Modeling Instabilities of Electrically Driven Jets Under Constant or Variable Applied Field and Non-Zero Basic State Velocity

We investigate the problem of instability of electrically forced axisymmetric jets with respect to temporally and spatially growing disturbances, within parameter regimes that affects the process of electrospinnning. Deriving a dispersion relation based on the relevant approximated versions of the equations of the electro-hydrodynamics for an electrically forced jet flow. For temporal instability, we find in the non-zero basic state velocity, the growth rate of the unstable mode is unaffected by the value of the basic state velocity. But, the basic state velocity affects the period of the unstable mode in the sense that it decreases the period, and the rate of increase of the frequency with respect to axial wave number increases with the basic state velocity. For spatial instability, we find that the growth rate of the unstable mode is dominated by the basic state velocity. The basic state velocity also affects the period of the unstable mode

Minimum-Weight Edge Discriminator in Hypergraphs

In this paper we introduce the concept of minimum-weight edge-discriminators in hypergraphs, and study its various properties. For a hypergraph $\mathcal H=(\mathcal V, \mathcal E)$, a function $\lambda: \mathcal V\rightarrow \mathbb Z^{+}\cup\{0\}$ is said to be an {\it edge-discriminator} on $\mathcal H$ if $\sum_{v\in E_i}{\lambda(v)}>0$, for all hyperedges $E_i\in \mathcal E$, and $\sum_{v\in E_i}{\lambda(v)}\ne \sum_{v\in E_j}{\lambda(v)}$, for every two distinct hyperedges $E_i, E_j \in \mathcal E$. An {\it optimal edge-discriminator} on $\mathcal H$, to be denoted by $\lambda_\mathcal H$, is an edge-discriminator on $\mathcal H$ satisfying $\sum_{v\in \mathcal V}\lambda_\mathcal H (v)=\min_\lambda\sum_{v\in \mathcal V}{\lambda(v)}$, where the minimum is taken over all edge-discriminators on $\mathcal H$. We prove that any hypergraph $\mathcal H=(\mathcal V, \mathcal E)$, with $|\mathcal E|=n$, satisfies $\sum_{v\in \mathcal V} \lambda_\mathcal H(v)\leq n(n+1)/2$, and equality holds if and only if the elements of $\mathcal E$ are mutually disjoint. For $r$-uniform hypergraphs $\mathcal H=(\mathcal V, \mathcal E)$, it follows from results on Sidon sequences that $\sum_{v\in \mathcal V}\lambda_{\mathcal H}(v)\leq |\mathcal V|^{r+1}+o(|\mathcal V|^{r+1})$, and the bound is attained up to a constant factor by the complete $r$-uniform hypergraph. Next, we construct optimal edge-discriminators for some special hypergraphs, which include paths, cycles, and complete $r$-partite hypergraphs. Finally, we show that no optimal edge-discriminator on any hypergraph $\mathcal H=(\mathcal V, \mathcal E)$, with $|\mathcal E|=n (\geq 3)$, satisfies $\sum_{v\in \mathcal V} \lambda_\mathcal H (v)=n(n+1)/2-1$, which, in turn, raises many other interesting combinatorial questions.Comment: 22 pages, 5 figure

Controlled Electrokinetic Particle Manipulation using Paper-and-Pencil Microfluidics

Dielectrophoresis is a very promising technique for particle manipulation on a chip. In this study, we demonstrate a controlled mannuvering of polystryrene particles on a simple paper-and-pencil based device by exploiting the underlying electrokinetics with primary contribution from dielectrophoretic (DEP) forces. On contrary to other reported DEP devices, the present configuration does not demand a shophitcated laboratory module for creating a non-uniform electric field, which is essential requirement in DEP settings. We demonstrate positive dielectrophoresis (pDEP) to trap 1 um size polystyrene particle for low-conductivity suspending medium, at an applied field strength of 100 V/cm. In addition, the switching of the trapping direction (positive to negative dielectrophoresis) can be simply achieved by manipulating the conductivity of the media. We further bring out an optimum range of pH for effective particle trapping. These results have significant implications towards designing cell-on-a-chip based point of care diagnostic devices for resource limited settings.Comment: 21 page

Phosphorus: A Boon or Curse for the Environment?

Phosphorus, a limiting nutrient of biosphere, exists as dissolved inorganic phosphorus (DIP), dissolved organic phosphorus (DOP), particulate inorganic phosphorus (PIP) and particulate organic phosphorus (POP) in water of soil as well as ponds, lakes, etc. The only available phosphorus for plants are DIP, while the other forms need to be converted to DIP by the decomposing microorganisms of the soil. The heavy metals (such as arsenic and chromium), which are the menace of both terrestrial and aquatic environment, are taken up by the plants and animals causing toxicity at physiological level. However, the metal (Cr and As) toxicity can be mitigated competitively by phosphorus, since the latter is a structural analogue. Since, phosphorus is an essential nutrient, plants prefer it over Cr or As. At the same time, if excess of phosphorus is applied in the soil in the form of fertilisers, it gets discharged into the water bodies (ponds, lakes, etc.) through agricultural runoff, causing eutrophication followed by harming the health of the water bodies. This can be further mitigated by employing the phenomenon of luxury uptake by the aquatic plants such as Pistia stratiotes

