3,107 research outputs found
Modelling with measures: Approximation of a mass-emitting object by a point source
We consider a linear diffusion equation on
, where
is a bounded domain. The time-dependent flux on the
boundary is prescribed. The aim of the
paper is to approximate the dynamics by the solution of the diffusion equation
on the whole of with a measure-valued point source in the origin
and provide estimates for the quality of approximation. For all time , we
derive an -bound on the difference in flux on the
boundary. Moreover, we derive for all an -bound and an
-bound for the difference of the solutions to the two
models
Letter from H. L. Hille to Senator Langer Regarding Construction Bids for the Garrison Dam Project, January 31, 1955
This letter, dated January 31, 1955, from Colonel H. L. Hille of the United States (US) Army Corps of Engineers, Garrison District, to US Senator William Langer, informs Langer of the planned invitation for bids for two components of the the Garrison Dam Project taking place on the Fort Berthold Indian Reservation: lawn construction in New Town, North Dakota, on which bids will be opened on or around March 1, 1955, and the construction of the East Abutment Grout Curtain, on which bids will be opened on or about March 15, 1955.
The letter includes more detailed descriptions of the two projects, and enclosed with it are advance notices for each of the two projects. Advance notices, Hille writes, have been sent to all parties who are known to be interesed in bidding on the work.
See also: Letter from Senator Langer to H. L. Hille Regarding Construction Bids for the Garrison Dam Project, February 8, 1955https://commons.und.edu/langer-papers/1993/thumbnail.jp
Letter from H. L. Hille to Representative Burdick Announcing Invitation of Bids for Lawn Construction on Fort Berthold Reservation, January 31, 1955
This letter dated January 31, 1955, from Colonel H. L. Hille to United States (US) Representative Usher Burdick, informs Burdick that the US Army Corps of Engineers proposes to issue an invitation for bids for lawn construction on the Fort Berthold Reservation. Hille details what the work will entail and where it will take place. Hille notes he has included a copy of the invitation for project bids with this letter.
The included invitation for project bids gives specifics needed for a firm to submit an accurate bid and lists the required components for a submission.https://commons.und.edu/burdick-papers/1382/thumbnail.jp
Effect of Interactions on Molecular Fluxes and Fluctuations in the Transport Across Membrane Channels
Transport of molecules across membrane channels is investigated theoretically
using exactly solvable one-dimensional discrete-state stochastic models. An
interaction between molecules and membrane pores is modeled via a set of
binding sites with different energies. It is shown that the interaction
potential strongly influences the particle currents as well as fluctuations in
the number of translocated molecules. For small concentration gradients the
attractive sites lead to largest currents and fluctuations, while the repulsive
interactions yield the largest fluxes and dispersions for large concentration
gradients. Interaction energies that lead to maximal currents and maximal
fluctuations are the same only for locally symmetric potentials, while they
differ for the locally asymmetric potentials. The conditions for the most
optimal translocation transport with maximal current and minimal dispersion are
discussed. It is argued that in this case the interaction strength is
independent of local symmetry of the potential of mean forces. In addition, the
effect of the global asymmetry of the interaction potential is investigated,
and it is shown that it also strongly affects the particle translocation
dynamics. These phenomena can be explained by analyzing the details of the
particle entering and leaving the binding sites in the channel.Comment: submitted to J. Chem. Phy
A nonlinear equation for ionic diffusion in a strong binary electrolyte
The problem of the one dimensional electro-diffusion of ions in a strong
binary electrolyte is considered. In such a system the solute dissociates
completely into two species of ions with unlike charges. The mathematical
description consists of a diffusion equation for each species augmented by
transport due to a self consistent electrostatic field determined by the
Poisson equation. This mathematical framework also describes other important
problems in physics such as electron and hole diffusion across semi-conductor
junctions and the diffusion of ions in plasmas. If concentrations do not vary
appreciably over distances of the order of the Debye length, the Poisson
equation can be replaced by the condition of local charge neutrality first
introduced by Planck. It can then be shown that both species diffuse at the
same rate with a common diffusivity that is intermediate between that of the
slow and fast species (ambipolar diffusion). Here we derive a more general
theory by exploiting the ratio of Debye length to a characteristic length scale
as a small asymptotic parameter. It is shown that the concentration of either
species may be described by a nonlinear integro-differential equation which
replaces the classical linear equation for ambipolar diffusion but reduces to
it in the appropriate limit. Through numerical integration of the full set of
equations it is shown that this nonlinear equation provides a better
approximation to the exact solution than the linear equation it replaces.Comment: 4 pages, 1 figur
Sensing of Fluctuating Nanoscale Magnetic Fields Using NV Centres in Diamond
New magnetometry techniques based on Nitrogen-Vacancy (NV) defects in diamond
allow for the imaging of static (DC) and oscillatory (AC) nanoscopic magnetic
systems. However, these techniques require accurate knowledge and control of
the sample dynamics, and are thus limited in their ability to image fields
arising from rapidly fluctuating (FC) environments. We show here that FC fields
place restrictions on the DC field sensitivity of an NV qubit magnetometer, and
that by probing the dephasing rate of the qubit in a magnetic FC environment,
we are able to measure fluctuation rates and RMS field strengths that would be
otherwise inaccessible with the use of DC and AC magnetometry techniques. FC
sensitivities are shown to be comparable to those of AC fields, whilst
requiring no additional experimental overheads or control over the sample.Comment: 5 pages, 4 figure
On a certain class of semigroups of operators
We define an interesting class of semigroups of operators in Banach spaces,
namely, the randomly generated semigroups. This class contains as a remarkable
subclass a special type of quantum dynamical semigroups introduced by
Kossakowski in the early 1970s. Each randomly generated semigroup is
associated, in a natural way, with a pair formed by a representation or an
antirepresentation of a locally compact group in a Banach space and by a
convolution semigroup of probability measures on this group. Examples of
randomly generated semigroups having important applications in physics are
briefly illustrated.Comment: 11 page
Ab initio molecular dynamics calculations of ion hydration free energies
We apply ab initio molecular dynamics (AIMD) methods in conjunction with the
thermodynamic integration or "lambda-path" technique to compute the intrinsic
hydration free energies of Li+, Cl-, and Ag+ ions. Using the
Perdew-Burke-Ernzerhof functional, adapting methods developed for classical
force field applications, and with consistent assumptions about surface
potential (phi) contributions, we obtain absolute AIMD hydration free energies
(Delta G(hyd)) within a few kcal/mol, or better than 4%, of Tissandier 's [J.
Phys. Chem. A 102, 7787 (1998)] experimental values augmented with the SPC/E
water model phi predictions. The sums of Li+/Cl- and Ag+/Cl- AIMD Delta G(hyd),
which are not affected by surface potentials, are within 2.6% and 1.2 % of
experimental values, respectively. We also report the free energy changes
associated with the transition metal ion redox reaction Ag++Ni+-> Ag+Ni2+ in
water. The predictions for this reaction suggest that existing estimates of
Delta G(hyd) for unstable radiolysis intermediates such as Ni+ may need to be
extensively revised.Comment: 18 pages, 8 figures. This version is essentially the one published in
J. Chem. Phy
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