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1. Superstring Theories
My interests in physics surround the central theme of developing a unified description of the
fundamental laws of the universe that is based on underlying symmetries and devoid of free,
dimensionless parameters. Superstring theories are one class of theory that endeavours to provide
such a description. My graduate research has included projects in both theoretical developments
using type IIB supergravity (SUGRA), as well as its application via the AdS/CFT correspondence.
A string theory description of a standard model–type theory is only made possible by the intro–
duction of D–branes as sources of background flux in compact extra dimensions. The dynamics of
the D–branes – and the fluxes supported by the branes themselves – are ... Show more content on
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We showed that including backreacting D3–branes in warped compactifications did not produce
divergences in the effective action and so represented a consistent theory from dimensional
reduction. Due to the self–duality of the five–form field strength (i.e. F5 = ⋆F5), we were able to
describe the D3–brane compensators in terms of either electric–like charge sources via d ⋆ F5 = ⋆Je
with dF5 = 0, or magnetic–like charge sources via dF5 = ⋆Jm with d ⋆ F5 = 0. We further showed
that other moduli of warped compactifications, such as the universal volume modulus and its
associated axion considered in [5], could be recast in terms of electric or magnetic descriptions
similar to the D3–branes.
In ongoing work with A. Frey, I am continuing to develop the description of monopole–like sources
in extra dimensions. As an application, we consider a magnetic monopole in Minkowski spacetime.
By writing the field strength as the sum of a local source term plus a global total derivative, we are
able to derive the magnetic analogue of the Lorentz force law without the need of non–physical dual
potentials.
One of the most widely recognized results to come from string theory is the gauge/gravity cor–
respondence [6]. The most famous AdS/CFT duality is between classical gravitation in AdS5×S5
and a superYang–Mills SU(N) gauge theory living on the conformal boundary of AdS5. However,
the duality exists more
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3. Finite Elements For Accurate, Large-Scale Quantum...
This work reviews the presentations "Finite elements for accurate, large–scale quantum mechanical
materials calculations: from classical to enriched to discontinuous" by Pask (2014). The review will
be structured to consider motivations through the aim of achieving the desired outcomes, prior work
related to the concept discussed with views of the uniqueness of the work, methodology, and results
as well as the critiques emanating from the work. Motivation The work demonstrates the use of
finite element techniques in solving the equations to model structures in the form of wave function
representation. These equations to be solved are made in the form of Kohn–Sham equation to enable
the calculations of large–scale quantum mechanical ... Show more content on Helpwriting.net ...
In this method, the challenges from that emanated from the previous methods are solved through the
development of a quicker way that solves the same problems in a short duration. The goal of the
project was to obtain an easier methodology that can help in solving systems of eigen problems. In
particular the study aimed at obtaining anything that solve a collection of problems. The new
methodology adopted not only maintains the solution requirements but also introduces systematic
improvability. Through the new insights added to the new method which distinguishes it from the
previous methodologies, the required accuracy coupled with a fewer degree of freedom can be
achieved. Methodology and key results The methodology surrounds the solution of a quantum
mechanical Schrodinger equation for large complex systems such as insulating or metallic materials
at either ambient or extreme conditions. The wave equation is first modified in the form of Kohn
Sham equation. The solution is then derived from the assumption that there is a linear combination
of piecewise polynomials. The formulation of the Schrodinger problem within the infinite crystal is
then reduced using the boundary value problem within the confines of a unit finite cell which is then
extended to the crystal potential which consists of an array of atoms. The formulation showed that
for higher derivatives of the first order, there exist finite discontinuities at
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5. Face Recognition Using Orthogonal Locality Preserving...
FACE RECOGNITION USING ORTHOGONAL LOCALITY PRESERVING PROJECTIONS.
Dr. Ravish R Singh Ronak K Khandelwal Manoj Chavan
Academic Advisor EXTC Engineering EXTC Engineering Thakur Educational Trust L.R.Tiwari
COE Thakur COE
Mumbai, India. Mumbai,India. Mumbai, India. ravishrsingh@yahoo.com
ronakkhandelwal2804@gmail.com prof.manoj@gmail.com
Abstract: In this paper a hybrid technique is used for determining the face from an image. Face
detection is one of the tedious job to achieve with very high accuracy. In this paper we proposed a
method that combines two techniques that is Orthogonal Laplacianface (OLPP) and Particle Swarm
Optimization (PSO). The formula for the OLPP relies on the Locality Preserving Projection (LPP)
formula, which aims at finding a linear approximation to the Eigen functions of the astronomer
Beltrami operator on the face manifold. However, LPP is non–orthogonal and this makes it difficult
to reconstruct the information. When the set of features is found by the OLPP, with the help of the
PSO, the grouping of the image features is done and the one with the best match from the database
is given as the result. This hybrid technique gives a higher accuracy in less processing time.
