scholarly journals Optimized Factor Approximants and Critical Index

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 903
Author(s):  
Simon Gluzman
Keyword(s):  
Effective Viscosity ◽  
Critical Index ◽  
Self Similarity ◽  
Critical Amplitude ◽  
Third Order ◽  
Symmetry Properties ◽  
Self Consistent ◽  
Minimal Difference ◽  
Order Coefficient

Based on expansions with only two coefficients and known critical points, we consider a minimal model of critical phenomena. The method of analysis is both based on and inspired with the symmetry properties of functional self-similarity relation between the consecutive functional approximations. Factor approximants are applied together with various natural optimization conditions of non-perturbative nature. The role of control parameter is played by the critical index by itself. The minimal derivative condition imposed on critical amplitude appears to bring the most reasonable, uniquely defined results. The minimal difference condition also imposed on amplitudes produces upper and lower bound on the critical index. While one of the bounds is close to the result from the minimal difference condition, the second bound is determined by the non-optimized factor approximant. One would expect that for the minimal derivative condition to work well, the bounds determined by the minimal difference condition should be not too wide. In this sense the technique of optimization presented above is self-consistent, since it automatically supplies the solution and the bounds. In the case of effective viscosity of passive suspensions the bounds could be found that are too wide to make any sense from either of the solutions. Other optimization conditions imposed on the factor approximants, lead to better estimates for the critical index for the effective viscosity. The optimization is based on equating two explicit expressions following from two different definitions of the critical index, while optimization parameter is introduced as the trial third-order coefficient in the expansion.

Beckett's Broken Circle: A Literary Fractal

2020 ◽  
Vol 29 (2) ◽  
pp. 196-215
Author(s):  
Luke Connolly
Keyword(s):  
Dynamic Chaos ◽  
Geometric Form ◽  
Self Similarity ◽  
Collision Point ◽  
Stable Order ◽  
Structural Principle ◽  
Recent Interest ◽  
Viable Solution ◽  
Specific Shape

This essay proposes that the picture of a broken circle encountered by Watt during the second part of his tale marks a crucial collision point between Beckett's literary and mathematical interests and triggers a process of fractal scaling self-similarity. Building on recent interest concerning the role of the mathematics and mathematical forms found in Beckett's work, I argue that the broken circle depicted in the picture from Watt is a geometric form which (re)appears within at least three interlocking scales throughout Beckett's novel-length prose: (i) its moment of arrival in the picture from Watt, (ii) a macroscopic reinscription in the names of the protagonists populating the five novels spanning Watt through to The Unnamable and (iii) buried within the narratological depths of How It Is. As a structural principle, the interminable irregularity of fractals offered Beckett a viable solution for what he considered the defining task of the modern artist: ‘to find a form to accommodate the mess’. Moreover, the specific shape selected for his fractal is shown to contain within its geometry one of Beckett's most universal and pressing concerns: the inevitable insufficiency of language. Therefore, although this essay restricts itself to examining Beckett's novel-length prose, the idea of a broken circle fractal promises to provide a valuable heuristic through which to reassess the author's other generic avenues. Fractals thus offer a means through which one can bind together the length and breadth of Beckett's oeuvre without ever reducing dynamic chaos to stable order.

scholarly journals A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 153 ◽  
Author(s):  
Christophe Humbert ◽  
Thomas Noblet
Keyword(s):  
Dielectric Response ◽  
Structure And Properties ◽  
Linear Optics ◽  
Third Order ◽  
Mathematical Functions ◽  
Sum Frequency ◽  
Non Linear Optics ◽  
Non Linear ◽  
Light Excitation

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

A multitechnique investigation of the second order NLO response of a 10,20-diphenylporphyrinato nickel(II) complex carrying a phenylethynyl based push-pull system in the 5- and 15-positions

2004 ◽  
Vol 08 (11) ◽  
pp. 1311-1324 ◽  
Author(s):  
Maddalena Pizzotti ◽  
Elisabetta Annoni ◽  
Renato Ugo ◽  
Silvia Bruni ◽  
Silvio Quici ◽  
...  
Keyword(s):  
Ab Initio ◽  
Planar Structure ◽  
Third Order ◽  
Incident Wavelength ◽  
Pull System ◽  
Nlo Response ◽  
Self Consistent ◽  
Order Of Magnitude ◽  
Zero Frequency

