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

Assessment of climatic risks in relation to the transport infrastructure of the northern regions of Russia

Theme. Infrastructure of transport systems of the permafrost zone of Russia, operated in conditions of global warming. Objectives. To quantify the risks of disrupting the functionality of transport infrastructure facilities, taking into account the soil and natural and climatic features in the territory of their operation. Methodology. Modeling the temperature dynamics of the soil massif, including the upper seasonal thawed layer and the lower layer of permafrost soil, identifying changes in its strength and deformation properties under the accepted scenario of climatic changes, assessing the impact of changes in the soil massif on the operational state and safety of various types of infrastructure facilities of transport systems (taking into account the appearance of additional precipitation of thawing soil and a decrease in its bearing capacity), determination of the values of predicted risks on a scale that is uniform for all types of objects. Results. New data have been obtained on the negative consequences of climate change for the infrastructure of transport systems in the permafrost zone of Russia. Under fairly conservative assumptions about a warming of 2 degrees Celsius, the risk of functional impairment for the road profile is predicted to be from 86 to 294 points on a 1000-point scale, and climatic risks increase with an increase in the temperature of permafrost. The magnitude of the expected risks in relation to the aerodrome pavement is approximately at the same level; these two types of objects are distinguished by the greatest resistance to climatic changes. Pile foundations are subject to risk ranging from 143 to 529 points. The most vulnerable to warming are strip and columnar foundations, for which the lowest risk value obtained during modeling is 389 points, and under unfavorable conditions (high-temperature permafrost in combination with low soil moisture), the risk increases to the maximum possible value of 1000 points. Implications. The risks of disrupting the functionality of infrastructural objects of the permafrost transport systems, predicted at warming up to 2 degrees Celsius, should be considered significant. With risks up to 400 points (road profile, airfield coverage), it is advisable to limit ourselves to monitoring the current state of the facility and, if necessary, restore its functionality. With risks from 400 to 600 points, it is recommended, and in case of risks over 600 points, it is mandatory to carry out preventive engineering and technical measures aimed at stabilizing the temperature regime of soils and preventing a sudden loss of functionality of individual elements of the transport system

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

Two center multipole expansion method: application to macromolecular systems

We propose a new theoretical method for the calculation of the interaction energy between macromolecular systems at large distances. The method provides a linear scaling of the computing time with the system size and is considered as an alternative to the well known fast multipole method. Its efficiency, accuracy and applicability to macromolecular systems is analyzed and discussed in detail.Comment: 23 pages, 7 figures, 1 tabl

Instability of coherent states of a real scalar field

We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic nonlinearity. The linear analysis of time-dependent parts of perturbations leads to the Hill equation with a singular coefficient. To evaluate the characteristic exponent we extend the Lindemann-Stieltjes method, usually applied to the Mathieu and Lame equations, to the case that the periodic coefficient in the general Hill equation is an unbounded function of time. As a result, we derive the formula for the characteristic exponent and calculate the stability-instability chart. Then we analyze the spatial structure of the perturbations. Using these results we show that the pulsons of any amplitudes, remaining well-localized objects, lose their coherence with time. This means that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for the nodeless pulsons the rate of the coherence breaking in narrow ranges of amplitudes is found to be very small, so that such pulsons can be long-lived. Further, we use the obtaned stability-instability chart to examine the Affleck-Dine type condensate. We conclude the oscillating condensate can decay into an ensemble of the nodeless pulsons.Comment: 11 pages, 8 figures, submitted to Physical Review

Kramers-Kronig constrained variational analysis of optical spectra

A universal method of extraction of the complex dielectric function $\epsilon(\omega)=\epsilon_{1}(\omega)+i\epsilon_{2}(\omega)$ from experimentally accessible optical quantities is developed. The central idea is that $\epsilon_{2}(\omega)$ is parameterized independently at each node of a properly chosen anchor frequency mesh, while $\epsilon_{1}(\omega)$ is dynamically coupled to $\epsilon_{2}(\omega)$ by the Kramers-Kronig (KK) transformation. This approach can be regarded as a limiting case of the multi-oscillator fitting of spectra, when the number of oscillators is of the order of the number of experimental points. In the case of the normal-incidence reflectivity from a semi-infinite isotropic sample the new method gives essentially the same result as the conventional KK transformation of reflectivity. In contrast to the conventional approaches, the proposed technique is applicable, without readaptation, to virtually all types of linear-response optical measurements, or arbitrary combinations of measurements, such as reflectivity, transmission, ellipsometry {\it etc.}, done on different types of samples, including thin films and anisotropic crystals.Comment: 10 pages, 7 figure

Central factorials under the Kontorovich-Lebedev transform of polynomials

We show that slight modifications of the Kontorovich-Lebedev transform lead to an automorphism of the vector space of polynomials. This circumstance along with the Mellin transformation property of the modified Bessel functions perform the passage of monomials to central factorial polynomials. A special attention is driven to the polynomial sequences whose KL-transform is the canonical sequence, which will be fully characterized. Finally, new identities between the central factorials and the Euler polynomials are found.Comment: also available at http://cmup.fc.up.pt/cmup/ since the 2nd August 201

Surface-plasmon-polariton wave propagation guided by a metal slab in a sculptured nematic thin film

Surface-plasmon-polariton~(SPP) wave propagation guided by a metal slab in a periodically nonhomogeneous sculptured nematic thin film~(SNTF) was studied theoretically. The morphologically significant planes of the SNTF on both sides of the metal slab could either be aligned or twisted with respect to each other. The canonical boundary-value problem was formulated, solved for SPP-wave propagation, and examined to determine the effect of slab thickness on the multiplicity and the spatial profiles of SPP waves. Decrease in slab thickness was found to result in more intense coupling of two metal/SNTF interfaces. But when the metal slab becomes thicker, the coupling between the two interfaces reduces and SPP waves localize to one of the two interfaces. The greater the coupling between the two metal/SNTF interfaces, the smaller is the phase speed.Comment: 17 page

Invariance Conditions for Nonlinear Dynamical Systems

Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions, sufficient and necessary conditions, under which some convex sets are invariant sets for linear dynamical systems. In this paper, by utilizing analogous methodology, we generalize the results for nonlinear dynamical systems. First, the Theorems of Alternatives, i.e., the nonlinear Farkas lemma and the \emph{S}-lemma, together with Nagumo's Theorem are utilized to derive invariance conditions for discrete and continuous systems. Only standard assumptions are needed to establish invariance of broadly used convex sets, including polyhedral and ellipsoidal sets. Second, we establish an optimization framework to computationally verify the derived invariance conditions. Finally, we derive analogous invariance conditions without any conditions