29,221 research outputs found
On the local dynamics of polynomial difference equations with fading stochastic perturbations
We examine the stability-instability behaviour of a polynomial difference equa- tion with state-independent, asymptotically fading stochastic perturbations. We find that the set of initial values can be partitioned into a stability region, an instability region, and a region of unknown dynamics that is in some sense \small". In the ĀÆrst two cases, the dynamic holds with probability at least 1 Ā” Ā°, a value corresponding to the statistical notion of a confidence level. Aspects of an equation with state-dependent perturbations are also treated. When the perturbations are Gaussian, the difference equation is the Euler-Maruyama dis- cretisation of an It^o-type stochastic differential equation with solutions displaying global a.s. asymptotic stability. The behaviour of any particular solution of the difference equation can be made consistent with the corresponding solution of the differential equation, with probability 1 Ā” Ā°, by choosing the stepsize parameter sufficiently small. We present examples illustrating the relationship between h, Ā° and the size of the stability region
Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
Model lattices consisting of balls connected by central-force springs provide
much of our understanding of mechanical response and phonon structure of real
materials. Their stability depends critically on their coordination number .
-dimensional lattices with are at the threshold of mechanical
stability and are isostatic. Lattices with exhibit zero-frequency
"floppy" modes that provide avenues for lattice collapse. The physics of
systems as diverse as architectural structures, network glasses, randomly
packed spheres, and biopolymer networks is strongly influenced by a nearby
isostatic lattice. We explore elasticity and phonons of a special class of
two-dimensional isostatic lattices constructed by distorting the kagome
lattice. We show that the phonon structure of these lattices, characterized by
vanishing bulk moduli and thus negative Poisson ratios and auxetic elasticity,
depends sensitively on boundary conditions and on the nature of the kagome
distortions. We construct lattices that under free boundary conditions exhibit
surface floppy modes only or a combination of both surface and bulk floppy
modes; and we show that bulk floppy modes present under free boundary
conditions are also present under periodic boundary conditions but that surface
modes are not. In the the long-wavelength limit, the elastic theory of all
these lattices is a conformally invariant field theory with holographic
properties, and the surface waves are Rayleigh waves. We discuss our results in
relation to recent work on jammed systems. Our results highlight the importance
of network architecture in determining floppy-mode structure.Comment: 12 pages, 7 figure
Evaluation of a locally homogeneous flow model of spray combustion
A model of spray combustion which employs a second-order turbulence model was developed. The assumption of locally homogeneous flow is made, implying infinitely fast transport rates between the phase. Measurements to test the model were completed for a gaseous n-propane flame and an air atomized n-pentane spray flame, burning in stagnant air at atmospheric pressure. Profiles of mean velocity and temperature, as well as velocity fluctuations and Reynolds stress, were measured in the flames. The predictions for the gas flame were in excellent agreement with the measurements. The predictions for the spray were qualitatively correct, but effects of finite rate interphase transport were evident, resulting in a overstimation of the rate development of the flow. Predictions of spray penetration length at high pressures, including supercritical combustion conditions, were also completed for comparison with earlier measurements. Test conditions involved a pressure atomized n-pentane spray, burning in stagnant air at pressures of 3, 5, and 9 MPa. The comparison between predictions and measurements was fair. This is not a very sensitive test of the model, however, and further high pressure experimental and theoretical results are needed before a satisfactory assessment of the locally homogeneous flow approximation can be made
Constraints on the average magnetic field strength of relic radio sources 0917+75 and 1401-33 from XMM-Newton observations
We observed two relic radio sources, 0917+75 and 1401-33, with the XMM-Newton
X-ray observatory. We did not detect any X-ray emission, thermal or
non-thermal, in excess of the local background level from either target. This
imposes new upper limits on the X-ray flux due to inverse Compton scattering of
photons from the cosmic microwave background by relativistic electrons in the
relic sources, and new lower limits on the magnetic field strength from the
relative strength of the radio and X-ray emission. The combination of radio and
X-ray observations provides a measure of the magnetic field independent of
equipartition or minimum energy assumptions. Due to increasing sensitivity of
radio observations, the known population of cluster relics has been growing;
however, studies of non-thermal X-ray emission from relics remain scarce. Our
study adds to the small sample of relics studied in X-rays. In both relics, our
field strength lower limits are slightly larger than estimates of the
equipartition magnetic field.Comment: 11 pages, 5 figures. Accepted by MNRA
Constraining f(R) Gravity as a Scalar Tensor Theory
We search for viable f(R) theories of gravity, making use of the equivalence
between such theories and scalar-tensor gravity. We find that models can be
made consistent with solar system constraints either by giving the scalar a
high mass or by exploiting the so-called chameleon effect. However, in both
cases, it appears likely that any late-time cosmic acceleration will be
observationally indistinguishable from acceleration caused by a cosmological
constant. We also explore further observational constraints from, e.g., big
bang nucleosynthesis and inflation.Comment: 15 pages, 5 figure
Detection of microgauss coherent magnetic fields in a galaxy five billion years ago
Magnetic fields play a pivotal role in the physics of interstellar medium in
galaxies, but there are few observational constraints on how they evolve across
cosmic time. Spatially resolved synchrotron polarization maps at radio
wavelengths reveal well-ordered large-scale magnetic fields in nearby galaxies
that are believed to grow from a seed field via a dynamo effect. To directly
test and characterize this theory requires magnetic field strength and geometry
measurements in cosmologically distant galaxies, which are challenging to
obtain due to the limited sensitivity and angular resolution of current radio
telescopes. Here, we report the cleanest measurements yet of magnetic fields in
a galaxy beyond the local volume, free of the systematics traditional
techniques would encounter. By exploiting the scenario where the polarized
radio emission from a background source is gravitationally lensed by a
foreground galaxy at z = 0.439 using broadband radio polarization data, we
detected coherent G magnetic fields in the lensing disk galaxy as seen 4.6
Gyrs ago, with similar strength and geometry to local volume galaxies. This is
the highest redshift galaxy whose observed coherent magnetic field property is
compatible with a mean-field dynamo origin.Comment: 29 pages, 5 figures (including Supplementary Information). Published
in Nature Astronomy on August 28, 201
Spin-spin correlators in Majorana representation
In the Majorana representation of a spin 1/2 we find an identity which
relates spin-spin correlators to one-particle fermionic correlators. This
should be contrasted with the straightforward approach in which two-particle
(four-fermion) correlators need to be calculated. We discuss applications to
the analysis of the dynamics of a spin coupled to a dissipative environment and
of a quantum detector performing a continuous measurement of a qubit's state
Quantum Reciprocity Conjecture for the Non-Equilibrium Steady State
By considering the lack of history dependence in the non-equilibrium steady
state of a quantum system we are led to conjecture that in such a system, there
is a set of quantum mechanical observables whose retarded response functions
are insensitive to the arrow of time, and which consequently satisfy a quantum
analog of the Onsager reciprocity relations. Systems which satisfy this
conjecture can be described by an effective Free energy functional. We
demonstrate that the conjecture holds in a resonant level model of a multi-lead
quantum dot.Comment: References revised to take account of related work on Onsager
reciprocity in mesoscopics by Christen, and in hydrodynamics by Mclennan,
Dufty and Rub
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