Scaling Conjecture Regarding the Number of Unknots among Polygons of N≫1 Edges

Alexander Y. Grosberg

doi:10.3390/physics3030039

Scaling Conjecture Regarding the Number of Unknots among Polygons of N≫1 Edges

Physics ◽

10.3390/physics3030039 ◽

2021 ◽

Vol 3 (3) ◽

pp. 664-668

Author(s):

Alexander Y. Grosberg

Keyword(s):

Power Law ◽

Exponential Law ◽

Numerical Result

The conjecture is made based on a plausible, but not rigorous argument, suggesting that the unknot probability for a randomly generated self-avoiding polygon of N≫1 edges has only logarithmic, and not power law corrections to the known leading exponential law: Punknot(N)∼exp−N/N0+o(lnN) with N0 being referred to as the random knotting length. This conjecture is consistent with the numerical result of 2010 by Baiesi, Orlandini, and Stella.

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Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity

Abstract and Applied Analysis ◽

10.1155/2014/585167 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

N. Mindu ◽

D. P. Mason

Keyword(s):

Conservation Laws ◽

Power Law ◽

Travelling Waves ◽

Travelling Wave ◽

Multiplier Method ◽

Reduction Theorem ◽

Double Reduction ◽

Exponential Law ◽

Spatial Derivatives ◽

Derivatives Of

The derivation of conservation laws for the magma equation using the multiplier method for both the power law and exponential law relating the permeability and matrix viscosity to the voidage is considered. It is found that all known conserved vectors for the magma equation and the new conserved vectors for the exponential laws can be derived using multipliers which depend on the voidage and spatial derivatives of the voidage. It is also found that the conserved vectors are associated with the Lie point symmetry of the magma equation which generates travelling wave solutions which may explain by the double reduction theorem for associated Lie point symmetries why many of the known analytical solutions are travelling waves.

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Photoluminescence and Electroluminescence in Partially Oxidized Porous Silicon

MRS Proceedings ◽

10.1557/proc-358-683 ◽

1994 ◽

Vol 358 ◽

Cited By ~ 4

Author(s):

L. Tsybeskov ◽

S. P. Duttagupta ◽

P. M. Fauchet

Keyword(s):

Activation Energy ◽

Porous Silicon ◽

Power Law ◽

Current Density ◽

Crystalline Silicon ◽

Exponential Law ◽

Current Voltage ◽

Device Applications ◽

Current Voltage Characteristics ◽

Oxidized Porous Silicon

ABSTRACTThe results of photoluminescence (PL) and electroluminescence (EL) studies from partially oxidized porous silicon (POPS) layers are presented. The PL from POPS is stable, peaks at 600-570 nm and its temperature dependence can be fitted by an exponential law with an activation energy Ea « 10 meV. The current-voltage characteristics of Au-(POPS)-crystalline silicon (c-Si) structures follow a power law I = Vn. When the index n becomes higher than 3, electroluminescence (EL) is found. The EL peaks at 760 nm and is stable for more than 100 hours of operation. The intensity of the EL is a linear function of current for all measured structures up to current density J ≈ 1 A/cm2. Our results suggest that partially oxidized porous silicon is more useful for device applications than freshly anodized porous silicon which has unstable properties or than fully oxidized porous silicon in which transport is poor.

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Use of mathematical laws for optimizing the dose of swollen and dry bentonite during the fining of white wines. Part II : influence on the volume of lies and economics

OENO One ◽

10.20870/oeno-one.2003.37.2.945 ◽

2003 ◽

Vol 37 (2) ◽

pp. 123

Author(s):

Richard Marchal ◽

S. Weingartner ◽

Philippe Jeandet ◽

Franck Chatelain

Keyword(s):

Power Law ◽

White Wine ◽

White Wines ◽

Good Relationship ◽

Exponential Law ◽

Low Efficiency ◽

The Cost ◽

Higher Doses

A Sauvignon white wine was fined with a dry bentonite (BS), e.g directly incorporated in the wine without swelling treatment, or with the same bentonite swelled in water 24 hours before utilization (BG). The volumes of lees generated by the fining were situated between 0,27 and 1,51 % (v/v) for BS, and between 1,07 and 4,59 % (v/v) for BG. The relation between the quantity of bentonite introduced in the wine (g/hl) and the volume of lees (v/v) follows a power law. The volume of lees only increased by 70 % when the dose of swelled bentonite was doubled; for higher doses of bentonite (rarely used), one can observe a packing of the lees. For BS, lees were approximately twice more volumetric when the dose was doubled. We also observe very good relationship between the clarifying efficiency and the volume of lees. When the clarifying efficiency of BG increased by 10 % the volume of lees increased by 74 %. For BS, when the clarifying efficiency increased by 10 % the volume of lees increased by 86 % because of its low efficiency during clarification. The decrease of the natural proteic haze risk and the volume of lees generated by bentonite fining were also closely correlated by an exponential law. For BG, the mathematical law showed that when the volume of lees increased by 0,1 % (v/v), colloidal haze risk decreased only by 22 %. On the contrary, for BS, when the volume of lees increased by 0,1 %, proteic haze risk decreased by 44 %. Finally, the estimation of the cost of fining showed that the use of a non swelled bentonite was economically more interesting than the utilization of a swelled bentonite. This was true when this Sauvignon wine is sold both in bottle or in bulk. For the studied wine, the estimated winning was 115 euros for 10 hl sold in bulk.

