Abstract:
We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally relevant spatial scales -- i.e., the correlation length for spin chains and the size of magnetic domains for thin films magnetized out of plane -- are deduced. Stability of chiral order inside domain walls against thermal fluctuations is also discussed.

Abstract:
There are settings where encryption must be performed by a sender under a time constraint. This paper de-scribes an encryption/decryption algorithm based on modular arithmetic of complex integers called Gaus-sians. It is shown how cubic extractors operate and how to find all cubic roots of the Gaussian. All validations (proofs) are provided in the Appendix. Detailed numeric illustrations explain how to use the method of digital isotopes to avoid ambiguity in recovery of the original plaintext by the receiver.

Abstract:
Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design stage of a cryptographic system is a formidable task. Fermat primality checking is one of the simplest of all tests. Unfortunately, there are composite integers (called Carmichael numbers) that are not detectable by the Fermat test. In this paper we consider modular arithmetic based on complex integers; and provide several tests that verify the primality of real integers. Although the new tests detect most Carmichael numbers, there are a small percentage of them that escape these tests.

Abstract:
Primitive elements play important roles in the Diffie-Hellman protocol for establishment of secret communication keys, in the design of the ElGamal cryptographic system and as generators of pseudo-random numbers. In general, a deterministic algorithm that searches for primitive elements is currently unknown. In information-hiding schemes, where a primitive element is the key factor, there is the freedom in selection of a modulus. This paper provides a fast deterministic algorithm, which computes every primitive element in modular arithmetic with special moduli. The algorithm requires at most O(log^{2}p) digital operations for computation of a generator. In addition, the accelerated-descend algorithm that computes small generators is described in this paper. Several numeric examples and tables illustrate the algorithms and their properties.

This paper describes and compares a variety of algorithms for secure transmission of information via open communication channels based on the discrete logarithm problem that do not require search for a generator (primitive element). Modifications that simplify the cryptosystem are proposed, and, as a result, accelerate its performance.It is shown that hiding information via exponentiation is more efficient than other seemingly simpler protocols. Some of these protocols also provide digital signature/sender identification. Numeric illustrations are provided.

The monomer fraction density based analysis of precise
thermophysical data for pure fluids is developed to study the molecular
structures in supercritical fluids in general and in CO_{2} in particular. The series expansion by
powers of the monomer fraction density of the potential energy density is used
to discover the cluster structure in supercritical fluids and the clusters’
bond energies in CO_{2}. The method of clusters separation between
classes of loose and dense clusters in the CO_{2} supercritical fluid
is developed. The method of the energetically averaged number of dense clusters
is developed to study the mechanism of the soft structural transition
between the gas-like and liquid-like fluids in the supercritical
CO_{2}.

This paper describes an algorithm for secure transmission of information via open communication channels based on the discrete logarithm problem. The proposed algorithm also provides sender identification (digital signature). It is twice as fast as the RSA algorithm and requires fifty per cent fewer exponentiations than the ElGamal cryptosystems. In addition, the algorithm requires twice less bandwidth than the ElGamal algorithm. Numerical examples illustrate all steps of the proposed algorithm: system design (selection of private and public keys), encryption, transmission of information, decryption and information recovery.

The thermal analysis of precise thermophysical data for pure fluids
from electronic databases is developed to investigate the molecular interaction
mechanisms and parameters and the structural features of heterogeneities in
fluids. The method is based on the series expansion of thermophysical values by
powers of the monomer fraction density. Unlike the virial expansion by powers
of the total density, the series expansion terms in this method directly
reflect properties of the corresponding cluster fractions. The internal energy
had been selected among thermophysical properties as the most informative for
this method. The thermal analysis of its series expansion coefficients permits
to estimate the temperature dependence of the pair bond parameters, the
clusters’ bond energies and equilibrium constants, the structural transitions
between dominating isomers of clusters. The application of method to different
pure fluids, including noble and molecular gases with van der Waals and polar
molecular interactions, brings unknown clusters’ characteristics for the
fluids under investigation. The thermal analysis of the ordinary and heavy
Water vapors points on no trivial isotopic effects. The unpredictable growth of
the pair bond energy with temperature in Alkanes points on existence in hydrocarbons
of some unknown molecular interaction forces in addition to dispersion forces.

To discover particular features of pure supercritical fluids, important for the supercritical fluid extraction and cleaning technologies, the preprocessed and generalized experimental data from the US National Institute of Standards and Technology (NIST) online database have been analyzed. The soft transition between gas-like and liquid-like structures in pure supercritical fluids has been considered in comparison with the abrupt vapor-liquid phase transition. A rough, diffused and boiling boundary between these structures in conditions of extra high gravity is opposed to a flat vapor-liquid boundary at a moderate gravity. The model for molecular diffusivity in carbon dioxide at temperatures near the critical temperature discovers its proportionality to the monomer fraction density. The cluster fraction based model for small molecular weight solids’ solubility in supercritical fluids has been suggested and successfully compared with the well-known experimental results for the solubility of silica in water.The model shows that at growing pressure the dissolution process has already startedin a real gas and discovers the cluster fractions’ role in the solubility process.

The aim of this research is to apply the author’s original computer aided analysis of thermophysical data for pure fluids to noble gases to investigate the unknown aspects in their equilibrium thermal physics. The methodology of the analysis is based on the potential energy density series expansion by the monomer fraction density. To discover the important details and particular features of pair atomic interactions in noble gases, the preprocessed and generalized experimental data have been taken from the US National Institute of Standards and Technology (NIST) online database. In this work the temperature range for analysis of the dimers’ bonding parameters is extended as compared to previous author’s works due to accounting for the specific temperature dependence of the repulsions’ contribution to the potential energy. The found temperature dependences of the pair interaction bond energies signal about the hindered rotation of atoms in dimers near the triple point due to the lack of rotational symmetry of their electronic outer shells. The discovered mutually correlated anomalous temperature dependences of the pair bond energy and the constant volume heat capacity in gaseous Helium require a special investigation of this remarkable phenomenon.