Keywords: OLPP, PSO,
INTRODUCTION:
Recently, appearance–based face recognition has received tons of attention. In general, a face image
of size n1 × n2 is delineating as a vector within the image house Rn1 × n2. We have a tendency to
denote
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7. The Effect Of Angular Momentum On Classical Mechanics
INTRODUCTION
We know the importance of Angular Momentum in Classical Mechanics; the total angular
momentum of an isolated physical system is a constant of the motion. For example, if a point
particle P, of mass m, is moving in a central potential (one which depends only on the distance
between P and a fixed point O), the force to which P is subjected is always directed towards O. Its
moment with respect to O is consequently zero, and the angular momentum theorem implies that
derivative of L (Angular momentum of P with respect to O) with respect to time is zero.
This fact has important consequences: the motion of the particle P is limited to a fixed plane (the
plane passing through O and perpendicular to the angular momentum L); moreover, this motion
obeys the law of constant areal velocity (Kepler's Second Law).
All these properties have their equivalents in Quantum Mechanics. With the angular momentum L of
a classical system is associated with an observable L, actually a set of three observables, Lx, Ly, and
Lz, which correspond to the three components of L in a Cartesian Frame. These three observables
commute with the Hamiltonian H for a particle in the central potential V(r). This property simplifies
the determination and classification of eigenstates of H.
Quantization of Angular Momentum: the component, along a fixed axis, of the intrinsic angular
momenta are quantized, which enables us to understand atomic magnetism, the Zeeman Effect, etc.
We shall denote by
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9. Understanding The Flow Dynamics Of An Aircraft
section{The Road to Transition.}
Understanding the flow dynamics of an aircraft in flight conditions is a very difficult task. The
process that the flow undergoes is complicated and many factors are involved. The main
understanding of this process is that it undergoes a transition from laminar flow (linear, parallel
streamlines) to turbulent (chaotic, mixed) one. The region where this changes is called laminar–
turbulent transition. It is important to understand the characteristics of the flow for prediction of this
transition location. Laminar flows are sensitive to adverse pressure gradients and are inclined to
separate, whereas turbulent flows create larger wall friction.
Reynolds cite{Reynolds1883} assessed this laminar–turbulent transition by performing experiments
in a pipe. He did this by injecting ink into a pipe with a water flow and observing the results. He
noted that there were different regimes based on the speed of the flow, laminar and turbulent
regions. A parameter, which is named after him, quantified this different behaviour of the fluid. The
Reynolds number is the ratio of the inertia forces over the viscous ones and it dictates the transition
process. We are interested in what caused this transition to occur and if there needs to be a critical
value for this transition to happen.
In aerodynamics many factors exist that contribute to the triggering of turbulence. In a three–
dimensional boundary–layer on a swept wing, various instabilities are
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11. Applying Two Kinds Of A Spherically Symmetric...
In this work, we consider two kinds of a spherically symmetric semiconductor quantum dots: (a)
type I single quantum dot (SQD) with radius r_1, in which electrons and holes are confined in the
same region of space, and (b) type II core/shell quantum dot (CCQD) with the same core radius, r_1,
coated with shell thickness t=r_2–r_1, in which the spatial confinement of electrons and holes
depends strongly on the geometrical parameters (core radius and shell thickness) and strain effects.
Due to the potential structure of CdSe/CdTe CCQD, electrons mainly reside in the CdSe core
region, while the holes dwell mainly in the CdTe shell region. This separation is shown in Fig. 1.
