scholarly journals NONUNIVERSAL PROPERTIES OF SELF-INTERACTING POLYMER IN NON-HOMOGENEOUS ENVIRONMENT MODELED BY 3-SIMPLEX FRACTAL LATTICE

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Dušanka Marčetić ◽  
Sunčica Elezović Hadžić ◽  
Ivan Živić
Keyword(s):  
Interaction Strength ◽  
Homogeneous Solution ◽  
Lattice Points ◽  
Extended Phase ◽  
Fractal Lattice ◽  
Connectivity Constant ◽  
The Mean ◽  
Simplex Lattice ◽  
Increasing Function ◽  
Limiting Value

We have studied lattice self-avoiding polygons with attractive interaction between contacts which are nonconsecutively visited nearest neighboring sites. The lattice of choice is 3-simplex fractal lattice and the model represents a ring polymer in non-homogeneous solution whose quality depends on the interaction parameter. It has already been shown, by the renormalization group approach, that polymer on this lattice at any nonzero temperature can exist only in the extended phase. Universal critical exponents, which do not depend on the interaction strength, have also been determined. In this paper we are concerned with two nonuniversal quantities: the connectivity constant related with the free energy of the model and the mean number of contacts related with the internal energy. We have shown that the connectivity constant is an unboundedly increasing function of the interaction strength, while the mean number of contacts is an increasing function asymptotically approaching a limiting value equal to one half, which is the mean number of contacts in the case of Hamiltonian walks on the same lattice. This limiting value is expected, since in the limit of infinite interaction (or zero temperature) each self-avoiding walk on 3-simplex lattice becomes maximally compact and occupies all lattice points, i.e. becomes Hamiltonian walk.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Mean Field ◽  
Interaction Strength ◽  
Bose Gas ◽  
Body Density ◽  
The Mean ◽  
The One ◽  
Mean Field Regime ◽  
Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

The reaction of μ-oxo-bis(phthalocyaninato)iron(III) with hydrogen sulphide in the presence of pyridine: Evidence for axial coordination of dichloromethane

2005 ◽  
Vol 09 (03) ◽  
pp. 198-205 ◽  
Author(s):  
Fabrizio Monacelli ◽  
Elisa Viola
Keyword(s):  
Reaction Mechanism ◽  
Linear Function ◽  
Rate Constant ◽  
Hydrogen Sulphide ◽  
Stoichiometric Ratio ◽  
First Order ◽  
Axial Coordination ◽  
Elementary Sulphur ◽  
Increasing Function ◽  
Limiting Value

The oxo-bridged complex ( py ) FePc - O - FePc ( py ) ( py = pyridine , Pc = phthalocyaninato dianion) reacts in dichloromethane with hydrogen sulphide giving elementary sulphur and the reduced ( py )2( FePc ) complex in the stoichiometric ratio 1:1. Under excess py and H2S , the reaction is first-order and the rate constant at a given py concentration is an increasing function of the reducing agent concentration, with asymptotic tendency to a limiting value. This latter depends on the pyridine concentration being higher the lower is the base concentration. When the reaction is carried out in pure pyridine, the rate constant is, instead, a strictly linear function of [ H2S ], with zero intercept. A reaction mechanism is proposed where the dichloromethane is directly involved in the axial coordination about the iron centers and H2S competes efficiently with both pyridine and solvent.

scholarly journals The volume coefficients of expansion of several gases at pressures below one metre

1934 ◽  
Vol 143 (850) ◽  
pp. 487-505 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Linear Function ◽  
Rate Of Change ◽  
Linear Extrapolation ◽  
Satisfactory Explanation ◽  
Volume Coefficient ◽  
Temperature Ranges ◽  
The Mean ◽  
Permanent Gases ◽  
Limiting Value

There have not appeared recently any new determinations of the rate of change of the volume coefficient of expansion of condensable gases at pressures in the neighbourhood of a half to one metre. The work of Henning and Heuse and Heuse and Otto has been confined to a study of the permanent gases, their results leading to the conclusion that up to a pressure of 1 metre the rate of change of either the pressure or volume coefficient is a linear function of the pressure. Our knowledge of the behaviour of the condensable gases in this connection rests almost entirely on the very careful work of Chappuis, who in 1907 made a series of accurate determinations of the volume coefficient of expansion of carbon dioxide at a series of pressures from 1500 mm. to 500 mm. and over several temperature ranges. The investigation led to one unexpected conclusion which Chappuis left largely unexplained. On linear extrapolation to zero pressure of the graph of pressure against the mean coefficient of expansion over temperature intervals 0-20º, 0-40º, 0-100ºC., the limiting value of the coefficient rose from the normal value of 0.003661 for the 0-20º determinations to 0.003671 for those made over the range 0-100ºC. Chappuis concludes "that condensation on the reservoir surface plays a part in the irregularities but it is difficult to obtain a satisfactory explanation." As far back as 1853 Magnus demonstrated that the adsorption of sukphur dioxide on glass was sufficient to affect measurements of the expansion coefficient of gasses, and the importance of this error was recognized by Chappuis who in 1879 applied a correction to Regnault's measurements. Richards and Mark and Baly and Ramsay have pointed out the necessity for a knowledge of the amount of adsorption on the walls of the containing vessels when undertaking such determinations.

