319 research outputs found
Coagulation kinetics beyond mean field theory using an optimised Poisson representation
Binary particle coagulation can be modelled as the repeated random process of
the combination of two particles to form a third. The kinetics can be
represented by population rate equations based on a mean field assumption,
according to which the rate of aggregation is taken to be proportional to the
product of the mean populations of the two participants. This can be a poor
approximation when the mean populations are small. However, using the Poisson
representation it is possible to derive a set of rate equations that go beyond
mean field theory, describing pseudo-populations that are continuous, noisy and
complex, but where averaging over the noise and initial conditions gives the
mean of the physical population. Such an approach is explored for the simple
case of a size-independent rate of coagulation between particles. Analytical
results are compared with numerical computations and with results derived by
other means. In the numerical work we encounter instabilities that can be
eliminated using a suitable 'gauge' transformation of the problem [P. D.
Drummond, Eur. Phys. J. B38, 617 (2004)] which we show to be equivalent to the
application of the Cameron-Martin-Girsanov formula describing a shift in a
probability measure. The cost of such a procedure is to introduce additional
statistical noise into the numerical results, but we identify an optimised
gauge transformation where this difficulty is minimal for the main properties
of interest. For more complicated systems, such an approach is likely to be
computationally cheaper than Monte Carlo simulation
Single particle multipole expansions from Micromagnetic Tomography
Micromagnetic tomography aims at reconstructing large numbers of individual
magnetizations of magnetic particles from combining high-resolution magnetic
scanning techniques with micro X-ray computed tomography (microCT). Previous
work demonstrated that dipole moments can be robustly inferred, and
mathematical analysis showed that the potential field of each particle is
uniquely determined. Here, we describe a mathematical procedure to recover
higher orders of the magnetic potential of the individual magnetic particles in
terms of their spherical harmonic expansions (SHE). We test this approach on
data from scanning superconducting quantum interference device microscopy and
microCT of a reference sample. For particles with high signal-to-noise ratio of
the magnetic scan we demonstrate that SHE up to order can be robustly
recovered. This additional level of detail restricts the possible internal
magnetization structures of the particles and provides valuable rock magnetic
information with respect to their stability and reliability as paleomagnetic
remanence carriers. Micromagnetic tomography therefore enables a new approach
for detailed rock magnetic studies on large ensembles of individual particles.Comment: 21 pages, 4 Figures, 3 Tables. For Supplemental Material see
"Ancillary files" in this arxiv websit
Wind-induced ground motion: dynamic model and non-uniform structure for ground
Wind-induced ground vibrations are a source of noise in seismic surveys. In a previous study, a wind-ground coupling theory was developed to predict the power spectral density (PSD) of ground motions caused by wind perturbations on the ground surface. The prediction was developed using a superposition of the point source response of an elastic isotropic homogeneous medium deforming quasi-statically with the statistical description of the wind-induced pressure fluctuations on the ground. Model predictions and field measurements were in agreement for the normal component of the displacement but under predicted the horizontal component. In this paper, two generalizations are investigated to see if they lead to increased horizontal displacement predictions: 1. First, the dynamic point source response is calculated and incorporated in the ground displacement calculation. Measured ground responses are used to incorporate losses into the dynamic calculation. 2. The quasi-static response function for three different types of non-uniform grounds are calculated and used in the seismic wind noise superposition. The dynamic point source response and the three more realistic ground models result in larger horizontal displacements for the point source at distances on the order of 1 m or greater from the source. However, the superposition to predict the seismic wind noise is dominated by the displacements very close to the point source where the prediction is unchanged. This research indicates that the modeling of the wind-induced pressure source distribution must be improved to predict the observed equivalency of the vertical and horizontal displacements
Integral transform solution of random coupled parabolic partial differential models
[EN] Random coupled parabolic partial differential models are solved numerically using random cosine Fourier transform together with non-Gaussian random numerical integration that captures the highly oscillatory behaviour of the involved integrands. Sufficient condition of spectral type imposed on the random matrices of the system is given so that the approximated stochastic process solution and its statistical moments are numerically convergent. Numerical experiments illustrate the results.Spanish Ministerio de Economia, Industria y Competitividad (MINECO); Agencia Estatal de Investigacion (AEI); Fondo Europeo de Desarrollo Regional (FEDER UE), Grant/Award Number: MTM2017-89664-PCasabĂĄn Bartual, MC.; Company Rossi, R.; Egorova, VN.; JĂłdar SĂĄnchez, LA. (2020). Integral transform solution of random coupled parabolic partial differential models. Mathematical Methods in the Applied Sciences. 43(14):8223-8236. https://doi.org/10.1002/mma.6492S822382364314BĂ€ck, J., Nobile, F., Tamellini, L., & Tempone, R. (2010). Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison. Spectral and High Order Methods for Partial Differential Equations, 43-62. doi:10.1007/978-3-642-15337-2_3Bachmayr, M., Cohen, A., & Migliorati, G. (2016). Sparse polynomial approximation of parametric elliptic PDEs.
