1,818 research outputs found
The linear Fokker-Planck equation for the Ornstein-Uhlenbeck process as an (almost) nonlinear kinetic equation for an isolated N-particle system
It is long known that the Fokker-Planck equation with prescribed constant
coefficients of diffusion and linear friction describes the ensemble average of
the stochastic evolutions in velocity space of a Brownian test particle
immersed in a heat bath of fixed temperature. Apparently, it is not so well
known that the same partial differential equation, but now with constant
coefficients which are functionals of the solution itself rather than being
prescribed, describes the kinetic evolution (in the infinite particle limit) of
an isolated N-particle system with certain stochastic interactions. Here we
discuss in detail this recently discovered interpretation.Comment: Minor revisions and corrections (including the title
Азовська операція Революційної Повстанської Армії України (махновців)
В історії України знайдеться не так вже й багато явищ та подій, які б значимістю та силою переросли рамки регіональної та національної історії і ставали повноправними надбаннями історії всесвітньої. Ще менше подібних подій та явищ існувало на рівні південноукраїнського регіону. І було б логічно, якби такі явища посилено досліджувались істориками, а результати досліджень ставали надбанням якомога ширшого загалу, що перетворювало б ці явища на бренд, який швидко вгадувався і запам’ятовувся будь-де. Проте в умовах сучасної України ми цього не спостерігаємо
The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics
The present work establishes the mean-field limit of a N-particle system
towards a regularized variant of the relativistic Vlasov-Maxwell system,
following the work of Braun-Hepp [Comm. in Math. Phys. 56 (1977), 101-113] and
Dobrushin [Func. Anal. Appl. 13 (1979), 115-123] for the Vlasov-Poisson system.
The main ingredients in the analysis of this system are (a) a kinetic
formulation of the Maxwell equations in terms of a distribution of
electromagnetic potential in the momentum variable, (b) a regularization
procedure for which an analogue of the total energy - i.e. the kinetic energy
of the particles plus the energy of the electromagnetic field - is conserved
and (c) an analogue of Dobrushin's stability estimate for the
Monge-Kantorovich-Rubinstein distance between two solutions of the regularized
Vlasov-Poisson dynamics adapted to retarded potentials.Comment: 34 page
On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations
We discuss the relationship between kinetic equations of the Fokker-Planck
type (two linear and one non-linear) and the Kolmogorov (a.k.a. master)
equations of certain N-body diffusion processes, in the context of Kac's
"propagation of chaos" limit. The linear Fokker-Planck equations are
well-known, but here they are derived as a limit N->infty of a simple linear
diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N)
(with C=1 or 4 depending on whether the system conserves energy only or energy
and momentum). In this case, a spectral gap separating the zero eigenvalue from
the positive spectrum of the Laplacian remains as N->infty,so that the
exponential approach to equilibrium of the master evolution is passed on to the
limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation
is known as Landau's equation in the plasma physics literature. Its N-particle
master equation, originally introduced (in the 1950s) by Balescu and Prigogine
(BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown
that the BP master equation represents a superposition of diffusion processes
on certain two-dimensional sub-manifolds of R^{3N} determined by the
conservation laws for two-particle collisions. The initial value problem for
the BP master equation is proved to be well-posed and its solutions are shown
to decay exponentially fast to equilibrium. However, the first non-zero
eigenvalue of the BP operator is shown to vanish in the limit N->infty. This
indicates that the exponentially fast approach to equilibrium may not be passed
from the finite-N master equation on to Landau's nonlinear kinetic equation.Comment: 20 pages; based on talk at the 18th ICTT Conference. Some typos and a
few minor technical fixes. Modified title slightl
Lifetime of magnetic excitations in supported ferromagnetic and antiferromagnetic spin-1/2 Heisenberg chains
