GENERALIZED ATMOSPHERIC SAMPLING OF KNOTTED POLYGONS

2011 ◽  
Vol 20 (08) ◽  
pp. 1145-1171 ◽  
Author(s):  
E. J. JANSE VAN RENSBURG ◽  
A. RECHNITZER
Keyword(s):  
Chemical Properties ◽  
Dominant Factor ◽  
Conformational Entropy ◽  
Cubic Lattice ◽  
Type K ◽  
Trefoil Knot ◽  
Ring Polymers ◽  
Atmospheric Sampling ◽  
Physical And Chemical ◽  
Lattice Polygons

Self-avoiding polygons in the cubic lattice are models of ring polymers in dilute solution. The conformational entropy of a ring polymer is a dominant factor in its physical and chemical properties, and this is modeled by the large number of conformations of lattice polygons. Cubic lattice polygons are embeddings of the circle in three space and may be used as a model of knotting in ring polymers. In this paper we study the effects of knotting on the conformational entropy of lattice polygons and so determine the relative fraction of polygons of different knot types at large lengths. More precisely, we consider the number of cubic lattice polygons of n edges with knot type K, pn(K). Numerical evidence strongly suggests that [Formula: see text] as n → ∞, where μ0 is the growth constant of unknotted lattice polygons, α is the entropic exponent of lattice polygons, and NK is the number of prime knot components in the knot type K (see the paper [Asymptotics of knotted lattice polygons, J. Phys. A: Math. Gen.31 (1998) 5953–5967]). Determining the exact value of pn(K) is far beyond current techniques for all but very small values of n. Instead we use the GAS algorithm (see the paper [Generalised atmospheric sampling of self-avoiding walks, J. Phys. A: Math. Theor.42 (2009) 335001–335030]) to enumerate pn (K) approximately. We then extrapolate ratios [pn(K)/pn(L)] to larger values of n for a number of given knot types. We give evidence that for the unknot 01 and the trefoil knot 31, there exists a number M01, 31 ≈170000 such that pn (01) > pn (31) if n < M01, 31 and pn (01) ≤pn (31) if n ≥M01, 31. In addition, the asymptotic relative frequencies for a variety of knot types are determined. For example, we find that [pn(31)/pn(41)] → 27.0 ± 2.2, implying that there are approximately 27 polygons of the trefoil knot type for every polygon of knot of type 41 (the figure eight knot), in the asymptotic limit. Finally, we examine the dominant knot types at moderate values of n and conjecture that the most frequent knot types in polygons of any given length n are of the form [Formula: see text] (or its chiral partner), where [Formula: see text] are right- and left-handed trefoils, and N increases with n.

Wiener index on rows of unit cells of the face-centred cubic lattice

2016 ◽  
Vol 72 (2) ◽  
pp. 243-249 ◽  
Author(s):  
Hamzeh Mujahed ◽  
Benedek Nagy
Keyword(s):  
Molecular Graph ◽  
Chemical Properties ◽  
Wiener Index ◽  
Crystal Lattices ◽  
Cubic Lattice ◽  
Wiener Number ◽  
Unit Cells ◽  
The Face ◽  
Physical And Chemical ◽  
Sum Of Distances

The Wiener index of a connected graph, known as the `sum of distances', is the first topological index used in chemistry to sum the distances between all unordered pairs of vertices of a graph. The Wiener index, sometimes called the Wiener number, is one of the indices associated with a molecular graph that correlates physical and chemical properties of the molecule, and has been studied for various kinds of graphs. In this paper, the graphs of lines of unit cells of the face-centred cubic lattice are investigated. This lattice is one of the simplest, the most symmetric and the most usual, cubic crystal lattices. Its graphs contain face centres of the unit cells and other vertices, called cube vertices. Closed formulae are obtained to calculate the sum of shortest distances between pairs of cube vertices, between cube vertices and face centres and between pairs of face centres. Based on these formulae, their sum, the Wiener index of a face-centred cubic lattice with unit cells connected in a row graph, is computed.

scholarly journals Geographical laws of the soil distribution of Pre-Gorganian Pre-Carpathian region