For clarity, we designate the band–gap energy, the conduction band minimum (CBM) and the
valence band maximum (VBM) of bulk semiconductor materials in the unstrained case by E_g0^i,
E_c0^i and E_v0^i, respectively. E_c^i and E_v^i denote the bulk band edges of each
nanoheterostructure compound including strain effect. In this paper, the index i=1,2,3 refers to the
CdSe region (1), CdTe region (2) and the external medium (3), c(v) holds for conduction (valence)
band and e(h) holds for electron (hole). E_g and V_(e(h)) are the bulk gap energy and the electron
(hole) confining potential of strained hetero–nanocrystal, respectively. In Fig 1, ε_1, ε_2 and ε_3 are
dielectric constants of core, shell and external medium, respectively. For simplicity, we assume that
the potential outside each kind of nanocrystal is
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13. Monte Carlo Simulation
Preface This is a book about Monte Carlo methods from the perspective of financial engineering.
Monte Carlo simulation has become an essential tool in the pricing of derivative securities and in
risk management; these applications have, in turn, stimulated research into new Monte Carlo
techniques and renewed interest in some old techniques. This is also a book about financial
engineering from the perspective of Monte Carlo methods. One of the best ways to develop an
understanding of a model of, say, the term structure of interest rates is to implement a simulation of
the model; and finding ways to improve the efficiency of a simulation motivates a deeper
investigation into properties of a model. My intended audience is a mix of graduate ... Show more
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Students often come to a course in Monte Carlo with limited exposure to this material, and the
implementation of a simulation becomes more meaningful if accompanied by an understanding of a
model and its context. Moreover, it is precisely in model details that many of the most interesting
simulation issues arise. If the first three chapters deal with running a simulation, the next three deal
with ways of running it better. Chapter 4 presents methods for increasing precision by reducing the
variance of Monte Carlo estimates. Chapter 5 discusses the application of deterministic quasi–
Monte Carlo methods for numerical integration. Chapter 6 addresses the problem of discretization
error that results from simulating discrete–time approximations to continuous–time models. The last
three chapters address topics specific to the application of Monte Carlo methods in finance. Chapter
7 covers methods for estimating price sensitivities or "Greeks." Chapter 8 deals with the pricing of
American options, which entails solving an optimal stopping problem within a simulation. Chapter 9
is an introduction to the use of Monte Carlo methods in risk management. It discusses the
measurement of market risk and credit risk in financial portfolios. The models and methods of this
final chapter are rather different from vii those in the other chapters,
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15. Ofdm Transmission By Stephen Kiambi
OFDM transmission
Author: Stephen Kiambi
Department of Electrical and Information Engineering, University of Nairobi
OFDM or Orthogonal Frequency Division Multiplexing is a transmission scheme that is widely used
in broadcast and wireless communication technologies. Some of the applications employing OFDM
include Digital Audio Broadcast (DAB), Digital Video Broadcasting Terrestrial (DVB–T2),
Wireless–LAN, Worldwide Interoperability for Microwave Access (WiMAX) and 4G Long Term
Evolution (LTE) radio technologies [1, 2]. Two of the main reasons to use OFDM are to increase
date rates and robustness against frequency–selective fading. In the rest of this document an
overview of OFDM transmission theory is given.
1 Basic principles of OFDM
OFDM is a multicarrier transmission technique that splits the total available bandwidth into many
narrowband sub–channels at equidistant frequencies. The sub–channel spectra overlap each other
but the subcarrier signals are still orthogonal. The single high–rate data stream is subdivided into
many low–rate data streams for the sub–channels. Each sub–channel is modulated individually and
all the sub–channels are transmitted simultaneously in a superimposed and parallel form.
