Kramers equation for a charged Brownian particle: The exact solution

We report the exact fundamental solution for Kramers equation associated to a brownian gas of charged particles, under the influence of homogeneous (spatially uniform) otherwise arbitrary, external mechanical, electrical and magnetic fields. Some applications are presented, namely the hydrothermodynamical picture for Brownian motion in the long time regime.Comment: minor correction

Small angle neutron scattering (SANS) studies of diffusion in bulk polystyrene near the glass transition temperature (Tg)

Ultraslow diffusion in bulk polymers has been measured by SANS. The experiment begins by measuring scattering from heterogeneous specimens containing domains of protonated‐and deuterated‐polymers at temperatures far below Tg. The samples are subsequently held [annealed] above Tg for a known time‐interval, then cooled below Tg where SANS is measured again. Scattering changes, from before to after annealing, are analysed to obtain diffusion coefficients. The recent Summerfield ‐ Ullman procedure is used to deconvolute portions of the scattering curve that decrease and increase with annealing time. Because of SANS sensitivity to small distances, the method yields D ≈ 10−18 to 10−15 cm2/s after annealing times of 1–24 h. Data analysis is complicated by “smearing effects” which produce apparent Q‐dependent diffusion coefficients. Representative experimental results on polystyrene at 108°–130°C are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112190/1/19880150127_ftp.pd

Growth rate and rupture rate of unruptured intracranial aneurysms: a population approach

<p>Abstract</p> <p>Background</p> <p>Understanding aneurysm growth rate allows us to predict not only the current rupture risk, but also accumulated rupture risk in the future. However, determining growth rate of unruptured intracranial aneurysms often requires follow-up of patients for a long period of time so that significant growth can be observed and measured. We investigate a relationship between growth rate and rupture rate and develop a theoretical model that can predict average behavior of unruptured intracranial aneurysms based on existing clinical data.</p> <p>Methods</p> <p>A mathematical model is developed that links growth rate and rupture rate. This model assumes a stable aneurysm size distribution so the number of aneurysm ruptures is balanced by the growth of aneurysms. Annual growth rates and growth profiles are calculated from a hypothetical size distribution and data from a previous clinical study.</p> <p>Results</p> <p>Our model predicts a growth rate of 0.34–1.63 mm/yr for three different growth models when the rupture rate at 10 mm is 1%. The growth rate is 0.56–0.65 mm/yr if annual rupture rate averaged over all aneurysm sizes is assumed to be 2%. The peak of aneurysm size distribution coincides with a period of slow growth between 5 mm and 8 mm.</p> <p>Conclusion</p> <p>This mathematical model can be used to predict aneurysm growth rate, and the results are consistent with previous clinical studies. Predictions from both hypothetical and clinical cases agree very well. This model explains why some aneurysms may grow into a stable size and remain so without rupture.</p

A dynamic method for magnetic torque measurement

In a magnetic suspension system, accurate force measurement will result in better control performance in the test section, especially when a wider range of operation is required. Although many useful methods were developed to obtain the desired model, however, significant error is inevitable since the magnetic field distribution of the large-gap magnetic suspension system is extremely nonlinear. This paper proposed an easy approach to measure the magnetic torque of a magnetic suspension system using an angular photo encoder. Through the measurement of the velocity change data, the magnetic torque is converted. The proposed idea is described and implemented to obtain the desired data. It is useful to the calculation of a magnetic force in the magnetic suspension system

Diffuse-interface model for rapid phase transformations in nonequilibrium systems

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe the transformation within the diffuse interface, we use the phase-field model which allows us to follow the steep but smooth change of phases within the width of diffuse interface. The governing equations of the phase-field model are derived for the hyperbolic model, model with memory, and for a model of nonlinear evolution of transformation within the diffuse-interface. The consistency of the model is proved by the condition of positive entropy production and by the outcomes of the fluctuation-dissipation theorem. A comparison with the existing sharp-interface and diffuse-interface versions of the model is given.Comment: 15 pages, regular article submitted to Physical Review

Jarzynski equality for the transitions between nonequilibrium steady states

Jarzynski equality [Phys. Rev. E {\bf 56}, 5018 (1997)] is found to be valid with slight modefication for the transitions between nonequilibrium stationary states, as well as the one between equilibrium states. Also numerical results confirm its validity. Its relevance for nonequilibrium thermodynamics of the operational formalism is discussed.Comment: 5 pages, 2 figures, revte

TDP-43 Proteinopathy and ALS: Insights into Disease Mechanisms and Therapeutic Targets

# The Author(s) 2015. This article is published with open access at Springerlink.com Abstract Therapeutic options for patients with amyotrophic lateral sclerosis (ALS) are currently limited. However, recent studies show that almost all cases of ALS, as well as tau-negative frontotemporal dementia (FTD), share a common neuropathology characterized by the deposition of TAR-DNA binding protein (TDP)-43-positive protein inclusions, offering an attractive target for the design and testing of novel therapeutics. Here we demonstrate how diverse environmental stressors linked to stress granule formation, as well as muta-tions in genes encoding RNA processing proteins and protein degradation adaptors, initiate ALS pathogenesis via TDP-43. We review the progressive development of TDP-43 proteinopathy from cytoplasmic mislocalization and misfolding through to macroaggregation and the addition of phosphate and ubiquitin moieties. Drawing from cellular and animal studies, we explore the feasibility of therapeutics that act at each point in pathogenesis, from mitigating genetic risk using antisense oligonucleotides to modulating TDP-43 proteinopathy itself using small molecule activators of au-tophagy, the ubiquitin-proteasome system, or the chaper-one network. We present the case that preventing the misfolding of TDP-43 and/or enhancing its clearance represents the most important target for effectively treating ALS and frontotemporal dementia

Vortex length, vortex energy and fractal dimension of superfluid turbulence at very low temperature

By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step the total energy of the vortices is conserved, but the total length can change. We obtain a relation between the fractal dimension and the exponent describing how the vortex energy per unit length changes with the length scale. This relation does not depend on the specific model, and shows that if smaller length scales make a decreasing relative contribution to the energy per unit length of vortex lines, the fractal dimension will be higher than unity. Finally, for the sake of more concrete illustration, we relate the fractal dimension of the tangle to the scaling exponents of amplitude and wavelength of a cascade of Kelvin waves.Comment: 12 pages, 1 figur

Test of Information Theory on the Boltzmann Equation

We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.Comment: 12 page

Magnetic Leviation System Design and Implementation for Wind Tunnel Application

This paper presents recent work in magnetic suspension wind tunnel development in National Cheng Kung University. In this phase of research, a control-based study is emphasized to implement a robust control system into the experimental system under study. A ten-coil 10 cm x 10 cm magnetic suspension wind tunnel is built using a set of quadrant detectors for six degree of freedom control. To achieve the attitude control of suspended model with different attitudes, a spacial electromagnetic field simulation using OPERA 3D is studied. A successful test for six degree of freedom control is demonstrated in this paper