Limnological studies on Different Ponds of Bihar, India: a Review

Pure water is essential for human survival. The availability of good quality water is an indispensable feature for preventing diseases and improving the quality of life. So, it is necessary to know about the different physicochemical parameters of water such as, temperature, electrical conductivity (EC), total suspended solid (TSS), total dissolved substance (TDS),turbidity, pH, alkalinity, hardness, chloride, sulphate, nitrate, fluoride, dissolved oxygen (DO), chemical oxygen demand (COD), biochemical oxygen demand (BOD), nitrate and phosphate. Also Biological parameters such as planktons were examined. Results of the study indicated that the pond water of Bihar is slightly contaminated

Next Generation of Genotype Imputation Methods

In the past several years, we have witnessed numerous human genetic studies that have systematically evaluated the contribution of genetic polymorphisms to various complex diseases, and enabled the evolution of multiple treatment strategies, particularly pharmaceutical therapies. Genotype imputation has been a key step in such studies - increasing the power of gene mapping analyses, facilitating harmonization of results across studies, and accelerating fine-mapping efforts. Imputation requires access to a reference panel of densely sequenced genomes and is a computationally intensive process, even with modern high performance computing. Furthermore, reference panels often have data privacy issues that inhibit users from having direct access to the data. The goal of this dissertation is to design novel strategies to address these challenges for the next generation of imputation methods. In the first project, I describe our efforts to create a reference panel of ~32,000 individuals with ~40M variants by combining genetic information obtained across 20 whole genome sequencing studies (Haplotype Reference Consortium). In the second project, I describe a novel idea called ‘state space reduction’ that reduces computational requirements of genotype imputation by orders of magnitude without any loss of accuracy (minimac3). I also present a web-based platform for imputation that greatly improves user experience and productivity. In the third project, I extend the idea of state space reduction by implementing a more complex version of the strategy that produces additional cost savings (minimac4). In the fourth project, I introduce the idea of meta-imputation: a novel approach that integrates imputed data from multiple reference panels at overlapping sites without interfering in the imputation algorithm (MetaMinimac). In summary, the purpose of this dissertation research is to develop statistical methods and computational tools that will benefit other researchers in the next generation of human gene mapping studies. These imputation tools will detect rare variants with higher accuracy, consequently increasing the power of association studies.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138466/1/sayantan_1.pd

On Temporal Instability of Electrically Forced Axisymmetric Jets with Variable Applied Field and Nonzero Basic State Velocity

The problem of instability of electrically forced axisymmetric jets with respect to temporally growing disturbances is investigated computationally. We derive a dispersion relation based on the relevant approximated versions of the equations of the electro-hydrodynamics for an electrically forced jet flow. For temporal instability, we find in the realistic cases of the non-zero basic state velocity that the growth rate of the unstable mode is unaffected by the value of the basic state velocity. However, the non-zero value of the basic state velocity affects significantly the period of the unstable mode in the sense that it decreases the period, and the rate of increase of the frequency with respect to the axial wave number increases with the basic state velocity. It is also observed from numerical investigations that there are two modes of instability for small values of the wavenumber

Minimum-Weight Edge Discriminators in Hypergraphs

In this paper we introduce the notion of minimum-weight edge-discriminators in hypergraphs, and study their various properties. For a hypergraph H = (V , E), a function λ : V → Z+∪{0} is said to be an edge-discriminator on H if ∑v∈Eiλ(v)\u3e0, for all hyperedges Ei ∈ E and ∑v∈Eiλ(v) ≠ ∑v∈Ejλ(v), for every two distinct hyperedges Ei,Ej, ∈ E. An optimal edge-discriminator on H, to be denoted by λH, is an edge-discriminator on H satisfying ∑v∈VλH(v) = minλ ∑v∈Vλ(v), where the minimum is taken over all edge-discriminators on H. We prove that any hypergraph H = (V , E), with |E| = m, satisfies ∑v∈VλH(v) ≤ m(m+1)/2, and the equality holds if and only if the elements of E are mutually disjoint. For r-uniform hypergraphs H = (V,E), it follows from earlier results on Sidon sequences that ∑v∈VλH(v) ≤ |V|r+1+o(|V|r+1), and the bound is attained up to a constant factor by the complete r-uniform hypergraph. Finally, we show that no optimal edge-discriminator on any hypergraph H = (V,E), with |E| = m (≥3), satisfies ∑v∈VλH(v) = m(m+1)/2−1. This shows that all integer values between m and m(m+1)/2 cannot be the weight of an optimal edge-discriminator of a hypergraph, and this raises many other interesting combinatorial questions

Managing the Risky Curve – A Case Report

Multirooted teeth represent a challenge to both endodontic diagnosis and treatment due to its complex and unusual root canal morphology in many cases and often encountered during endodontic treatment. Success depends on understanding the unusual root canal morphology. One of the variant root canal morphology is the ‘S’ shaped or bayonet shaped root canal. This case report discusses the endodontic management  of ‘S’ shaped root canal in maxillary first premolar

Simulated Annealing Approach onto VLSI Circuit Partitioning

Decompositions of inter-connected components, to achieve modular independence, poses the major problem in VLSI circuit partitioning. This problem is intractable in nature, Solutions of these problems in computational science is possible through appropriate heuristics. Reduction of the cost that occurs due to interconnectivity between several VLSI components is referred to in this paper. Modification of results derived by classical iterative procedures with probabilistic methods is attempted. Verification has been done on ISCAS-85 benchmark circuits. The proposed design tool shows remarkable improvement results in comparison to the traditional one when applied to the standard benchmark circuits like ISCAS-85