705 research outputs found
Multiscale approach to radiation damage induced by ion beams: complex DNA damage and effects of thermal spikes
We present the latest advances of the multiscale approach to radiation damage
caused by irradiation of a tissue with energetic ions and report the most
recent advances in the calculations of complex DNA damage and the effects of
thermal spikes on biomolecules. The multiscale approach aims to quantify the
most important physical, chemical, and biological phenomena taking place during
and following irradiation with ions and provide a better means for
clinically-necessary calculations with adequate accuracy. We suggest a way of
quantifying the complex clustered damage, one of the most important features of
the radiation damage caused by ions. This method can be used for the
calculation of irreparable DNA damage. We include thermal spikes, predicted to
occur in tissue for a short time after ion's passage in the vicinity of the
ions' tracks in our previous work, into modeling of the thermal environment for
molecular dynamics analysis of ubiquitin and discuss the first results of these
simulations.Comment: 14 pages, 3 figures, submitted to EPJ
Alpha helix-coil phase transition: analysis of ab initio theory predictions
In the present paper we present results of calculations obtained with the use
of the theoretical method described in our preceding paper [1] and perform
detail analysis of alpha helix-random coil transition in alanine polypeptides
of different length. We have calculated the potential energy surfaces of
polypeptides with respect to their twisting degrees of freedom and construct a
parameter-free partition function of the polypeptide using the suggested method
[1]. From the build up partition function we derive various thermodynamical
characteristics for alanine polypeptides of different length as a function of
temperature. Thus, we analyze the temperature dependence of the heat capacity,
latent heat and helicity for alanine polypeptides consisting of 21, 30, 40, 50
and 100 amino acids. Alternatively, we have obtained same thermodynamical
characteristics from the use of molecular dynamics simulations and compared
them with the results of the new statistical mechanics approach. The comparison
proves the validity of the statistical mechanic approach and establishes its
accuracy.Comment: 34 pages, 12 figure
On the variance of the number of occupied boxes
We consider the occupancy problem where balls are thrown independently at
infinitely many boxes with fixed positive frequencies. It is well known that
the random number of boxes occupied by the first n balls is asymptotically
normal if its variance V_n tends to infinity. In this work, we mainly focus on
the opposite case where V_n is bounded, and derive a simple necessary and
sufficient condition for convergence of V_n to a finite limit, thus settling a
long-standing question raised by Karlin in the seminal paper of 1967. One
striking consequence of our result is that the possible limit may only be a
positive integer number. Some new conditions for other types of behavior of the
variance, like boundedness or convergence to infinity, are also obtained. The
proofs are based on the poissonization techniques.Comment: 34 page
Ab initio theory of helix-coil phase transition
In this paper we suggest a theoretical method based on the statistical
mechanics for treating the alpha-helix-random coil transition in alanine
polypeptides. We consider this process as a first-order phase transition and
develop a theory which is free of model parameters and is based solely on
fundamental physical principles. It describes essential thermodynamical
properties of the system such as heat capacity, the phase transition
temperature and others from the analysis of the polypeptide potential energy
surface calculated as a function of two dihedral angles, responsible for the
polypeptide twisting. The suggested theory is general and with some
modification can be applied for the description of phase transitions in other
complex molecular systems (e.g. proteins, DNA, nanotubes, atomic clusters,
fullerenes).Comment: 24 pages, 3 figure
Fluctuation of maximal particle energy of quantum ideal gas and random partitions
We investigate the limiting distribution of the fluctuations of the maximal
summand in a random partition of a large integer with respect to a
multiplicative statistics. We show that for a big family of Gibbs measures on
partitions (so called generalized Bose--Einstein statistics) this distribution
is the well-known Gumbel distribution which usually appears in the context of
indepedent random variables. In particular, it means that the (properly
rescaled) maximal energy of an individual particle in the grand canonical
ensemble of the -dimensional quantum ideal gas has the Gumbel distribution
in the limit. We also apply our result to find the fluctuations of the height
of a random 3D Young diagram (plane partition) and investigate the order
statistics of random partitions under generalized Bose--Einstein statistics.Comment: 13 p., Ref. 1
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