2,057 research outputs found
A non-local inequality and global existence
In this article we prove a collection of new non-linear and non-local
integral inequalities. As an example for and we
obtain \int_{\threed} dx ~ u^{p+1}(x) \le (\frac{p+1}{p})^2 \int_{\threed}
dx ~ \{(-\triangle)^{-1} u(x) \} \nsm \nabla u^{\frac{p}{2}}(x)\nsm^2. We
use these inequalities to deduce global existence of solutions to a non-local
heat equation with a quadratic non-linearity for large radial monotonic
positive initial conditions. Specifically, we improve \cite{ksLM} to include
all .Comment: 6 pages, to appear in Advances in Mathematic
2D Continuous Wavelet Transform of potential fields due to extended source distributions
AbstractWe analyse the real Continuous Wavelet Transform 2D (CWT2D) of potential fields for the investigation of potential field singularities. We focus our attention to extended geological sources, in order to verify the reliability of this method with realistic fields. 3D space-scale representation (3D Scalogram) related to synthetic models were generated, showing the Wavelet Transform Modulus Maxima (WTMM) at each scale. The WTMM are related to the shape of the source, so defining some sort of source boundary analysis through the CWT. Wavelets of different order may help to gain resolution and define source features. Selecting a range of scales where the sources behave as if they are approximately isolated, the depth to the source may be estimated basing on the property that the lines joining the modulus maxima of the wavelet coefficients at different scales (WTMML) intersect each other at the edges of the causative body. Therefore, it is possible to manage the information contained in the wavelet transform of fields related to extended sources. In the real case of the anomaly gravity map of the Vesuvius area (Italy), we estimated the depth of the Mesozoic carbonate basement in the Pompei Basin. We showed also how the WTMML information can be integrated to that of another multiscale method, the Depth from Extreme Points (DEXP) transformation, which is also related to the source density distribution of a given region
Optimal time decay of the non cut-off Boltzmann equation in the whole space
In this paper we study the large-time behavior of perturbative classical
solutions to the hard and soft potential Boltzmann equation without the angular
cut-off assumption in the whole space \threed_x with \DgE. We use the
existence theory of global in time nearby Maxwellian solutions from
\cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to
determine the large time decay rates for the soft potential Boltzmann equation
in the whole space, with or without the angular cut-off assumption
\cite{MR677262,MR2847536}. For perturbative initial data, we prove that
solutions converge to the global Maxwellian with the optimal large-time decay
rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the
L^2_\vel(L^r_x)-norm for any .Comment: 31 pages, final version to appear in KR
Results and recommendations from an intercomparison of six Hygroscopicity-TDMA systems
The performance of six custom-built Hygrocopicity-Tandem Differential Mobility Analyser (H-TDMA) systems was investigated in the frame of an international calibration and intercomparison workshop held in Leipzig, February 2006. The goal of the workshop was to harmonise H-TDMA measurements and develop recommendations for atmospheric measurements and their data evaluation. The H-TDMA systems were compared in terms of the sizing of dry particles, relative humidity (RH) uncertainty, and consistency in determination of number fractions of different hygroscopic particle groups. The experiments were performed in an air-conditioned laboratory using ammonium sulphate particles or an external mixture of ammonium sulphate and soot particles. The sizing of dry particles of the six H-TDMA systems was within 0.2 to 4.2% of the selected particle diameter depending on investigated size and individual system. Measurements of ammonium sulphate aerosol found deviations equivalent to 4.5% RH from the set point of 90% RH compared to results from previous experiments in the literature. Evaluation of the number fraction of particles within the clearly separated growth factor modes of a laboratory generated externally mixed aerosol was done. The data from the H-TDMAs was analysed with a single fitting routine to investigate differences caused by the different data evaluation procedures used for each H-TDMA. The differences between the H-TDMAs were reduced from +12/-13% to +8/-6% when the same analysis routine was applied. We conclude that a common data evaluation procedure to determine number fractions of externally mixed aerosols will improve the comparability of H-TDMA measurements. It is recommended to ensure proper calibration of all flow, temperature and RH sensors in the systems. It is most important to thermally insulate the aerosol humidification unit and the second DMA and to monitor these temperatures to an accuracy of 0.2 degrees C. For the correct determination of external mixtures, it is necessary to take into account size-dependent losses due to diffusion in the plumbing between the DMAs and in the aerosol humidification unit.Peer reviewe
