2Si-Si is taken into consideration with varying cutting tools. Latin square method is applied to find out the effect of cutting velocity, feed as well as insert type onto force requirement. Results show that in relatively high cutting velocity range, feed has significant effect on forces. Under 60 –75 m/min cutting velocity with 0.06-0.08 mm/rev feed, good machinability is obtained, and hence, these cutting conditions may be recommended for application in the industry. 

Shantanu Das

Papers

Oscillatory Spreading and Surface Instability of a Non-Newtonian Fluid under Compression

A proof via polygons

Squeeze flow of potato starch gel: effect of loading history on visco-elastic properties

Simulation based characterization of negative permeability plasmonic structures at X band

An Investigation on Machinability during Turning Al-Mg2Si-Si Composite in Dry Condition