21,546 research outputs found
Range separation: The divide between local structures and field theories
This work presents parallel histories of the development of two modern
theories of condensed matter: the theory of electron structure in quantum
mechanics, and the theory of liquid structure in statistical mechanics.
Comparison shows that key revelations in both are not only remarkably similar,
but even follow along a common thread of controversy that marks progress from
antiquity through to the present. This theme appears as a creative tension
between two competing philosophies, that of short range structure (atomistic
models) on the one hand, and long range structure (continuum or density
functional models) on the other. The timeline and technical content are
designed to build up a set of key relations as guideposts for using density
functional theories together with atomistic simulation.Comment: Expanded version of a 30 minute talk delivered at the 2018 TSRC
workshop on Ions in Solution, to appear in the March, 2019 issue of
Substantia (https://riviste.fupress.net/index.php/subs/index
Hidden-variable theory versus Copenhagen quantum mechanics
The main assumptions the Copenhagen quantum mechanics has been based on will
be summarized and the known (not yet decided) contradiction between Einstein
and Bohr will be newly analyzed. The given assumptions have been represented
basically by time-dependent Schroedinger equation, to which some further
assumptions have been added. Some critical comments have been raised against
the given mathematical model structure by Pauli (1933) and by Susskind and
Glogover (1964). They may be removed if only the Schroedinger equation is
conserved and the additional assumptions are abandoned, as shown recently. It
seems to be in contradiction to the numerous declarations that the Copenhagen
model has been approved by experimental results.
However, in the most of these experiments only the agreement with the mere
Schroedinger equation has been tested. All mentioned assumptions have been
tested practically only in the EPR experiment (measurement of coincidence light
transmission through two polarizers) proposed originally by Einstein (1935).
Also these experimental results have been interpreted as supporting the
Copenhagen alternative, which has not been, however, true. In fact the
microscopic world may be described correspondingly only with the help of the
hidden-variable theory that is represented by the Schroedinger equation without
mentioned additional assumptions, which has the consequence that the earlier
interpretation gap between microscopic and macroscopic worlds has been removed.
The only difference concerns the existence of discrete states. The
possibilities of the human reason of getting to know the nature will be also
shortly discussed in the beginning of this contribution.Comment: 10 pages, 2 figures; v2: local refinements and improvements of the
tex
Stochastic modeling of excitable dynamics: improved Langevin model for mesoscopic channel noise
Influence of mesoscopic channel noise on excitable dynamics of living cells
became a hot subject within the last decade, and the traditional biophysical
models of neuronal dynamics such as Hodgkin-Huxley model have been generalized
to incorporate such effects. There still exists but a controversy on how to do
it in a proper and computationally efficient way. Here we introduce an improved
Langevin description of stochastic Hodgkin-Huxley dynamics with natural
boundary conditions for gating variables. It consistently describes the channel
noise variance in a good agreement with discrete state model. Moreover, we show
by comparison with our improved Langevin model that two earlier Langevin models
by Fox and Lu also work excellently starting from several hundreds of ion
channels upon imposing numerically reflecting boundary conditions for gating
variables.Comment: V.M. Mladenov and P.C. Ivanov (Eds.): NDES 2014, Communications in
Computer and Information Science, vol. 438 (Springer, Switzerland, 2014), pp.
325-33
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