Part I: affine coefficients. ESAIM: Mathematical Modelling and Numerical Analysis, 51(1), 321-339. doi:10.1051/m2an/2016045Ernst, O. G., Sprungk, B., & Tamellini, L. (2018). Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs). SIAM Journal on Numerical Analysis, 56(2), 877-905. doi:10.1137/17m1123079Sheng, D., & Axelsson, K. (1995). Uncoupling of coupled flows in soilâa finite element method. International Journal for Numerical and Analytical Methods in Geomechanics, 19(8), 537-553. doi:10.1002/nag.1610190804Mitchell, J. K. (1991). Conduction phenomena: from theory to geotechnical practice. GĂ©otechnique, 41(3), 299-340. doi:10.1680/geot.1991.41.3.299Das, P. K. (1991). Optical Signal Processing. doi:10.1007/978-3-642-74962-9Ashkenazy, Y. (2017). Energy transfer of surface wind-induced currents to the deep ocean via resonance with the Coriolis force. Journal of Marine Systems, 167, 93-104. doi:10.1016/j.jmarsys.2016.11.019Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500-544. doi:10.1113/jphysiol.1952.sp004764Galiano, G. (2012). On a cross-diffusion population model deduced from mutation and splitting of a single species. Computers & Mathematics with Applications, 64(6), 1927-1936. doi:10.1016/j.camwa.2012.03.045CasabĂĄn, M. C., Company, R., & JĂłdar, L. (2019). Numerical solutions of random mean square FisherâKPP models with advection. Mathematical Methods in the Applied Sciences, 43(14), 8015-8031. doi:10.1002/mma.5942CasabĂĄn, M. C., Company, R., & JĂłdar, L. (2019). Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness. Mathematics, 7(9), 853. doi:10.3390/math7090853Shampine, L. F. (2008). Vectorized adaptive quadrature in MATLAB. Journal of Computational and Applied Mathematics, 211(2), 131-140. doi:10.1016/j.cam.2006.11.021Iserles, A. (2004). On the numerical quadrature of highly-oscillating integrals I: Fourier transforms. IMA Journal of Numerical Analysis, 24(3), 365-391. doi:10.1093/imanum/24.3.365Ma, J., & Liu, H. (2018). On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels. Symmetry, 10(7), 239. doi:10.3390/sym10070239JĂłdar, L., & Goberna, D. (1996). Exact and analytic numerical solution of coupled diffusion problems in a semi-infinite medium. Computers & Mathematics with Applications, 31(9), 17-24. doi:10.1016/0898-1221(96)00038-7JĂłdar, L., & Goberna, D. (1998). A matrix DâAlembert formula for coupled wave initial value problems. Computers & Mathematics with Applications, 35(9), 1-15. doi:10.1016/s0898-1221(98)00052-2Ostrowski, A. M. (1959). A QUANTITATIVE FORMULATION OF SYLVESTERâS LAW OF INERTIA. Proceedings of the National Academy of Sciences, 45(5), 740-744. doi:10.1073/pnas.45.5.740Ashkenazy, Y., Gildor, H., & Bel, G. (2015). The effect of stochastic wind on the infinite depth Ekman layer model. EPL (Europhysics Letters), 111(3), 39001. doi:10.1209/0295-5075/111/3900
Heisenberg XXZ Model and Quantum Galilei Group
The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed in
terms of the symmetry given by the quantum Galilei group Gamma_q(1). We show
that the magnon excitations and the s=1/2, n-magnon bound states are determined
by the algebra. Thus the Gamma_q(1) symmetry provides a description that
naturally induces the Bethe Ansatz. The recurrence relations determined by
Gamma_q(1) permit to express the energy of the n-magnon bound states in a
closed form in terms of Tchebischeff polynomials.Comment: (pag. 10
Regularization of multi-soliton form factors in sine-Gordon model
A general and systematic regularization is developed for the exact solitonic
form factors of exponential operators in the (1+1)-dimensional sine-Gordon
model by analytical continuation of their integral representations. The
procedure is implemented in Mathematica. Test results are shown for four- and
six- soliton form factors.Comment: 12 pages, no figures. v2: minor corrections, some references adde
Can slow roll inflation induce relevant helical magnetic fields?