A multitechnique investigation of the determination of the order of magnitude of the second and third order NLO response of [5-[(4-dimethylaminophenyl)ethynyl]-15-[(4-nitrophenyl)ethynyl]-10,20-diphenylporphyrinato]nickel(II) (1) is reported with the aim to produce self consistent evidence for a significant NLO response of this kind of push-pull porphyrin chromophore. The experimental multitechnique approach is based on the EFISH technique, working with a non-resonant incident wavelength of 1.907 μm, on the solvatochromic method and finally on a vibrational method, avoiding any fluorescence or resonance interference. A theoretical MNDO-TDHF evaluation of the zero-frequency quadratic and cubic hyperpolarizabilities of an ab initio optimized planar structure is also reported. The order of magnitude of the quadratic hyperpolarizability of (1) at zero frequency (β0), was found to be significantly lower than that reported for the corresponding Cu (II) or Zn (II) complexes with the same push-pull porphyrin chromophore.

scholarly journals The Role of IL-37 and IL-38 in Obstetrics Abnormalities

2021 ◽  
Vol 8 ◽  
Author(s):  
Mei Wang
Keyword(s):  
Diabetes Mellitus ◽  
Gestational Diabetes ◽  
Gestational Diabetes Mellitus ◽  
Inflammatory Mediator ◽  
Inflammatory Responses ◽  
Medical Practitioners ◽  
Minimal Difference ◽  
Anti Inflammatory ◽  
Umbilical Cords

There are two fairly common complications during pregnancy, i.e., gestational diabetes mellitus (GDM) and pre-eclampsia, which are independent, but are also closely linked in prevalence in pregnant women, with potential serious adverse consequences. IL-37 and IL-38, which belong to the IL-1 superfamily, participate in anti-inflammatory responses. Dysregulation of IL-37 and IL-38 has been observed in many auto-immune diseases. IL-37 is substantially reduced in the umbilical cords and placentas of GDM subjects, but IL-37 is significantly induced in the placentas of pre-eclampsia patients, suggesting there are differential regulatory roles of IL-37 in obstetrics, despite IL-37 being an anti-inflammatory mediator. Furthermore, IL-38 is substantially increased in the umbilical cords and placentas of GDM subjects, but minimal difference is observed in the placentas from pre-eclampsia patients. These data imply that IL-38 is also regulated independently within the diseased placentas. This review provides some insight for both basic scientists and medical practitioners to manage these patients effectively.

scholarly journals Topographic Analysis of Wetlandscapes: Fractal Dimension and Scaling Properties

10.29007/c7r5 ◽  
2018 ◽  
Author(s):  
Leonardo Enrico Bertassello ◽  
P. Suresh Rao ◽  
Gianluca Botter ◽  
Antoine Aubeneau
Keyword(s):  
Fractal Dimension ◽  
The United States ◽  
Self Similarity ◽  
Topographic Analysis ◽  
Scaling Properties ◽  
Dem Analysis ◽  
Water Filling ◽  
Topographic Depressions ◽  
And Storage

Wetlands are ubiquitous topographic depressions on landscapes and form criticalelements of the mosaic of aquatic habitats. The role of wetlands in the global hydrological and biogeochemical cycles is intimately tied to their geometric characteristics. We used DEM analysis and local search algorithms to identify wetland attributes (maximum stage, surface area and storage volume) in four wetlandscapes across the United States. We then derived the exceedance cumulative density functions (cdfs) of these attributes for the identified wetlands, applied the concept of fractal dimension to investigate the variability in wetland’ shapes. Exponentially tempered Pareto distributions were fitted to DEM derived wetland attributes. In particular, the scaling exponents appear to remain constant through the progressive water-filling of the landscapes, suggesting self-similarity of wetland geometrical attributes. This tendency is also reproduced by the fractal dimension (D) of wetland shorelines, which remains constant across different water-filling levels. In addition, the variability in D is constrained within a narrow range (1 <D < 1.33) in all the four wetlandscapes. Finally, the comparison between wetlands identified by the DEM-based model are consistentwith actual data.

scholarly journals Nested Recharge Systems in Mountain Block Hydrology: High-Elevation Snowpack Generates Low-Elevation Overwinter Baseflow in a Rocky Mountain River

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2249
Author(s):  
Éowyn M. S. Campbell ◽  
M. Cathryn Ryan
Keyword(s):  
Rocky Mountain ◽  
High Elevation ◽  
Third Order ◽  
Relative Temperature ◽  
Local Flow ◽  
Fracture Systems ◽  
Lower Elevation ◽  
Flow Systems ◽  
Longitudinal Sampling