The Hawk–Dove game as an average-cost problem

1991 ◽  
Vol 23 (04) ◽  
pp. 667-682
Author(s):  
J. M. McNamara ◽  
S. Merad ◽  
E. J. Collins
Keyword(s):  
Average Cost ◽  
Transition Probabilities ◽  
Energy Reserves ◽  
Stationary Policy ◽  
Evolutionarily Stable Strategies ◽  
Cost Criterion ◽  
Single Animal ◽  
The Mean ◽  
Evolutionarily Stable ◽  
Limiting Value

This paper considers a version of the Hawk–Dove game of Maynard Smith and Price (1973) in which animals compete for a sequence of food items. Actions may depend on an animal's energy reserves. Costs and transition probabilities under a given policy depend on the mean level of aggressiveness, p, of the rest of the population. We find the optimal policy for a single animal under an average cost criterion when ρ is constant over time. We then consider the whole interacting population when individual members follow the same stationary policy. It is shown that the mean aggressiveness, p, asymptotically approaches a limiting value in this population. We then consider the existence of evolutionarily stable strategies for the population. It is shown that such strategies always exist but may not be unique.

Glucose absorption by isolated perfused rat proximal straight tubules

1990 ◽  
Vol 259 (4) ◽  
pp. F580-F586 ◽  
Author(s):  
J. L. Garvin
Keyword(s):  
Glucose Concentration ◽  
Maximum Rate ◽  
Glucose Absorption ◽  
Fluid Absorption ◽  
Flow Rates ◽  
Straight Tubules ◽  
Proximal Straight Tubule ◽  
Rate Of Absorption ◽  
The Mean ◽  
Limiting Value

Glucose absorption was investigated in isolated perfused proximal straight tubules from rats by use of a newly developed ultramicrofluorometric assay. This assay takes advantage of the increase in fluorescence associated with the reduction of NAD to NADH while glucose is degraded to 6-phosphogluconate. When tubules were perfused at 6.70 +/- 0.42 nl.mm-1.min-1, the mean rate of glucose absorption was 11.0 +/- 1.0 pmol.mm-1.min-1, and the mean rate of fluid absorption was 0.61 +/- 0.06 nl.mm-1.min-1. Glucose transport is generally due to Na-glucose cotransport in the proximal nephron. In the rat proximal straight tubule, glucose absorption also appeared to be primarily due to Na-glucose cotransport, since 10(-4) M phlorizin inhibited absorption by 100%, as did inhibition of Na(+)-K(+)-ATPase by K removal. To determine the maximum rate of transport, tubules were perfused at rates greater than 20 nl.mm-1.min-1 with a solution containing 5.5 mM glucose. The maximum rate of glucose absorption was approximately 20 pmol.mm-1.min-1 under these conditions. The concentration of glucose that supports 50% of the maximum rate of absorption, Km, was 0.6 mM. When tubules were perfused at flow rates of less than or equal to 2 nl.mm-1.min-1, the luminal glucose concentration reached a limiting value of 0.47 mM with 5.5 mM glucose in the bath. The glucose permeability was 3.1 X 10(-6) cm/s.

AN UPPER BOUNDARY FOR THE SEX RATIO IN A HAPLODIPLOID INSECT

1976 ◽  
Vol 108 (12) ◽  
pp. 1399-1402 ◽  
Author(s):  
M. Mackauer
Keyword(s):  
Sex Ratio ◽  
Aphid Parasite ◽  
The Mean ◽  
Favourable Environment ◽  
Number Of Males ◽  
Limiting Value ◽  
Upper Boundary

AbstractMated females of the aphid parasite Aphidius smithi produced only unfertilized eggs (i.e. sons) for the first 2–3 h after copulation and a variable proportion of fertilized eggs (i.e. daughters) thereafter. As a result, the mean proportion of daughters among the offspring of single females was always less than unity, even in a highly favourable environment; the limiting value of the sex ratio was estimated at approximately 85% females. An argument is presented that in haplodiploid species with a variable and environmentally controlled sex ratio a male-producing mechanism is required to ensure the production of a sufficient number of males for the fertilization of all females.

