2,455 research outputs found
Space Charge Limited 2-d Electron Flow between Two Flat Electrodes in a Strong Magnetic Field
An approximate analytic solution is constructed for the 2-d space charge
limited emission by a cathode surrounded by non emitting conducting ledges of
width Lambda. An essentially exact solution (via conformal mapping) of the
electrostatic problem in vacuum is matched to the solution of a linearized
problem in the space charge region whose boundaries are sharp due to the
presence of a strong magnetic field. The current density growth in a narrow
interval near the edges of the cathode depends strongly on Lambda. We obtain an
empirical formula for the total current as a function of Lambda which extends
to more general cathode geometries.Comment: 4 pages, LaTex, e-mail addresses: [email protected],
[email protected]
Influence of Hydrodynamic Interactions on the Kinetics of Colloidal Particle's Adsorption
The kinetics of irreversible adsorption of spherical particles onto a flat
surface is theoretically studied. Previous models, in which hydrodynamic
interactions were disregarded, predicted a power-law behavior for
the time dependence of the coverage of the surface near saturation.
Experiments, however, are in agreement with a power-law behavior of the form
. We outline that, when hydrodynamic interactions are considered, the
assymptotic behavior is found to be compatible with the experimental results in
a wide region near saturation.Comment: 4 pages, 1 figures, Phys. Rev. Lett. (in press
Modes of Growth in Dynamic Systems
Regardless of a system's complexity or scale, its growth can be considered to
be a spontaneous thermodynamic response to a local convergence of down-gradient
material flows. Here it is shown how growth can be constrained to a few
distinct modes that depend on the availability of material and energetic
resources. These modes include a law of diminishing returns, logistic behavior
and, if resources are expanding very rapidly, super-exponential growth. For a
case where a system has a resolved sink as well as a source, growth and decay
can be characterized in terms of a slightly modified form of the predator-prey
equations commonly employed in ecology, where the perturbation formulation of
these equations is equivalent to a damped simple harmonic oscillator. Thus, the
framework presented here suggests a common theoretical under-pinning for
emergent behaviors in the physical and life sciences. Specific examples are
described for phenomena as seemingly dissimilar as the development of rain and
the evolution of fish stocks.Comment: 16 pages, 6 figures, including appendi
On the formation/dissolution of equilibrium droplets
We consider liquid-vapor systems in finite volume at parameter
values corresponding to phase coexistence and study droplet formation due to a
fixed excess of particles above the ambient gas density. We identify
a dimensionless parameter and a
\textrm{universal} value \Deltac=\Deltac(d), and show that a droplet of the
dense phase occurs whenever \Delta>\Deltac, while, for \Delta<\Deltac, the
excess is entirely absorbed into the gaseous background. When the droplet first
forms, it comprises a non-trivial, \textrm{universal} fraction of excess
particles. Similar reasoning applies to generic two-phase systems at phase
coexistence including solid/gas--where the ``droplet'' is crystalline--and
polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas
is presented; generalizations are discussed heuristically.Comment: An announcement of a forthcoming rigorous work on the 2D Ising model;
to appear in Europhys. Let
Transport across nanogaps using semiclassically consistent boundary conditions
Charge particle transport across nanogaps is studied theoretically within the
Schrodinger-Poisson mean field framework and the existence of limiting current
investigated. It is shown that the choice of a first order WKB wavefunction as
the transmitted wave leads to self consistent boundary conditions and gives
results that are significantly different in the non-classical regime from those
obtained using a plane transmitted wave. At zero injection energies, the
quantum limiting current density, J_c, is found to obey the local scaling law
J_c ~ (V_g)^alpha/(D)^{5-2alpha} with the gap separation D and voltage V_g. The
exponent alpha > 1.1 with alpha --> 3/2 in the classical regime of small de
Broglie wavelengths. These results are consistent with recent experiments using
nanogaps most of which are found to be in a parameter regime where classical
space charge limited scaling holds away from the emission dominated regime.Comment: 4 pages, 4 ps figure
Dynamic Scaling of an Adsorption-Diffusion Process on Fractals
A dynamic scaling of a diffusion process involving the Langmuir type
adsorption is studied. We find dynamic scaling functions in one and two
