Search results for "Exponent"
showing 10 items of 896 documents
Codimension growth of central polynomials of Lie algebras
2019
Abstract Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic zero and let I be the T-ideal of polynomial identities of the adjoint representation of L. We prove that the number of multilinear central polynomials in n variables, linearly independent modulo I, grows exponentially like ( dim L ) n {(\dim L)^{n}} .
The ${JV}$ -Characteristic of Intermediate Band Solar Cells With Overlapping Absorption Coefficients
2017
An analytic expression for the $\textit {JV}$ -characteristic of intermediate band (IB) solar cells with overlapping absorption coefficients is derived. The characteristic contains six voltage-independent parameters that are calculated from material properties, cell properties, and external conditions. Combined with exponential functions containing the cell voltage, these describe the full $\textit {JV}$ -characteristic. Expressions are also derived for the short-circuit current and open-circuit voltage. The model represents a major simplification compared with the existing model for this type of devices. The simplicity will facilitate the understanding of the operation of such cells. Furth…
Refractive index controlled by film morphology and free carrier density in undoped ZnO through sol-pH variation
2018
Abstract Zinc oxide thin films, prepared by the sol-gel process, were deposited on glass substrate using spin coating technique. The sol-pH effect on the optical parameters was studied for alkaline sol. The surface roughness was investigated by atomic force microscopy (AFM) and varied from 20 to 40 nm. The optical transmission measurements were carried out to evaluate the behavior of the extinction coefficient and the refractive index. An exponential decay of the refractive index ‘n’ as a function of wavelength was observed. The refractive index increases slightly when the pH increases to pH = 9.5 where it reaches its maximum. Beyond this value, it decreases sharply. This behavior has been …
Effect of surface disorder on the domain structure of PLZT ceramics
2017
ABSTRACTPb1-xLax(Zr0.65Ti0.35)1-x/4O3 (PLZT x/65/35) ceramics were studied by Piezoresponse Force Microscopy in order to understand the origin of domain structure as a function of La content. We show that the domain topology is mainly determined by the composition and grain size. The characteristic correlation length decreases with increasing La content, being sensitive also to the synthesis method. The behavior of the correlation length is linked to the macroscopic properties, showing a strong increase of disorder with La doping. The roughness exponent for the domain wall in PLZT 9/65/35 is close to 2/3 indicating 1D character of domain walls in relaxors.
On the thermodynamic origin of metabolic scaling
2018
The origin and shape of metabolic scaling has been controversial since Kleiber found that basal metabolic rate of animals seemed to vary as a power law of their body mass with exponent 3/4, instead of 2/3, as a surface-to-volume argument predicts. The universality of exponent 3/4 -claimed in terms of the fractal properties of the nutrient network- has recently been challenged according to empirical evidence that observed a wealth of robust exponents deviating from 3/4. Here we present a conceptually simple thermodynamic framework, where the dependence of metabolic rate with body mass emerges from a trade-off between the energy dissipated as heat and the energy efficiently used by the organi…
Distance decay 2.0 – a global synthesis of taxonomic and functional turnover in ecological communities
2021
AbstractUnderstanding the variation in community composition and species abundances, i.e., β-diversity, is at the heart of community ecology. A common approach to examine β-diversity is to evaluate directional turnover in community composition by measuring the decay in the similarity among pairs of communities along spatial or environmental distances. We provide the first global synthesis of taxonomic and functional distance decay along spatial and environmental distance by analysing 149 datasets comprising different types of organisms and environments. We modelled an exponential distance decay for each dataset using generalized linear models and extracted r2 and slope to analyse the streng…
Flow Control of Fluid in Pipelines Using PID Controller
2019
In this paper, a PID controller is utilized in order to control the flow rate of the heavy oil in pipelines by controlling the vibration in a motor pump. A torsional actuator is placed on the motor pump in order to control the vibration on a motor and consequently controlling the flow rates in pipelines. The necessary conditions for the asymptotic stability of the proposed controller are validated by implementing the Lyapunov stability theorem. The theoretical concepts are validated utilizing numerical simulations and analysis, which proves the effectiveness of the PID controller in the control of flow rates in pipelines.
Time-varying Sampled-data Observer with Asynchronous Measurements
2019
International audience; In this paper a time-varying observer for a linear continuous-time plant with asynchronous sampled measurements is proposed. The observer is contextualized in the hybrid systems framework providing an elegant setting for the proposed solution. In particular some theoretical tools are provided, in terms of LMIs, certifying asymptotic stability of a certain compact set where the estimation error is zero. We consider sampled asynchronous measurements that occur at arbitrary times in a certain window with an upper and lower bound. The design procedure, that we propose for the selection of the time-varying gain, is based on a constructive algorithm that is guaranteed to f…
Networked Bio-Inspired Evolutionary Dynamics on a Multi-Population
2019
We consider a multi-population, represented by a network of groups of individuals. Every player of each group can choose between two options, and we study the problem of reaching consensus. The dynamics not only depend on the dynamics within the group, but they also depend on the topology of the network, so neighboring groups influence individuals as well. First, we develop a mathematical model of this networked bio-inspired evolutionary behavior and we study its steady-state. We look at the special case where the underlying network topology is a regular and unweighted graph and show that the steady-state is a consensus equilibrium. A sufficient condition for exponential stability is given.…
New delay-dependent stability of Markovian jump neutral stochastic systems with general unknown transition rates
2015
This paper investigates the delay-dependent stability problem for neutral Markovian jump systems with generally unknown transition rates GUTRs. In this neutral GUTR model, each transition rate is completely unknown or only its estimate value is known. Based on the study of expectations of the stochastic cross-terms containing the integral, a new stability criterion is derived in terms of linear matrix inequalities. In the mathematical derivation process, bounding stochastic cross-terms, model transformation and free-weighting matrix are not employed for less conservatism. Finally, an example is provided to demonstrate the effectiveness of the proposed results.