2017 ◽  
pp. 224-233
Author(s):  
Stepan Malyk
Keyword(s):  
Chemical Properties ◽  
Dominant Factor ◽  
Mountain Forest ◽  
Peat Soils ◽  
The Carpathians ◽  
River Terraces ◽  
Carpathian Region ◽  
Groundwater Occurrence ◽  
Soil Distribution ◽  
Physical And Chemical

Being part of the Pre-Carpathian Region, Pre-Gorganian Carpathians are situated between the Svicha River in the northwest and the Lychka River in the southeast. Taking into account the analysis of soil maps, the computer program ArcGis 10,0 and own field researches were determined the areas of the main types of soils within the studied territory and the indicators of their agricultural usage. The agricultural usage of the lands of the Pre-Gorganian Pre-Carpathian Region is 47,5 %, and the plowing of agricultural lands is 53,8 %. Under perennial plantations, hayfields and pastures were occupied 1,4 %, 3,4 %, and 11,2 % of agricultural territories. The distribution of soils within the Pre-Gorganian Pre-Carpathian Region is due to high altitude zonation. The change in absolute and relative heights from the Dniester River to the Carpathians is the dominant factor that determines the distribution of soils. Alterations of the hypsometric levels define the parameters of climate changes, the level of groundwater occurrence and types of plant formations, which together determine the morphological features and physical and chemical properties of the soils of the Pre-Gorganian Pre-Carpathian Region. The floodplain of the Dniester, Prut and their tributaries are alluvial-ray, alluvial and peat soils. On the first and second terraces are turf gley, meadow, meadow marsh, turf podzolized soils. The third and fourth terraces are covered with turf-podzolic surface-gleyed soils, which are background in the Prehistory of the Pre-Carpathian Region. In the fifth and sixth terraces, brown-ground-podzolic and sod-brown soils are common. The surface of the seventh terrace is occupied by brown mountain-forest soils, which are background for the mountains of the Carpathians. Key words: Pre-Gorganian Pre-Carpathian Region, soils, patterns of distribution, relief, river terraces.

Statistical criteria of stellar population types

1966 ◽  
Vol 24 ◽  
pp. 101-110
Author(s):  
W. Iwanowska
Keyword(s):  
Stellar Population ◽  
Chemical Properties ◽  
Spectrophotometric Study ◽  
Physical And Chemical Properties ◽  
Population Type ◽  
The Galaxy ◽  
Distribution Parameters ◽  
Physical And Chemical ◽  
Statistical Criteria ◽  
And Chemical Properties

In connection with the spectrophotometric study of population-type characteristics of various kinds of stars, a statistical analysis of kinematical and distribution parameters of the same stars is performed at the Toruń Observatory. This has a twofold purpose: first, to provide a practical guide in selecting stars for observing programmes, second, to contribute to the understanding of relations existing between the physical and chemical properties of stars and their kinematics and distribution in the Galaxy.

Biophysical Measurement of Molecular Weight of Foot-and-Mouth Disease RNA Fragments

1974 ◽  
Vol 32 ◽  
pp. 262-263
Author(s):  
Sydney S. Breese ◽  
Howard L. Bachrach
Keyword(s):  
Chemical Properties ◽  
Foot And Mouth Disease ◽  
Mouth Disease ◽  
Distilled Water ◽  
Bovine Plasma ◽  
Mouth Disease Virus ◽  
Foot And Mouth ◽  
Carbon Coated ◽  
Rna Fragments ◽  
Physical And Chemical

Continuing studies on the physical and chemical properties of foot-and-mouth disease virus (FMDV) have included electron microscopy of RNA strands released when highly purified virus (1) was dialyzed against demlneralized distilled water. The RNA strands were dried on formvar-carbon coated electron microscope screens pretreated with 0.1% bovine plasma albumin in distilled water. At this low salt concentration the RNA strands were extended and were stained with 1% phosphotungstic acid. Random dispersions of strands were recorded on electron micrographs, enlarged to 30,000 or 40,000 X and the lengths measured with a map-measuring wheel. Figure 1 is a typical micrograph and Fig. 2 shows the distributions of strand lengths for the three major types of FMDV (A119 of 6/9/72; C3-Rezende of 1/5/73; and O1-Brugge of 8/24/73.