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EXPERIMENTAL OBSERVATION OF INTERMITTENCY IN COUPLED CHAOTIC PENDULUMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127499001395 ◽

1999 ◽

Vol 09 (10) ◽

pp. 1907-1916 ◽

Cited By ~ 9

Author(s):

H. J. T. SMITH ◽

JAMES A. BLACKBURN ◽

GREGORY L. BAKER

Keyword(s):

Experimental Data ◽

Experimental Observation ◽

Conditional Probability ◽

Power Law ◽

Coupling Strength ◽

Chaotic Motion ◽

Threshold Level ◽

Exponential Law ◽

Angular Velocities ◽

The Difference

We have experimentally realized on–off intermittency in a pair of mutually coupled damped driven pendula. The pendula interacted bidirectionally via a torque which was proportional to the difference in their angular velocities. Experimental data show that the intervals of synchronized chaotic motion are distributed in agreement with the theory for on–off intermittency: The conditional probability of short laminar times is found to follow a power law whilst the conditional probability of long laminar times follows the expected exponential law. The experimental data also reveal that the intermittent properties vary with the coupling strength, and that the average laminar time inferred from the results depends on the choice of threshold level.

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DIFFUSIONAL MODEL FOR NOISY ON–OFF INTERMITTENCY

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127499000225 ◽

1999 ◽

Vol 09 (02) ◽

pp. 355-359 ◽

Cited By ~ 2

Author(s):

A. ČENYS ◽

J. ULBIKAS ◽

A. N. ANAGNOSTOPOULOS ◽

G. L. BLERIS

Keyword(s):

Critical Point ◽

Power Law ◽

Statistical Properties ◽

Exponential Law ◽

Universal Distribution ◽

Diffusional Model

Statistical properties of the laminar lengths for the noisy on–off intermittency are studied analytically. The universal distribution of the laminar phases is obtained at the critical point. It can be approximated by the power law with the exponent -3/2 and the exponential law describing fast falloff.

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AN ANALYSIS OF SOME STATISTICAL PROPERTIES OF AURORAL RADAR REFLECTIONS AND THEIR RELATIONSHIPS TO THE DETECTION CAPABILITIES OF THE RADAR

Canadian Journal of Physics ◽

10.1139/p60-043 ◽

1960 ◽

Vol 38 (3) ◽

pp. 425-438

Author(s):

A. G. McNamara

Keyword(s):

Statistical Model ◽

Power Law ◽

Cross Sections ◽

Continuous Operation ◽

Probability Density Distribution ◽

Exponential Form ◽

Exponential Law ◽

Inverse Power Law ◽

Detection Capabilities ◽

Mathematical Relations

A statistical model of auroral echo occurrence has been made from an analysis of observations at 48.5 Mc/s obtained over a number of years of continuous operation. The probability density distribution of auroral target cross sections (σ) has been examined experimentally, and the resulting curve fitted by simple mathematical relations. Both an inverse power law and an exponential law have been derived, of the forms[Formula: see text]and[Formula: see text]These models have been interpreted in terms of distributed and localized targets, and used to analyze the echo occurrence indices and the effect which variation of radar parameters will have upon them. Both forms of the target law are useful although it is considered that the exponential form yields better agreement with observations over a wider range of the variables.

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Tracking the Covid-19 pandemic : Simple visualization of the epidemic states and trajectories of select European countries & assessing the effects of delays in official response

10.1101/2020.03.14.20035964 ◽

2020 ◽

Cited By ~ 5

Author(s):

A. Kévorkian ◽

T. Grenet ◽

H. Gallée

Keyword(s):

Power Law ◽

Growth Phase ◽

European Countries ◽

Robust Method ◽

Delayed Reaction ◽

Exponential Law

AbstractWe present a self-synchronizing and robust method for comparing the progression of the Covid-19 epidemics among multiple countries. In their growth phase the epidemics show power law rather than exponential law time dependences. They are similar enough for the earlier China outbreak to guide other countries projections. The delayed reaction of European countries is shown to produce a significantly worse outcome compared to China.

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Application of the chaotic power law to the study of cardiac dynamics in patients with arrhythmias

Revista de la Facultad de Medicina ◽

10.15446/revfacmed.v62n4.43444 ◽

2015 ◽

Vol 62 (4) ◽

pp. 539-546 ◽

Cited By ~ 2

Author(s):

Javier Rodríguez ◽

Signed Prieto ◽

Dario Dominguez ◽

Catalina Correa ◽

Martha Melo ◽

...

Keyword(s):

Fractal Dimension ◽

Power Law ◽

Normal Subjects ◽

Kappa Coefficient ◽

Acute Illness ◽

Exponential Law ◽

Cardiac Dynamics ◽

Clinical Applicability ◽

Mathematical Evaluation ◽

Sensitivity Specificity

Background. An exponential law for chaotic cardiac dynamics, found previously, allows the quantification of the differences between normal cardiac dynamics and those with acute diseases, as well as the cardiac dynamics of the evolution between these states. Objective. To confirm the clinical applicability of the developed methodology through the mathematical law for cardiac dynamics in dynamics with arrhythmias. Materials and methods. 60 Holter electrocardiograms were analyzed, 10 corresponded to normal subjects, and 50 to subjects with different arrhythmias. For each Holter, an attractor was performed, and its fractal dimension and spatial occupancy were measured. A mathematical evaluation was applied in order to differentiate normal dynamics from pathological ones. Sensitivity, specificity and the Kappa coefficient were calculated. Results. The mathematical evaluation differentiated occupation spaces, normal dynamics, acute illness dynamics, and evolution between these states. The sensitivity and specificity values were 100%, and the Kappa coefficient was 1.Conclusions. The clinical applicability of the methodology for cases with arrhythmia was shown. It is also applicable for the detection of changes in dynamics that are not classified clinically as pathological.

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