We study the generation of helical magnetic fields during single field
inflation induced by an axial coupling of the electromagnetic field to the
inflaton. During slow roll inflation, we find that such a coupling always leads
to a blue spectrum with , as long as the theory is treated
perturbatively. The magnetic energy density at the end of inflation is found to
be typically too small to backreact on the background dynamics of the inflaton.
We also show that a short deviation from slow roll does not result in strong
modifications to the shape of the spectrum. We calculate the evolution of the
correlation length and the field amplitude during the inverse cascade and
viscous damping of the helical magnetic field in the radiation era after
inflation. We conclude that except for low scale inflation with very strong
coupling, the magnetic fields generated by such an axial coupling in single
field slow roll inflation with perturbative coupling to the inflaton are too
weak to provide the seeds for the observed fields in galaxies and clusters.Comment: 33 pages 6 figures; v4 to match the accepted version to appear in
JCA
The gravitational-wave memory from eccentric binaries
The nonlinear gravitational-wave memory causes a time-varying but
nonoscillatory correction to the gravitational-wave polarizations. It arises
from gravitational waves that are sourced by gravitational waves. Previous
considerations of the nonlinear memory effect have focused on quasicircular
binaries. Here, I consider the nonlinear memory from Newtonian orbits with
arbitrary eccentricity. Expressions for the waveform polarizations and
spin-weighted spherical-harmonic modes are derived for elliptic, hyperbolic,
parabolic, and radial orbits. In the hyperbolic, parabolic, and radial cases
the nonlinear memory provides a 2.5 post-Newtonian (PN) correction to the
leading-order waveforms. This is in contrast to the elliptical and
quasicircular cases, where the nonlinear memory corrects the waveform at
leading (0PN) order. This difference in PN order arises from the fact that the
memory builds up over a short "scattering" time scale in the hyperbolic case,
as opposed to a much longer radiation-reaction time scale in the elliptical
case. The nonlinear memory corrections presented here complete our knowledge of
the leading-order (Peters-Mathews) waveforms for elliptical orbits. These
calculations are also relevant for binaries with quasicircular orbits in the
present epoch which had, in the past, large eccentricities. Because the
nonlinear memory depends sensitively on the past evolution of a binary, I
discuss the effect of this early-time eccentricity on the value of the
late-time memory in nearly circularized binaries. I also discuss the
observability of large "memory jumps" in a binary's past that could arise from
its formation in a capture process. Lastly, I provide estimates of the
signal-to-noise ratio of the linear and nonlinear memories from hyperbolic and
parabolic binaries.Comment: 25 pages, 8 figures. v2: minor changes to match published versio
H^+_2$ in a strong magnetic field described via a solvable model
We consider the hydrogen molecular ion in the presence of a strong
homogeneous magnetic field. In this regime, the effective Hamiltonian is almost
one dimensional with a potential energy which looks like a sum of two Dirac
delta functions. This model is solvable, but not close enough to our exact
Hamiltonian for relevant strenght of the magnnetic field. However we show that
the correct values of the equilibrium distance as well as the binding energy of
the ground state of the ion, can be obtained when incorporating perturbative
corrections up to second order. Finally, we show that exists for
sufficiently large magnetic fields
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