Tailoring microstructures of materials through biomimetics

1993 ◽  
Vol 51 ◽  
pp. 500-501
Author(s):  
Mehmet Sarikaya ◽  
Ilhan A. Aksay
Keyword(s):  
Chemical Properties ◽  
Design And Synthesis ◽  
Structure Sensitive ◽  
Macro Scale ◽  
Methods Of Synthesis ◽  
Successive Level ◽  
Engineering Materials ◽  
Physical And Chemical ◽  
And Chemical Properties ◽  
Synthesis Of Materials

Biomimetics involves investigation of structure, function, and methods of synthesis of biological composite materials. The goal is to apply this information to the design and synthesis of materials for engineering applications.Properties of engineering materials are structure sensitive through the whole spectrum of dimensions from nanometer to macro scale. The goal in designing and processing of technological materials, therefore, is to control microstructural evolution at each of these dimensions so as to achieve predictable physical and chemical properties. Control at each successive level of dimension, however, is a major challenge as is the retention of integrity between successive levels. Engineering materials are rarely fabricated to achieve more than a few of the desired properties and the synthesis techniques usually involve high temperature or low pressure conditions that are energy inefficient and environmentally damaging.In contrast to human-made materials, organisms synthesize composites whose intricate structures are more controlled at each scale and hierarchical order.

Response of corn (Zea mays L.) to various organic-based fertilizers in marginal upland of Sta. Rita, Samar

2017 ◽  
pp. 31-43
Author(s):  
Berta Ratilla ◽  
Loreme Cagande ◽  
Othello Capuno
Keyword(s):  
Block Design ◽  
Management Strategies ◽  
Chemical Properties ◽  
Organic Fertilizers ◽  
Growth And Yield ◽  
Physical And Chemical Properties ◽  
Total N ◽  
Randomized Complete Block Design ◽  
Physical And Chemical ◽  
And Chemical Properties

Organic farming is one of the management strategies that improve productivity of marginal uplands. The study aimed to: (1) evaluate effects of various organic-based fertilizers on the growth and yield of corn; (2) determine the appropriate combination for optimum yield; and (3) assess changes on the soil physical and chemical properties. Experiment was laid out in Randomized Complete Block Design, with 3 replications and 7 treatments, namely; T0=(0-0-0); T1=1t ha-1 Evans + 45-30-30kg N, P2O5, K2O ha-1; T2=t ha-1 Wellgrow + 45-30-30kg N, P2O5, K2O ha-1; T3=15t ha-1 chicken dung; T4=10t ha-1 chicken dung + 45-30-30kg N, P2O5, K2O ha-1; T5=15t ha-1 Vermicast; and T6=10t ha-1 Vermicast + 45-30-30kg N, P2O5, K2O ha-1. Application of organic-based fertilizers with or without inorganic fertilizers promoted growth of corn than the control. But due to high infestation of corn silk beetle(Monolepta bifasciata Horns), its grain yield was greatly affected. In the second cropping, except for Evans, any of these fertilizers applied alone or combined with 45-30-30kg N, P2O5, K2O ha-1 appeared appropriate in increasing corn earyield. Soil physical and chemical properties changed with addition of organic fertilizers. While bulk density decreased irrespective of treatments, pH, total N, available P and exchangeable K generally increased more with chicken dung application.

THE IMPORTANCE OF THE RED BOOK OF SOILS FOR MONITORING AND JUSTIFICATION OF CONSERVATION MEASURES

2020 ◽  
Author(s):  
O.S. Bezuglova ◽  
Keyword(s):  
Chemical Properties ◽  
Natural State ◽  
Soil Maps ◽  
Rostov Region ◽  
Conservation Measures ◽  
Background Data ◽  
The Russian Federation ◽  
Physical And Chemical ◽  
And Chemical Properties

Rostov Region belongs to the highly protected natural territories characterized by the continuous plowing. There territories are the only reserves with the soils preserved in their natural state. However, these areas often lack detailed information about the soils quality and composition. Surveying soils on these territories is crucial for determination of their basic physical and chemical properties. The resulted compilation of soil maps could lay a foundation for creating the Red Book of Soils and the formation of a section in the soil-geographical database of the Russian Federation. Subsequently, such information can be used as a background data for the main types of soils in the region. It will be also valuable during monitoring and justification of conservation measures.

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