The majority of each year′s overwinter baseflow (i.e., winter streamflow) in a third-order eastern slopes tributary is generated from annual melting of high-elevation snowpack which is transmitted through carbonate and siliciclastic aquifers. The Little Elbow River and its tributaries drain a bedrock system formed by repeated thrust faults that express as the same siliciclastic and carbonate aquifers in repeating outcrops. Longitudinal sampling over an 18 km reach was conducted at the beginning of the overwinter baseflow season to assess streamflow provenance. Baseflow contributions from each of the two primary aquifer types were apportioned using sulfate, δ34SSO4, and silica concentrations, while δ18OH2O composition was used to evaluate relative temperature and/or elevation of the original precipitation. Baseflow in the upper reaches of the Little Elbow was generated from lower-elevation and/or warmer precipitation primarily stored in siliciclastic units. Counterintuitively, baseflow generated in the lower-elevation reaches originated from higher-elevation and/or colder precipitation stored in carbonate units. These findings illustrate the role of nested flow systems in mountain block recharge: higher-elevation snowmelt infiltrates through fracture systems in the cliff-forming—often higher-elevation—carbonates, moving to the lower-elevation valley through intermediate flow systems, while winter baseflow in local flow systems in the siliciclastic valleys reflects more influence from warmer precipitation. The relatively fast climatic warming of higher elevations may alter snowmelt timing, leaving winter water supply vulnerable to climatic change.

scholarly journals Chemical insights into the electronic structure of Fe(II) porphyrin using FCIQMC, DMRG, and generalized active spaces

2020 ◽  
Author(s):  
Oskar Weser ◽  
Leon Freitag ◽  
Kai Guther ◽  
Ali Alavi ◽  
Giovanni Li Manni
Keyword(s):  
Electron Correlation ◽  
Quantitative Measure ◽  
Model System ◽  
Quintet State ◽  
Consistent Field ◽  
Self Consistent ◽  
Stabilizing Effect ◽  
Self Consistent Field ◽  
Preliminary Version

<div>Stochastic-CASSCF and DMRG procedures have been utilized to quantify the role of the electron correlation mechanisms that in a Fe-porphyrin model system are responsible for the differential stabilization of the triplet over the quintet state. Orbital entanglement diagrams and CI-coefficients of the wave function in a localised orbital basis allow for an effective interpretation of the role of charge-transfer configurations. A preliminary version of the <i>Stochastic Generalized Active Space Self-Consistent Field</i> method has been developed and is here introduced to further assess the pi-backdonation stabilizing effect.</div><div>By the new method excitations between metal and ligand orbitals can selectively be removed from the complete CI expansion. It is demonstrated that these excitations are key to the differential stabilization of the triplet, effectively leading to a quantitative measure of the correlation enhanced pi-backdonation.</div><div><br></div>

scholarly journals Self-consistent determination of spin Hall angle and spin diffusion length in Pt and Pd: The role of the interface spin loss

2018 ◽  
Vol 4 (6) ◽  
pp. eaat1670 ◽  
Author(s):  
Xinde Tao ◽  
Qi Liu ◽  
Bingfeng Miao ◽  
Rui Yu ◽  
Zheng Feng ◽  
...  
Keyword(s):  
Spin Diffusion ◽  
Diffusion Length ◽  
Self Consistent ◽  
Hall Angle ◽  
Spin Diffusion Length

scholarly journals The Enigma of the Muon and Tau Solved by Emergent Quantum Mechanics?

2019 ◽  
Vol 9 (7) ◽  
pp. 1471
Author(s):  
Theo van Holten
Keyword(s):  
Quantum Mechanics ◽  
Droplet Model ◽  
Matter Waves ◽  
Equilibrium Configurations ◽  
Self Consistent ◽  
Usual Quantum ◽  
Electron Models ◽  
Charged Leptons ◽  
Emergent Quantum Mechanics

This paper addresses the long-standing question of how it may be explained that the three charged leptons (the electron, muon and tau particle) have different masses, despite their conformity in other respects. In the field of Emergent Quantum Mechanics non-singular electron models are being revisited, and from this exploration has come a possible answer. In this paper a deformable droplet model is considered. It is shown how the model can be made self-consistent, whilst obeying the laws of momentum and energy conservation as well as Larmor’s radiation law. The droplet appears to have three different static equilibrium configurations, each with a different mass. Tentatively, these three equilibrium masses were assumed to correspond with the measured masses of the charged leptons. The droplet model was tuned accordingly, and was thereby completely quantified. The dynamics of the droplet then showed a “De Broglie-like” relation p = K / λ . Beat patterns in the vibrations of the droplet play the role of the matter waves of usual quantum mechanics. The value of K , calculated by the droplet theory, practically equals Planck’s constant: K ≅ h . This fact seems to confirm the correctness of identifying the three types of charged leptons with the equilibria of a droplet of charge.

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