THE HELIX-COIL TRANSITION IN A DOUBLE-STRANDED POLYNUCLEOTIDE AND THE TWO-DIMENSIONAL RANDOM WALK

The helix-coil transition in a double-stranded homopolynucleotide is considered. The new approach to the melted loops account is proposed. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of hydrogen bonds between complementary units. To take into account the interaction of monomers inside the chains, we consider various regimes of return to the origin. One of them involves two competing interactions and demonstrates a nontrivial sharp denaturation transition. The rich phase behavior of the double-stranded homopolynucleotide is discussed in terms of the proposed approach.

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Two-dimensional interlocked pentagonal bilayer ice: how do water molecules form a hydrogen bonding network?

Physical Chemistry Chemical Physics ◽

10.1039/c5cp07524f ◽

2016 ◽

Vol 18 (21) ◽

pp. 14216-14221 ◽

Cited By ~ 16

Author(s):

Weiduo Zhu ◽

Wen-Hui Zhao ◽

Lu Wang ◽

Di Yin ◽

Min Jia ◽

...

Keyword(s):

Hydrogen Bonding ◽

Water Molecules ◽

Two Dimensional ◽

Rich Phase ◽

Nanoconfined Water ◽

Hydrogen Bonding Network ◽

The Rich ◽

Phase Behaviors

The tradeoff between the conditions of an ideal hydrogen bonding network can serve as a generic guidance to understand the rich phase behaviors of nanoconfined water.

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Термодинамические и магнитные свойства двумерной анизотропной модели Изинга с конкурирующими взаимодействиями

Физика твердого тела ◽

10.21883/ftt.2019.10.48269.461 ◽

2019 ◽

Vol 61 (10) ◽

pp. 1911

Author(s):

А.К. Муртазаев ◽

Ж.Г. Ибаев

Keyword(s):

Exchange Interactions ◽

Square Lattice ◽

Wave Number ◽

Two Dimensional ◽

Competing Interactions ◽

Distinctive Features ◽

Magnetic Parameters ◽

Modulated Structures ◽

Temperature Dependences ◽

Competing Interaction

The two-dimensional anisotropic Ising model was studied with competing interactions on a square lattice using Monte-Carlo methods using the Wang-Landau algorithm. The temperature dependences of the main thermodynamic and magnetic parameters are calculated. The distinctive features of the temperature dependences of these parameters are shown for different values of the competing interaction. The graphs of the dependence of the wave number of modulated structures on the ratio of the parameters of exchange interactions are plotted. Built phase diagram of the model. Interpolating the phase boundaries of the diagram, the coordinates of the Lifshchits point and phase localization areas with different wave vector values are calculated.

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Wald's identity and absorption probabilities for two-dimensional random walks

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100039098 ◽

1965 ◽

Vol 61 (3) ◽

pp. 747-762 ◽

Cited By ~ 5

Author(s):

V. D. Barnett

Keyword(s):

Random Walk ◽

Double Series ◽

Moment Generating Function ◽

Square Lattice ◽

Two Dimensional ◽

Finite Region ◽

Discrete Random Variables ◽

Image Position ◽

Wald's Identity ◽

Absorption Probabilities

SummarySuppose a particle executes a random walk on a two-dimensional square lattice, starting at the origin. The position of the particle after n steps of the walk is Xn = (Xl, n, X2n), whereand we will assume that the Yi are independent bivariate discrete random variables with common moment generating function (m.g.f.)where a, b, c and d are non-negative. We assume further that (i) pi, j is non-zero for some finite positive and negative i, and some finite positive and negative j (− a ≤ i ≤ b, − c ≤ jd), such values of i and j including – a, b and – c, d, respectively, whenever a, b, c or d is finite, and (ii) the double series defining Φ(α, β) is convergent at least in some finite region D, of the real (α, β) plane, which includes the origin.

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Critical properties of the two-dimensional Ising model on a square lattice with competing interactions

Physica B Condensed Matter ◽

10.1016/j.physb.2015.06.021 ◽

2015 ◽

Vol 476 ◽

pp. 1-5 ◽

Cited By ~ 26

Author(s):

A.K. Murtazaev ◽

M.K. Ramazanov ◽

M.K. Badiev

Keyword(s):

Ising Model ◽

Square Lattice ◽

Two Dimensional ◽

Critical Properties ◽

Competing Interactions

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Triaquabenzoatocalcium(II) monobenzoate: coordination polymer chains linked into a two-dimensional framework by hydrogen bonds

Acta Crystallographica Section C Crystal Structure Communications ◽

10.1107/s0108270105027484 ◽

2005 ◽

Vol 61 (10) ◽

pp. m448-m449 ◽

Cited By ~ 14

Author(s):

Irena Senkovska ◽

Ulf Thewalt

Keyword(s):

Coordination Polymer ◽

Hydrogen Bonds ◽

Polymer Chains ◽

Two Dimensional

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Chalcogen S∙∙∙S Bonding in Supramolecular Assemblies of Cadmium(II) Coordination Polymers with Pyridine-Based Ligands

Crystals ◽

10.3390/cryst11060697 ◽

2021 ◽

Vol 11 (6) ◽

pp. 697

Author(s):

Nives Matijaković Mlinarić ◽

Nikolina Penić ◽

Boris-Marko Kukovec ◽

Marijana Đaković

Keyword(s):

Hydrogen Bonds ◽

Nicotinic Acid ◽

Coordination Polymers ◽

Acid Hydrazide ◽

Polymer Chains ◽

Supramolecular Interactions ◽

Two Dimensional ◽

Coordination Networks ◽

One Dimensional ◽

Polymeric Chains

Two cadmium(II) coordination polymers, with thiocyanate and pyridine-based ligands e.g., 3-acetamidopyridine (3-Acpy) and niazid (nicotinic acid hydrazide, nia), namely one-dimensional {[Cd(SCN)2(3-Acpy)]}n (1) and two-dimensional {[Cd(SCN)2(nia)]}n (2), are prepared in the mixture of water and ethanol. The adjacent cadmium(II) ions in 1 are bridged by two N,S-thiocyanate ions and an N,O-bridging 3-Acpy molecule, forming infinite one-dimensional polymeric chains, which are assembled by the intermolecular N–H∙∙∙S hydrogen bonds in one direction and by the intermolecular S∙∙∙S chalcogen bonds in another direction. Within the coordination network of 2, the adjacent cadmium(II) ions are bridged by N,S-thiocyanate ions in one direction and by N,O,N’-chelating and bridging nia molecules in another direction. The coordination networks of 2 are assembled by the intermolecular N–H∙∙∙S and N–H∙∙∙N hydrogen bonds and S∙∙∙S chalcogen bonds. Being the only supramolecular interactions responsible for assembling the polymer chains of 1 in the particular direction, the chalcogen S∙∙∙S bonds are more significant in the structure of 1, whilst the chalcogen S∙∙∙S bonds which act in cooperation with the N–H∙∙∙S and N–H∙∙∙N hydrogen bonds are of less significance in the structure of 2.

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