161,230 research outputs found
Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production
The solution to nonlinear Fokker-Planck equation is constructed in terms of
the minimal Markov semigroup generated by the equation. The semigroup is
obtained by a purely functional analytical method via Hille-Yosida theorem. The
existence of the positive invariant measure with density is established and a
weak form of Foguel alternative proven. We show the equivalence among
self-adjoint of the elliptic operator, time-reversibility, and zero entropy
production rate of the stationary diffusion process. A thermodynamic theory for
diffusion processes emerges.Comment: 23 page
Stochastic Dynamics of Electrical Membrane with Voltage-Dependent Ion Channel Fluctuations
Brownian ratchet like stochastic theory for the electrochemical membrane
system of Hodgkin-Huxley (HH) is developed. The system is characterized by a
continuous variable , representing mobile membrane charge density, and
a discrete variable representing ion channel conformational dynamics. A
Nernst-Planck-Nyquist-Johnson type equilibrium is obtained when multiple
conducting ions have a common reversal potential. Detailed balance yields a
previously unknown relation between the channel switching rates and membrane
capacitance, bypassing Eyring-type explicit treatment of gating charge
kinetics. From a molecular structural standpoint, membrane charge is a
more natural dynamic variable than potential ; our formalism treats
-dependent conformational transition rates as intrinsic
parameters. Therefore in principle, vs. is experimental
protocol dependent,e.g., different from voltage or charge clamping
measurements. For constant membrane capacitance per unit area and
neglecting membrane potential induced by gating charges, , and
HH's formalism is recovered. The presence of two types of ions, with different
channels and reversal potentials, gives rise to a nonequilibrium steady state
with positive entropy production . For rapidly fluctuating channels, an
expression for is obtained.Comment: 8 pages, two figure
Neutrino Gravitational Redshift and the Electron Fraction Above Nascent Neutron Stars
Neutrinos emitted from near the surface of the hot proto-neutron star
produced by a supernova explosion may be subject to significant gravitational
redshift at late times. Electron antineutrinos decouple deeper in the
gravitational potential well of the neutron star than do the electron
neutrinos, so that the electron antineutrinos experience a larger redshift
effect than do the electron neutrinos. We show how this differential redshift
can increase the electron fraction Ye in the neutrino-heated ejecta from the
neutron star. Any r-process nucleosynthesis originating in the neutrino-heated
ejecta would require a low Ye, implying that the differential redshift effect
cannot be too large. In turn, this effect may allow nucleosynthesis to probe
the nuclear equation of state parameters which set the neutron star radius and
surface density scale height at times of order tpb = 10 to 25 s after core
bounce.Comment: 4 pages, uses espcrc2.sty, contribution to Festschrift for G. E.
Brown on the occasion of his 70th birthda
rHARM: Accretion and Ejection in Resistive GR-MHD
Turbulent magnetic diffusivity plays an important role for accretion disks
and the launching of disk winds. We have implemented magnetic diffusivity,
respective resistivity in the general relativistic MHD code HARM. This paper
describes the theoretical background of our implementation, its numerical
realization, our numerical tests and preliminary applications. The test
simulations of the new code rHARM are compared with an analytic solution of the
diffusion equation and a classical shock tube problem. We have further
investigated the evolution of the magneto-rotational instability (MRI) in tori
around black holes for a range of magnetic diffusivities. We find indication
for a critical magnetic diffusivity (for our setup) beyond which no MRI
develops in the linear regime and for which accretion of torus material to the
black hole is delayed. Preliminary simulations of magnetically diffusive thin
accretion disks around Schwarzschild black holes that are threaded by a
large-scale poloidal magnetic field show the launching of disk winds with mass
fluxes of about 50% of the accretion rate. The disk magnetic diffusivity allows
for efficient disk accretion that replenishes the mass reservoir of the inner
disk area and thus allows for long-term simulations of wind launching for more
than 5000 time units.Comment: 21 pages, 43 figures, accepted by Ap
- …