scholarly journals Investigation of the Validity of the Universal Scaling Law on Linear Chains of Silver Nanoparticles

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Mohammed Alsawafta ◽  
Mamoun Wahbeh ◽  
Vo-Van Truong
Keyword(s):  
Scaling Law ◽  
Surrounding Medium ◽  
Interparticle Spacing ◽  
Nanoparticle Size ◽  
Decay Length ◽  
Universal Scaling ◽  
Linear Chains ◽  
Interparticle Separation ◽  
Wide Range ◽  
Universal Law

Due to the wide range of variation in the plasmonic characteristics of the metallic nanoparticles arranged in linear arrays, the optical spectra of these arrays provide a powerful platform for spectroscopic studies and biosensing applications. Due to the coupling effect between the interacting nanoparticles, the excited resonance mode is shifted with the interparticle separation. The change in the resonance energy of the coupled mode is expressed by the fractional plasmon shift which would normally follow a universal scaling behavior. Such a universal law has been successfully applied on a system of dimers under parallel polarization. It has been found that the plasmon shift decays exponentially over interparticle spacing. The decay length is independent of both the nanoparticle and dielectric properties of the surrounding medium. In this paper, the discrete dipole approximation (DDA) is used to examine the validity of extending the universal scaling law to linear chains of several interacting nanoparticles embedded in various host media for both parallel and perpendicular polarizations. Our calculations reveal that the decay length of both the coupled longitudinal mode (LM) and transverse modes (TM) is strongly dependent on the refractive index of the surrounding mediumnm. The decay constant of the LM is linearly proportional tonmwhile the corresponding constant of the TM decays exponentially withnm. Upon changing the nanoparticle size, the change in the peak position of the LM decreases exponentially with the interparticle separation and hence, it obeys the universal law. The sensitivity of coupled LM to the nanoparticle size is more pronounced at both smaller nanoparticle sizes and separations. The sensitivity of the coupled TM to the nanoparticle size on the other hand changes linearly with the separation and therefore, the universal law does not apply in the case of the excited TM.

scholarly journals Cope’s Rule and the Universal Scaling Law of Ornament Complexity

2015 ◽  
Vol 186 (2) ◽  
pp. 165-175 ◽  
Author(s):  
Pasquale Raia ◽  
Federico Passaro ◽  
Francesco Carotenuto ◽  
Leonardo Maiorino ◽  
Paolo Piras ◽  
...  
Keyword(s):  
Scaling Law ◽  
Universal Scaling ◽  
Cope’S Rule

scholarly journals A universal scaling law for the evolution of granular gases

2016 ◽  
Vol 114 (1) ◽  
pp. 10002 ◽  
Author(s):  
Mathias Hummel ◽  
James P. D. Clewett ◽  
Marco G. Mazza
Keyword(s):  
Scaling Law ◽  
Granular Gases ◽  
Universal Scaling

The attachment length in orificed hollow cathodes

2021 ◽  
Author(s):  
Christopher Wordingham ◽  
Pierre-Yves Taunay ◽  
Edgar Choueiri
Keyword(s):  
Electron Temperature ◽  
Plasma Density ◽  
Hollow Cathode ◽  
Computational Models ◽  
Closed Form Solution ◽  
Form Solution ◽  
Decay Length ◽  
Plasma Density Profile ◽  
Wide Range ◽  
Approximate Boundary Condition

Abstract A first-principles approach to obtain the attachment length within a hollow cathode with a constrictive orifice, and its scaling with internal cathode pressure, is developed. This parameter, defined herein as the plasma density decay length scale upstream of (away from) the cathode orifice, is critical because it controls the utilization of the hollow cathode insert and influences cathode life. A two-dimensional framework is developed from the ambipolar diffusion equation for the insert-region plasma. A closed-form solution for the plasma density is obtained using standard partial differential equation techniques by applying an approximate boundary condition at the cathode orifice plane. This approach also yields the attachment length and electron temperature without reliance on measured plasma property data or complex computational models. The predicted plasma density profile is validated against measurements from the NSTAR discharge cathode, and calculated electron temperatures and attachment lengths agree with published values. Nondimensionalization of the governing equations reveals that the solution depends almost exclusively on the neutral pressure-diameter product in the insert plasma region. Evaluation of analytical results over a wide range of input parameters yields scaling relations for the variation of the attachment length and electron temperature with the pressure-diameter product. For the range of orifice-to-insert diameter ratio studied, the influence of orifice size is shown to be small except through its effect on insert pressure, and the attachment length is shown to be proportional to the insert inner radius, suggesting high-pressure cathodes should be constructed with larger-diameter inserts.

scholarly journals Health and disease imprinted in the time variability of the human microbiome

2015 ◽  
Author(s):  
Jose Manuel Marti ◽  
Daniel M Martinez ◽  
Manuel Pena ◽  
Cesar Gracia ◽  
Amparo Latorre ◽  
...  
Keyword(s):  
Temporal Variability ◽  
Scaling Law ◽  
Human Microbiome ◽  
Time Variability ◽  
Clinical Use ◽  
Gut Development ◽  
Research Activity ◽  
Health And Disease ◽  
Fluctuation Scaling ◽  
Universal Law