dimensions and compare them with direct numerical simulations, and we further
study the dynamic scaling law on fractal surfaces. The adsorption-diffusion
process obeys the fracton dynamics on the fractal surfaces.Comment: 9 pages, 7 figure
Diffusion-limited reactions and mortal random walkers in confined geometries
Motivated by the diffusion-reaction kinetics on interstellar dust grains, we
study a first-passage problem of mortal random walkers in a confined
two-dimensional geometry. We provide an exact expression for the encounter
probability of two walkers, which is evaluated in limiting cases and checked
against extensive kinetic Monte Carlo simulations. We analyze the continuum
limit which is approached very slowly, with corrections that vanish
logarithmically with the lattice size. We then examine the influence of the
shape of the lattice on the first-passage probability, where we focus on the
aspect ratio dependence: Distorting the lattice always reduces the encounter
probability of two walkers and can exhibit a crossover to the behavior of a
genuinely one-dimensional random walk. The nature of this transition is also
explained qualitatively.Comment: 18 pages, 16 figure
Chiral and herringbone symmetry breaking in water-surface monolayers
We report the observation from monolayers of eicosanoic acid in the L′2 phase of three distinct out-of-plane first-order diffraction peaks, indicating molecular tilt in a nonsymmetry direction and hence the absence of mirror symmetry. At lower pressures the molecules tilt in the direction of their nearest neighbors. In this region we find a structural transition, which we tentatively identify as the rotator-herringbone transition L2d−L2h
Properties of Physical Systems: Transient Singularities on Borders and Surface Transitive Zones
Certain alternative properties of physical systems are describable by
supports of arguments of response functions (e.g. light cone, borders of media)
and expressed by projectors; corresponding equations of restraints lead to
dispersion relations, theorems of counting, etc. As supports are measurable,
their absolutely strict borders contradict the spirit of quantum theory and
their quantum evolution leading to appearance of subtractions or certain needed
flattening would be considered. Flattening of projectors introduce transitive
zones that can be examined as a specification of adiabatic hypothesis or the
Bogoliubov regulatory function in QED. For demonstration of their possibilities
the phenomena of refraction and reflection of electromagnetic wave are
considered; they show, in particular, the inevitable appearing of double
electromagnetic layers on all surfaces that formerly were repeatedly
postulated, etc. Quantum dynamics of projectors proves the neediness of
subtractions that usually are artificially adding and express transient
singularities and zones in squeezed forms.Comment: 12 p
The Stern-Gerlach Experiment Revisited
The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment
of quantum physics providing evidence for several fundamental properties of
quantum systems. Based on today's knowledge we illustrate the different
benchmark results of the SGE for the development of modern quantum physics and
chemistry.
The SGE provided the first direct experimental evidence for angular momentum
quantization in the quantum world and thus also for the existence of
directional quantization of all angular momenta in the process of measurement.
It measured for the first time a ground state property of an atom, it produced
for the first time a `spin-polarized' atomic beam, it almost revealed the
electron spin. The SGE was the first fully successful molecular beam experiment
with high momentum-resolution by beam measurements in vacuum. This technique
provided a new kinematic microscope with which inner atomic or nuclear
properties could be investigated.
The original SGE is described together with early attempts by Einstein,
Ehrenfest, Heisenberg, and others to understand directional quantization in the
SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are
presented. The first realization of these proposals by Stern, Phipps, Frisch
and Segr\`e is described. The set-up suggested by Einstein can be considered an
anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which
the directional quantization process and possible interference effects of the
two different spin states are investigated.
In full agreement with the results of the new quantum theory directional
quantization appears as a general and universal feature of quantum
measurements. One experimental example for such directional quantization in
scattering processes is shown. Last not least, the early history of the
`almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig
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