1,072 research outputs found
Nonlinear Schroedinger equation with two symmetric point interactions in one dimension
We consider a time-dependent one-dimensional nonlinear Schroedinger equation
with a symmetric potential double well represented by two delta interactions.
Among our results we give an explicit formula for the integral kernel of the
unitary semigroup associated with the linear part of the Hamiltonian. Then we
establish the corresponding Strichartz-type estimate and we prove local
existence and uniqueness of the solution to the original nonlinear problem
When is a bottleneck a bottleneck?
Bottlenecks, i.e. local reductions of capacity, are one of the most relevant
scenarios of traffic systems. The asymmetric simple exclusion process (ASEP)
with a defect is a minimal model for such a bottleneck scenario. One crucial
question is "What is the critical strength of the defect that is required to
create global effects, i.e. traffic jams localized at the defect position".
Intuitively one would expect that already an arbitrarily small bottleneck
strength leads to global effects in the system, e.g. a reduction of the maximal
current. Therefore it came as a surprise when, based on computer simulations,
it was claimed that the reaction of the system depends in non-continuous way on
the defect strength and weak defects do not have a global influence on the
system. Here we reconcile intuition and simulations by showing that indeed the
critical defect strength is zero. We discuss the implications for the analysis
of empirical and numerical data.Comment: 8 pages, to appear in the proceedings of Traffic and Granular Flow
'1
Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials
We consider semiclassical Schr\"odinger operators on the real line of the
form with
small. The potential is assumed to be smooth, positive and exponentially
decaying towards infinity. We establish semiclassical global representations of
Jost solutions with error terms that are uniformly
controlled for small and , and construct the scattering matrix as
well as the semiclassical spectral measure associated to . This is
crucial in order to obtain decay bounds for the corresponding wave and
Schr\"odinger flows. As an application we consider the wave equation on a
Schwarzschild background for large angular momenta where the role of the
small parameter is played by . It follows from the results
in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1},
\cite{DS} for individual angular momenta can be summed to yield the
sharp decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published
version, will appear in Annales Henri Poincar
The importance of circulating tumor products as âliquid biopsiesâ in colorectal cancer
Liquid biopsies represent an array of plasma analysis tests that are studied to evaluate and identify circulating tumor products, especially circulating tumor cells (CTCs) and circulating tumor DNA (ctDNA). Examining such biomarkers in the plasma of colorectal cancer patients has attracted attention due to its clinical significance in the treatment of malignant diseases. Given that tissue samples are sometimes challenging to procure or unsatisfactory for genomic profiling from patients with colorectal cancer, trustworthy biomarkers are mandatory for guiding treatment, monitoring therapeutic response, and detecting recurrence.
This review considers the relevance of flowing tumor products like circulating tumor cells (CTCs), circulating tumor DNA (ctDNA), circulating messenger RNA (mRNA), circulating micro RNA (miRNA), circulating exosomes, and tumor educated platelets (TEPs) for patients with colorectal cancer
Collaborative procurement and private-sector housebuilding and refurbishment works: A pilot study investigation of the UK
Purpose
Framed as a pilot study, the purpose of this paper is to study the perceived appropriateness of an existing collaborative procurement procedures (CPP) framework from the housebuilderâs perspective; seeking to improve its utility and stimulate further exploration.
Design/methodology/approach
Informed by an existing CPP framework, and conducted by a UK-based development professional, four in-depth semi-structured interviews were undertaken with senior housebuilding practitioners from London and surrounding counties. A qualitative analysis was then conducted for this sociological study.
Findings
Perceived appropriateness of the framework was high; however, a number of procedural improvements were identified, along with limitations. Future studies are recommended including the influence upon project performance of groundworker integration at the design stage.
Research limitations/implications
Limited to four interviews from one regional area, the study is an initial insight into the appropriateness of an existing CPP framework. Insights into why CP uptake is marginal within housebuilding were also gained. The research purpose was achieved but by offering a self-reflection upon practice (vis-Ă -vis wider generalisations) the findings provide a springboard for further studies.
Practical implications
The research identifies with current practice, industry perceptions, and paths towards improving the utility of the CPP framework.
Social implications
This study offers insights into the perceptions of private housebuilding practitioners of their own practices and the factors they find challenging within the social constructs of their industry.
Originality/value
This research constitutes one of the first studies in the UK to examine the CPP framework from the perspective of the private housebuilder and is undertaken with the express purpose of furthering that frameworkâs utility
Comment on "Critique of the foundations of time-dependent density functional theory" [Phys. Rev.A. 75, 022513 (2007)]
A recent paper (Phys. Rev A. 75, 022513 (2007), arXiv:cond-mat/0602020)
challenges exact time-dependent density functional theory (TDDFT) on several
grounds. We explain why these criticisms are either irrelevant or incorrect,
and that TDDFT is both formally exact and predictive.Comment: 4 pages; This is a Comment on the paper cited above, also at
arXiv:cond-mat/060202
On the spectral properties of L_{+-} in three dimensions
This paper is part of the radial asymptotic stability analysis of the ground
state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon
equations in three dimensions. We demonstrate by a rigorous method that the
linearized scalar operators which arise in this setting, traditionally denoted
by L_{+-}, satisfy the gap property, at least over the radial functions. This
means that the interval (0,1] does not contain any eigenvalues of L_{+-} and
that the threshold 1 is neither an eigenvalue nor a resonance. The gap property
is required in order to prove scattering to the ground states for solutions
starting on the center-stable manifold associated with these states. This paper
therefore provides the final installment in the proof of this scattering
property for the cubic Klein-Gordon and Schrodinger equations in the radial
case, see the recent theory of Nakanishi and the third author, as well as the
earlier work of the third author and Beceanu on NLS. The method developed here
is quite general, and applicable to other spectral problems which arise in the
theory of nonlinear equations
Central limit theorem for multiplicative class functions on the symmetric group
Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for
the characteristic polynomial of a permutation matrix with respect to the
uniform measure on the symmetric group. We generalize this result in several
ways. We prove here a central limit theorem for multiplicative class functions
on symmetric group with respect to the Ewens measure and compute the covariance
of the real and the imaginary part in the limit. We also estimate the rate of
convergence with the Wasserstein distance.Comment: 23 pages; the mathematics is the same as in the previous version, but
there are several improvments in the presentation, including a more intuitve
name for the considered function
- âŠ