On the current enhancement at the edge of a crack in a lattice of resistors

1998 ◽  
Vol 30 (2) ◽  
pp. 342-364 ◽  
Author(s):  
Howard M. Taylor ◽  
Dennis E. Sweitzer
Keyword(s):  
Random Walk ◽  
Vertical Direction ◽  
Potential Gradient ◽  
Domain Of Attraction ◽  
Lattice Points ◽  
Fourier Methods ◽  
The North ◽  
The Mean ◽  
Mean Time ◽  
Cauchy Process

Consider a network whose nodes are the integer lattice points and whose arcs are fuses of 1Ω resistance. Remove a horizontal segment ofNadjacent vertical arcs, forming a ‘crack’ of lengthN. Subject the network to a uniform potential gradient ofvvolts per arc in the north-south (or vertical) direction and measure the current in one of the two vertical arcs at the ends of the crack. We write this current in the forme(N)v, and calle(N) thecurrent enhancement.We show that the enhancement grows at a rate that is the order of the square root of the crack length. Our method is to identify the enhancement with the mean time to exit an interval for a certain integer valued random walk, and then to use some of the well-known Fourier methods for studying random walk. Our random walk has no mean or higher moments and is in the domain of attraction of the Cauchy law. We provide a good approximation to the enhancement using the explicitly known mean time to exit an interval for a Cauchy process. Weak convergence arguments together with an estimate of a recurrence probability enable us to show that the current in an intact fuse, that is in the interior of a crack of lengthN, grows p roportionally withN/logN.

scholarly journals Interaction capacity underpins community diversity

2020 ◽  
Author(s):  
Masayuki Ushio
Keyword(s):  
Interspecific Interactions ◽  
Experimental Studies ◽  
Interaction Strength ◽  
Single Species ◽  
Species Interaction ◽  
Community Diversity ◽  
Ecological Communities ◽  
Total Dna ◽  
Mathematical Equations ◽  
The Mean

AbstractHow patterns in community diversity emerge is a long-standing question in ecology. Theories and experimental studies suggested that community diversity and interspecific interactions are interdependent. However, evidence from multitaxonomic, high-diversity ecological communities is lacking because of practical challenges in characterizing speciose communities and their interactions. Here, I analyzed time-varying causal interaction networks that were reconstructed using 1197 species, DNA-based ecological time series taken from experimental rice plots and empirical dynamic modeling, and show that species interaction capacity, namely, the sum of interaction strength that a single species gives and receives, underpins community diversity. As community diversity increases, the number of interactions increases exponentially but the mean species interaction capacity of a community becomes saturated, weakening interaction among species. These patterns are explicitly modeled with simple mathematical equations, based on which I propose the “interaction capacity hypothesis”, namely, that species interaction capacity and network connectance are proximate drivers of community diversity. Furthermore, I show that total DNA concentrations and temperature influence species interaction capacity and connectance nonlinearly, explaining a large proportion of diversity patterns observed in various systems. The interaction capacity hypothesis enables mechanistic explanations of community diversity, and how species interaction capacity is determined is a key question in ecology.

scholarly journals Counting equilibria of large complex systems by instability index

2021 ◽  
Vol 118 (34) ◽  
pp. e2023719118 ◽  
Author(s):  
Gérard Ben Arous ◽  
Yan V. Fyodorov ◽  
Boris A. Khoruzhenko
Keyword(s):  
Autonomous System ◽  
Degrees Of Freedom ◽  
Stable Equilibrium ◽  
Interaction Strength ◽  
Absolute Instability ◽  
Instability Index ◽  
Random Interactions ◽  
Stable Equilibria ◽  
The Mean ◽  
Nonlinear Autonomous System

We consider a nonlinear autonomous system of N≫1 degrees of freedom randomly coupled by both relaxational (“gradient”) and nonrelaxational (“solenoidal”) random interactions. We show that with increased interaction strength, such systems generically undergo an abrupt transition from a trivial phase portrait with a single stable equilibrium into a topologically nontrivial regime of “absolute instability” where equilibria are on average exponentially abundant, but typically, all of them are unstable, unless the dynamics is purely gradient. When interactions increase even further, the stable equilibria eventually become on average exponentially abundant unless the interaction is purely solenoidal. We further calculate the mean proportion of equilibria that have a fixed fraction of unstable directions.

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