1,518 research outputs found
Fracturing rock with ultra high pressure water
Modelling issues are considered for the process of cracking rock in mines using ultra high pressure water. The elevated pressures are caused by the ignition of a propellant and may be as large as 1000MPa. We first consider time, length and pressure scales and then derive a model for the propagation of a two-dimensional crack. A number of aspects of this model are considered and similarity solutions and behaviour near the crack tip are investigated. Consideration is given to a simplified model where the elastic component of the interaction between the rock and the fluid is handled using an elementary closure law: in this case much progress may be made and closed-form solutions may be determined. Conditions are also identified where a model based on “impulsive” lubrication theory is appropriate. However, this leads to a very challenging problem. Finally, some other ways of extending the model to include (for example) fluid leak-off into the rock are discussed
Rare Decay Modes of Quarter BPS Dyons
The degeneracy of quarter BPS dyons in N=4 supersymmetric string theories is
known to jump across walls of marginal stability on which a quarter BPS dyon
can decay into a pair of half BPS dyons. We show that as long as the electric
and magnetic charges of the original dyon are primitive elements of the charge
lattice, the subspaces of the moduli space on which a quarter BPS dyon becomes
marginally unstable against decay into a pair of quarter BPS dyons or a half
BPS dyon and a quarter BPS dyon are of codimension two or more. As a result any
pair of generic points in the moduli space can be connected by a path avoiding
these subspaces and there is no jump in the spectrum associated with these
subspaces.Comment: LaTeX file, 9 pages; v2: a minor logical error corrected with no
change in the result
How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
Single centered supersymmetric black holes in four dimensions have
spherically symmetric horizon and hence carry zero angular momentum. This leads
to a specific sign of the helicity trace index associated with these black
holes. Since the latter are given by the Fourier expansion coefficients of
appropriate meromorphic modular forms of Sp(2,Z) or its subgroup, we are led to
a specific prediction for the signs of a subset of these Fourier coefficients
which represent contributions from single centered black holes only. We
explicitly test these predictions for the modular forms which compute the index
of quarter BPS black holes in heterotic string theory on T^6, as well as in Z_N
CHL models for N=2,3,5,7.Comment: LaTeX file, 17 pages, 1 figur
A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines
This paper presents a novel idea for the general case of the Common Due-Date
(CDD) scheduling problem. The problem is about scheduling a certain number of
jobs on a single or parallel machines where all the jobs possess different
processing times but a common due-date. The objective of the problem is to
minimize the total penalty incurred due to earliness or tardiness of the job
completions. This work presents exact polynomial algorithms for optimizing a
given job sequence for single and identical parallel machines with the run-time
complexities of for both cases, where is the number of jobs.
Besides, we show that our approach for the parallel machine case is also
suitable for non-identical parallel machines. We prove the optimality for the
single machine case and the runtime complexities of both. Henceforth, we extend
our approach to one particular dynamic case of the CDD and conclude the chapter
with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page
Scaling in Plasticity-Induced Cell-Boundary Microstructure: Fragmentation and Rotational Diffusion
We develop a simple computational model for cell boundary evolution in
plastic deformation. We study the cell boundary size distribution and cell
boundary misorientation distribution that experimentally have been found to
have scaling forms that are largely material independent. The cell division
acts as a source term in the misorientation distribution which significantly
alters the scaling form, giving it a linear slope at small misorientation
angles as observed in the experiments. We compare the results of our simulation
to two closely related exactly solvable models which exhibit scaling behavior
at late times: (i) fragmentation theory and (ii) a random walk in rotation
space with a source term. We find that the scaling exponents in our simulation
agree with those of the theories, and that the scaling collapses obey the same
equations, but that the shape of the scaling functions depend upon the methods
used to measure sizes and to weight averages and histograms
Dyon Death Eaters
We study general two-body decays of primitive and non-primitive 1/4-BPS dyons
in four-dimensional type IIB string compactifications. We find a ``master
equation'' for marginal stability that generalises the curve found by Sen for
half-BPS decay, and analyse this equation in a variety of cases including
decays to 1/4-BPS products. For half-BPS decays, an interesting and useful
relation is exhibited between walls of marginal stability and the mathematics
of Farey sequences and Ford circles. We exhibit an example in which two curves
of marginal stability intersect in the interior of moduli space.Comment: 24 pages, 1 figure, v2: section on non-primitive dyons slightly
modified and expanded, few other small change
Chiral radiative corrections and D_s(2317)/D(2308) mass puzzle
We show that one loop chiral corrections for heavy-light mesons in potential
model can explain the small mass of D_s(2317) as well as the small mass gap
between D_s(2317) and D(2308).Comment: To appear in EPJC. A figure and references addede
The mixed black hole partition function for the STU model
We evaluate the mixed partition function for dyonic BPS black holes using the
recently proposed degeneracy formula for the STU model. The result factorizes
into the OSV mixed partition function times a proportionality factor. The
latter is in agreement with the measure factor that was recently conjectured
for a class of N=2 black holes that contains the STU model.Comment: 14 page
Three String Junction and N=4 Dyon Spectrum
The exact spectrum of dyons in a class of N=4 supersymmetric string theories
gives us information about dyon spectrum in N=4 supersymmetric gauge theories.
This in turn can be translated into prediction about the BPS spectrum of three
string junctions on a configuration of three parallel D3-branes. We show that
this prediction agrees with the known spectrum of three string junction in
different domains in the moduli space separated by walls of marginal stability.Comment: LaTeX file, 14 page
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