Human microbiota plays an important role in determining changes from health to disease. Increasing research activity is dedicated to understand its diversity and variability. We analyse 16S rRNA and whole genome sequencing (WGS) data from the gut microbiota of 97 individuals monitored in time. Temporal fluctuations in the microbiome reveal significant differences due to factors that affect the microbiota such as dietary changes, antibiotic intake, early gut development or disease. Here we show that a fluctuation scaling law describes the temporal variability of the system and that a noise-induced phase transition is central in the route to disease. The universal law distinguishes healthy from sick microbiota and quantitatively characterizes the path in the phase space, which opens up its potential clinical use and, more generally, other technological applications where microbiota plays an important role.

scholarly journals A scaled MP-PIC method for bubbling fluidization

2021 ◽  
Author(s):  
Xing Zhao ◽  
Yong Jiang ◽  
Fei Li ◽  
Wei Wang
Keyword(s):  
Fluidized Beds ◽  
Volume Fraction ◽  
Phase Particle ◽  
Scaling Law ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Particle In Cell ◽  
Wide Range ◽  
Pic Method ◽  
Multi Phase

Coarse-grained methods have been widely used in simulations of gas-solid fluidization. However, as a key parameter, the coarse-graining ratio, and its relevant scaling law is still far from reaching a consensus. In this work, a scaling law is developed based on a similarity analysis, and then it is used to scale the multi-phase particle-in-cell (MP-PIC) method, and validated in the simulation of two bubbling fluidized beds. The simulation result shows this scaled MP-PIC can reduce the errors of solids volume fraction and velocity distributions over a wide range of coarse-graining ratios. In future, we expect that a scaling law with consideration of the heterogeneity inside a parcel or numerical particle will further improve the performance of coarse-grained modeling in simulation of fluidized beds.

Generalization, similarity, and Bayesian inference

2001 ◽  
Vol 24 (4) ◽  
pp. 629-640 ◽  
Author(s):  
Joshua B. Tenenbaum ◽  
Thomas L. Griffiths
Keyword(s):  
Natural Kinds ◽  
Explanatory Power ◽  
Theoretic Model ◽  
Decay Function ◽  
Ideal Case ◽  
Basic Assumptions ◽  
Realistic Situation ◽  
Wide Range ◽  
Universal Law ◽  
The Ideal

Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models.

Clocking the buildup dynamics of light-induced states through attosecond transient absorption spectrum

2021 ◽  
Author(s):  
Xiaoxia Wu ◽  
Shaofeng Zhang ◽  
Difa Ye
Keyword(s):  
Floquet Theory ◽  
Transient Absorption ◽  
Scaling Law ◽  
Time Lag ◽  
Time Dependent ◽  
Transient Absorption Spectroscopy ◽  
Transient Absorption Spectrum ◽  
Wide Range ◽  
Maximal Shift ◽  
Buildup Time

Abstract The buildup processes of the light-induced states (LISs) in attosecond transient absorption spectroscopy are studied by solving the time-dependent Schrödinger equation and compared with the quasistatic Floquet theory, revealing a time lag of the maximal shift and strongest absorbance of the LIS with respect to the zero delay that is referred to as the buildup time. We analytically derive a scaling law for the buildup time that confirms the numerical results over a wide range of detunings. Our theory verifies the commonly accepted scenario of nearly instantaneous response of matter to light if the pump field is blue-detuned, but some differences are found in the near-resonant and red-detuning cases. Implications of the buildup time in petahertz optoelectronics are discussed.

Phase Drift in Networks of Coupled Colpitts Oscillators

2021 ◽  
Vol 31 (04) ◽  
pp. 2130010
Author(s):  
Lourdes Coria ◽  
Horacio Lopez ◽  
Antonio Palacios ◽  
Visarath In ◽  
Patrick Longhini
Keyword(s):  
Collective Behavior ◽  
Traveling Wave ◽  
Scaling Law ◽  
Industrial Applications ◽  
Basins Of Attraction ◽  
Navigation Systems ◽  
Negative Effects ◽  
Phase Drift ◽  
Wide Range ◽  
Wave Patterns

In modern times, satellite-based global positioning and navigation systems, such as the GPS, include precise time-keeping devices, e.g. atomic clocks, which are crucial for navigation and for a wide range of economic and industrial applications. However, precise timing might not be available when the environment renders satellite equipment inoperable. In response to this critical need, we have been carrying out, over the past three years, theory and preliminary experiments [Buono et al., 2018a; Buono et al., 2018b; Palacios et al., 2020], towards developing a novel and inexpensive precision timing device that can function independently of GPS availability. The fundamental idea is to exploit collective behavior generated by networks of coupled nonlinear oscillators. Common sense may suggest that synchronized oscillations may lead to higher accuracy. Previous works show, however, that it is not synchronization but rather, traveling wave patterns, in which consecutive oscillators are out of phase by a constant amount, that can better reduce the negative effects of noise and material imperfections which cause phase drift. In this work we advance the state-of-art in the network-based concept by studying, mainly computationally, collective behavior in networks of Colpitts oscillators. These type of oscillators are chosen because they offer a wide range of advantages (such as the ability to tune up the oscillations over a broad frequency range). The results highlight the regions of parameter space, including coupling strength, where traveling wave patterns have the largest basins of attraction and the ability to reduce phase drift by a [Formula: see text] scaling law, where [Formula: see text] is the number of oscillators in the network. The results should also provide guidelines for follow-up design and fabrication tasks of a network-based technology for precision timing.

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