Variational method and duality in the 2D square Potts model
The ferromagnetic q-state Potts model on a square lattice is analyzed, for
q>4, through an elaborate version of the operatorial variational method. In the
variational approach proposed in the paper, the duality relations are exactly
satisfied, involving at a more fundamental level, a duality relationship
between variational parameters. Besides some exact predictions, the approach is
very effective in the numerical estimates over the whole range of temperature
and can be systematically improved.Comment: 20 pages, 5 EPS figure
The dissipative linear Boltzmann equation for hard spheres
We prove the existence and uniqueness of an equilibrium state with unit mass
to the dissipative linear Boltzmann equation with hard--spheres collision
kernel describing inelastic interactions of a gas particles with a fixed
background. The equilibrium state is a universal Maxwellian distribution
function with the same velocity as field particles and with a non--zero
temperature lower than the background one, which depends on the details of the
binary collision. Thanks to the H--theorem we then prove strong convergence of
the solution to the Boltzmann equation towards the equilibrium.Comment: 17 pages, submitted to Journal of Statistical Physic
Diffeomorphic random sampling using optimal information transport
In this article we explore an algorithm for diffeomorphic random sampling of
nonuniform probability distributions on Riemannian manifolds. The algorithm is
based on optimal information transport (OIT)---an analogue of optimal mass
transport (OMT). Our framework uses the deep geometric connections between the
Fisher-Rao metric on the space of probability densities and the right-invariant
information metric on the group of diffeomorphisms. The resulting sampling
algorithm is a promising alternative to OMT, in particular as our formulation
is semi-explicit, free of the nonlinear Monge--Ampere equation. Compared to
Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when
a large number of samples from a low dimensional nonuniform distribution is
needed.Comment: 8 pages, 3 figure
Celebrating Cercignani's conjecture for the Boltzmann equation
Cercignani's conjecture assumes a linear inequality between the entropy and
entropy production functionals for Boltzmann's nonlinear integral operator in
rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities
and spectral gap inequalities, this issue has been at the core of the renewal
of the mathematical theory of convergence to thermodynamical equilibrium for
rarefied gases over the past decade. In this review paper, we survey the
various positive and negative results which were obtained since the conjecture
was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani,
powerful mind and great scientist, one of the founders of the modern theory
of the Boltzmann equation. 24 pages. V2: correction of some typos and one
ref. adde
Maternal and Paternal Representations in Assisted Reproductive Technology and Spontaneous Conceiving Parents: A Longitudinal Study
Aim of this study was to investigate whether parental mental representations during pregnancy and after delivery differed between parents who conceived after Assisted Reproductive Treatments (ART) and spontaneous conceiving (SC) parents. Effects of specific ART variables (previous ART attempts, treatment type and cause of infertility) were also taken into account. Seventeen ART couples and 25 SC couples were recruited at Santa Maria Nuova Hospital (Reggio Emilia, Italy). At both 32 weeks of gestation (T1) and 3 months postpartum (T2) participants completed the Semantic Differential of the IRMAG, a self-report tool which measures specific domains of mental representations pertaining either individual (Child, Self-as-woman/man, and Partner) or parental (Self-as-parent, Own parent) characteristics. Results showed that ART parents had significantly more positive representations of the child compared to SC parents, while the scores at Partner dimension improved from T1 to T2 for SC parents only. With regards to ART history, scores at the Self-as-woman/man dimension were significantly less positive for ICSI than IVF parents and improved substantially from T1 to T2 only in case of mothers with previous ART attempts and of fathers at the first ART cycle. The representation of own parents increased from T1 to T2 in case of infertility diagnosis due to male factors, while a decrease emerged when infertility was due to female factors. Findings suggest the need to investigate parental mental representations after ART, in order to improve the understanding on the transition to parenthood of infertile couples and to target more specific intervention for parenting support
- …