1,713 research outputs found
Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds
In this paper, we study the efficient numerical integration of functions with
sharp gradients and cusps. An adaptive integration algorithm is presented that
systematically improves the accuracy of the integration of a set of functions.
The algorithm is based on a divide and conquer strategy and is independent of
the location of the sharp gradient or cusp. The error analysis reveals that for
a function (derivative-discontinuity at a point), a rate of convergence
of is obtained in . Two applications of the adaptive integration
scheme are studied. First, we use the adaptive quadratures for the integration
of the regularized Heaviside function---a strongly localized function that is
used for modeling sharp gradients. Then, the adaptive quadratures are employed
in the enriched finite element solution of the all-electron Coulomb problem in
crystalline diamond. The source term and enrichment functions of this problem
have sharp gradients and cusps at the nuclei. We show that the optimal rate of
convergence is obtained with only a marginal increase in the number of
integration points with respect to the pure finite element solution with the
same number of elements. The adaptive integration scheme is simple, robust, and
directly applicable to any generalized finite element method employing
enrichments with sharp local variations or cusps in -dimensional
parallelepiped elements.Comment: 22 page
Majorana spin-flip transitions in a magnetic trap
Atoms confined in a magnetic trap can escape by making spin-flip Majorana
transitions due to a breakdown of the adiabatic approximation. Several papers
have studied this process for atoms with spin or . The present
paper calculates the escape rate for atoms with spin . This problem has
new features because the perturbation which allows atoms to escape
satisfies a selection rule and multi-step
processes contribute in leading order. When the adiabatic approximation is
satisfied the leading order terms can be summed to yield a simple expression
for the escape rate.Comment: 16page
CONTINUITY OF CONDITION SPECTRUM AND ITS LEVEL SET IN BANACH ALGEBRA
For 0 < � < 1 and a Banach algebra element a, this thesis aims to establish
the results related to continuity of condition spectrum and its level set correspondence
at (�; a). Here we propose a method of study to achieve the continuity. We
first identify the Banach algebras at which the interior of the level set of condition
spectrum is empty and then we obtain the continuity results.
This thesis consists of four chapters. Chapter 1 contains all the prerequisites
which are crucial for the development of the thesis. In particular, this chapter
has a quick review of the basic properties of spectrum, condition spectrum, upper
and lower hemicontiuous correspondences. We also concentrate on analytic vector
valued maps and generalized maximum modulus theorem for them.
For an element a in A, Chapter 2 has the results related to interior of the level of
set of the condition spectrum of a. At first, we focus on
Generalized Duffy transformation for integrating vertex singularities
For an integrand with a 1/r vertex singularity, the Duffy transformation from a triangle (pyramid) to a square (cube) provides an accurate and efficient technique to evaluate the integral. In this paper, we generalize the Duffy transformation to power singularities of the form p(x)/r
α
, where p is a trivariate polynomial and α > 0 is the strength of the singularity. We use the map (u, v, w) → (x, y, z) : x = u
β
, y = x
v, z = x
w, and judiciously choose β to accurately estimate the integral. For α = 1, the Duffy transformation (β = 1) is optimal, whereas if α ≠ 1, we show that there are other values of β that prove to be substantially better. Numerical tests in two and three dimensions are presented that reveal the improved accuracy of the new transformation. Higher-order partition of unity finite element solutions for the Laplace equation with a derivative singularity at a re-entrant corner are presented to demonstrate the benefits of using the generalized Duffy transformation
An Effective Sentence Ordering Approach For Multi-Document Summarization Using Text Entailment
With the rapid development of modern technology electronically available textual information has increased to a considerable amount. Summarization of textual inform ation manually from unstructured text sources creates overhead to the user, therefore a systematic approach is required. Summarization is an approach that focuses on providing the user with a condensed version of the origina l text but in real time applicat ions extended document summarization is required for summarizing the text from multiple documents. The main focus of multi - document summarization is sentence ordering and ranking that arranges the collected sentences from multiple document in order to gene rate a well - organized summary. The improper order of extracted sentences significantly degrades readability and understandability of the summary. The existing system does multi document summarization by combining several preference measures such as chronology, probabilistic, precedence, succession, topical closeness experts to calculate the preference value between sentences. These approach to sent ence ordering and ranking does not address context based similarity measure between sentences which is very ess ential for effective summarization. The proposed system addresses this issues through textual entailment expert system. This approach builds an entailment model which incorpo rates the cause and effect between sentences in the documents using the symmetric measure such as cosine similarity and non - symmetric measures such as unigram match, bigram match, longest common sub - sequence, skip gram match, stemming. The proposed system is efficient in providing user with a contextual summary which significantly impro ves the readability and understandability of the final coherent summa
PT-symmetric square well and the associated SUSY hierarchies
The PT-symmetric square well problem is considered in a SUSY framework. When
the coupling strength lies below the critical value
where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY
partner potentials, depicting an unbroken SUSY situation and reducing to the
family of -like potentials in the limit. For above
, there is a rich diversity of SUSY hierarchies, including
some with PT-symmetry breaking and some with partial PT-symmetry restoration.Comment: LaTeX, 18 pages, no figure; broken PT-symmetry case added (Sec. 6
Second Order Darboux Displacements
The potentials for a one dimensional Schroedinger equation that are displaced
along the x axis under second order Darboux transformations, called 2-SUSY
invariant, are characterized in terms of a differential-difference equation.
The solutions of the Schroedinger equation with such potentials are given
analytically for any value of the energy. The method is illustrated by a
two-soliton potential. It is proven that a particular case of the periodic
Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the
corresponding Schroedinger equation equation are found for any value of the
energy. A simple analytic expression for a family of two-gap potentials is
derived
Medical History for Anesthesiologists: Continuation of a Primer
Editor’s note: The absence of a recognized formal curriculum in anesthesia history means that many of us have known and unknown gaps in our knowledge. These gaps limit our ability to understand how things came to be, how things may become and how we can affect the future. I have asked Dr. Manisha Desai and Dr. Sukumar Desai to provide a primer on the history of medicine and anesthesia history. The goals of this primer are to educate and to help individuals target future study. Below is the second article in a continuing series
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