An OFDM transmit signal therefore consists of adjacent orthogonal subcarriers spaced by the
frequency distance on the frequency axis. All subcarrier signals are mutually orthogonal within the
symbol duration, , if the –th unmodulated subcarrier signal is described
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17. Project Description Of A Mathematical Model
Project Description In many science and engineering applications, such as petroleum engineering,
aerospace engineer– ing and material sciences, inference based on a mathematical model and
available observations from the model has garnered importance in recent years. With the lack of the
analytical expres– sion, in most scenarios this solution involves numerical approximation. The
underlying system may contain unknown parameters which requires solving an inverse problem
based on the ob– served data. In many cases the underlying model may contain high dimensional
field which varies in multiple scales such as composite material, porous media etc. This high
dimensional solution can become computationally taxing even with the recent advent of ... Show
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For example, in petroleum engineering the reservoir permeability may be unknown. From oil/water
pressure data from different well locations estimating the unknown κ is an inverse problem. 1
Figure 1: Left hand panel shows one dimensional basis at coarse level of discretization at grid
points 1,2,3,.... Basis corresponding grid point 2, φ2 is supported in [1,3] interval and zero otherwise
and linear in [1,2] and [2,3]. Right hand panel shows typical multiscale basis at two dimension,
which takes non zero value on coarse neighborhood of some coarse grid points but has high
resolution by solving a local problem. The solution u, the parameter κ can have oscillatory nature
(both in temporal and spatial scale) with multiple scales/periods. A numerical solution that captures
the local property of this solution requires capturing the local structure which involves solving a
homogenous version of (1) locally and use these solutions as basis to capture the global solution,
which is known as multiscale solution (Fish et al., 2012; Franca et al., 2005). A highly oscillatory
κ(x, t) = κ(x) is given for a two dimensional domain in Figure 2 . In numerical solution, the domain
is split into many small grids and basis corresponding to each grid, also known as fine scale basis,
can capture the oscillatory solution (see Figure 1). The linear pde system can be reduced into
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19. Hippocampal Shape Analysis
Many studies focus on the statistical analysis of volume measurements of the hippocampus as for
example for the study of Alzheimer's disease [6]. But such studies do not capture the shape
complexity of the structures observed in MRI. Analyzing shapes of structures can provide a better
understanding of the anatomical variability of the brain, which is a very challenging problem since
healthy brains have a high variability, and it is important to understand the mechanisms, the
morphological changes and the impacts of diseases.
Predicting or classifying dementia based on hippocampal shape analysis is an active field of
research. In [7], Statistical Shape Models (SSMs) have been used to model the variability in the
hippocampal shapes among the population. In [8], they characterize shape abnormalities of
subcortical and ventricular structures as well as the subregions of the hippocampus and the
amygdala in subjects with MCI or AD within framework of Large Deformation Diffeomorphic
Metric (LDDMM). In [9] they propose a template–based analysis of anatomical variability in
populations, also in the framework of LDMM. ... Show more content on Helpwriting.net ...
This method solves the correspondence problem by the alignment of the spherical parametrization
using a first order ellipsoid [10]. In [11], they propose a method to automatically discriminate
between patients with Alzheimer's disease (AD) or mild cognitive impairment (MCI) and elderly
controls, based on multidimensional classification of hippocampal shape features. This approach
uses spherical harmonics (SPHARM) coefficients to model the shape of the hippocampi. However,
as this method establishes correspondence on simplified spherical models of surfaces, it is restricted
to surfaces with spherical topology and is computationally
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21. Mars-K And Misk Lab Report
Benchmarking of the kinetic RWM stability codes MARS–K and MISK has been extended by
including additional physics and utilized to calculate the stability of ITER in a realistic high beta
projected operating space. It should be mentioned that although this effort expands upon the physics
that is benchmarked between MARS–K and MISK and strives to present a more realistic picture of
ITER stability, there remain some potentially important areas of physics not be considered here,
including self–consistency of the eigenfunction, (–– removed HTML ––) (–– removed HTML ––)
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barriers in ITER, (–– removed HTML ––) (–– removed HTML ––) 38 (–– removed HTML ... Show
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This tends to reduce the low–rotation stability, but also to reduce the instability in between
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23. Physics Of Prime Numbers
Abstract The Physics of Prime Numbers [1] Yeow Liiyung University of Leeds Introduces the prime
numbers and the Riemann Hypothesis as an im– portant unsolved problem in mathematics, and
suggests that there may be a physical interpretation or embodiment of the problem. Although several
physical interpretations are on offer, this paper focuses primarily on how the primes may be
connected to quantum physics and classical chaos, and seeks to compile evidence hitherto that this
might be true. We take a spec– ulative look into the currently unknown Hermitian Hˆ operator, and
explore the attempts to identify it. Although the idea is rather complex, and most calculations and
evidence reach a level of technicality far beyond undergrad– uate level, this paper tries to put the
idea forward on a level suitable for second–year physics undergraduates' understanding. 1. Prime
Numbers Mathematics is intricately related to physics, and is often employed to aid calculations or
derive further understanding on physical concepts. One fundamental field of mathematics is number
theory, specifically the area con– cerning prime numbers. Prime numbers are numbers that do not
have factors other than itself and the number 1; they are not products of other numbers. In this sense,
they are like the atoms of numbers and arithmetic, because it is possible to uniquely construct the
rest of the numbers from products of prime numbers. While Christian Goldbach's conjecture that
every number is a sum of two
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