The lifetime of magnetic excitations in finite 1D-supported Heisenberg chains of magnetic atoms is studied theoretically for a model system formed of S = 1/2 spins. Both ferromagnetic and antiferromagnetic cases are considered as well as open chains and rings of atoms. Different chain lengths are considered allowing extrapolation to infinite chains. All the excited magnetic states in the finite chains and rings are studied, not only the spin-wave mode. The magnetic excitations decay by electron-hole pair creation in the substrate. As the main result, for all the systems considered, the decay rate appears to vary approximately proportionally to the excitation energy of the state, with a proportionality constant independent of the strength of the Heisenberg exchange term. In certain finite systems, a stable state is evidenced at low energy, associated with a special spin coupling structure. © 2012 American Physical Society.Peer Reviewe
Absorption reconstruction improves biodistribution assessment of fluorescent nanoprobes using hybrid Fluorescence-mediated tomography
Aim: Fluorescence-mediated tomography (FMT) holds potential for accelerating diagnostic and theranostic drug development. However, for proper quantitative fluorescence reconstruction, knowledge on optical scattering and absorption, which are highly heterogeneous in different (mouse) tissues, is required. We here describe methods to assess these parameters using co-registered micro Computed Tomography (µCT) data and nonlinear whole-animal absorption reconstruction, and evaluate their importance for assessment of the biodistribution and target site accumulation of fluorophore-labeled drug delivery systems.\ud
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Methods: Besides phantoms with varying degrees of absorption, mice bearing A431 tumors were imaged 15 min and 48 h after i.v. injection of a fluorophore-labeled polymeric drug carrier (pHPMA-Dy750) using µCT-FMT. The outer shape of mice and a scattering map were derived using automated segmentation of the µCT data. Furthermore, a 3D absorption map was reconstructed from the trans-illumination data. We determined the absorption of five interactively segmented regions (heart, liver, kidney, muscle, tumor). Since blood is the main near-infrared absorber in vivo, the absorption was also estimated from the relative blood volume (rBV), determined by contrast-enhanced µCT. We compared the reconstructed absorption with the rBV-based values and analyzed the effect of using the absorption map on the fluorescence reconstruction.\ud
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Results: Phantom experiments demonstrated that absorption reconstruction is possible and necessary for quantitative fluorescence reconstruction. In vivo, the reconstructed absorption showed high values in strongly blood-perfused organs such as the heart, liver and kidney. The absorption values correlated strongly with the rBV-based absorption values, confirming the accuracy of the absorption reconstruction. Usage of homogenous absorption instead of the reconstructed absorption map resulted in reduced values in the heart, liver and kidney, by factors of 3.5, 2.1 and 1.4, respectively. For muscle and subcutaneous tumors, which have a much lower rBV and absorption, absorption reconstruction was less important.\ud
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Conclusion: Quantitative whole-animal absorption reconstruction is possible and can be validated in vivo using the rBV. Usage of an absorption map is important when quantitatively assessing the biodistribution of fluorescently labeled drugs and drug delivery systems, to avoid a systematic underestimation of fluorescence in strongly absorbing organs, such as the heart, liver and kidney
Об анатомическом строении членистостебельного растения Annulina Neuburgiana Radczenko
The purpose was to compare two approaches for the acquisition and analysis of dynamic-contrast-enhanced MRI data with respect to differences in the modelling of the arterial input-function (AIF), the dependency of the model parameters on physiological parameters and their numerical stability. Eight hundred tissue concentration curves were simulated for different combinations of perfusion, permeability, interstitial volume and plasma volume based on two measured AIFs and analysed according to the two commonly used approaches. The transfer constants (Approach 1) K (trans) and (Approach 2) k (ep) were correlated with all tissue parameters. K (trans) showed a stronger dependency on perfusion, and k (ep) on permeability. The volume parameters (Approach 1) v (e) and (Approach 2) A were mainly influenced by the interstitial and plasma volume. Both approaches allow only rough characterisation of tissue microcirculation and microvasculature. Approach 2 seems to be somewhat more robust than 1, mainly due to the different methods of CA administration
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