Search results for "Exponential function"
showing 10 items of 173 documents
Sustainable Method Using Filtering Techniques for a Fermentation Process State Estimation
2020
Winemaking is concerned about sustainable energy availability that implies new methods for process monitoring and control. The aim of this paper is to realize a comparative analysis of the possibilities offered using estimation techniques, balances, and filtering techniques such as the Kalman filter (KF) and the extended Kalman filter (EKF), to obtain indirect information about the alcoholic fermentation process during winemaking. Thus, an estimation solution of the process variables in the exponential growing phase is proposed, using an extended observer. In addition, two estimation solutions of this process with the EKF and an estimation of the decay phase of the fermentation process are …
Computer simulation of models for orientational glasses
1991
Abstract Monte Carlo studies of two- and three-dimensional lattice models where quadrupoles interact with a nearest-neighbor Gaussian coupling are reviewed. None of these models has a thermodynamic glass phase transition at non-zero temperature like the Ising spin glass: rather, phase transitions at zero temperature occur that exhibit a dynamical freeze-in spread out over a wide temperature range and are characterized by a strongly non-exponential relaxation. The time-dependent glass order parameter, q(t), decays with time, t, compatible with a stretched exponential decay q(t) ∼ exp [− (t/τ)y] with a strongly temperature-dependent exponent. While the static glass ‘susceptibility’ for isotro…
DIELECTRIC AGEING IN LAYERED FERROELECTRICS
2008
ABSTRACT Studies of the effects of sample history on long-term relaxation of polarization in the Na0.5Bi8.5Ti2Nb4O27 and Na0.5Bi8.5Ti2Ta4O27 ferroelectrics of layered structures are reported. The type of functional relationship of e′(t) at measuring procedures including heating or cooling to the temperature being examined Ta is found to change from exponential (Kohlrausch function) to logarithmic. Results are discussed within the assumption of presence of defect complexes in disordered ferroelectrics.
Fracture Processes Observed with A Cryogenic Detector
2006
In the early stages of running of the CRESST dark matter search using sapphire detectors at very low temperature, an unexpectedly high rate of signal pulses appeared. Their origin was finally traced to fracture events in the sapphire due to the very tight clamping of the detectors. During extensive runs the energy and time of each event was recorded, providing large data sets for such phenomena. We believe this is the first time the energy release in fracture has been directly and accurately measured on a microscopic event-by-event basis. The energy threshold corresponds to the breaking of only a few hundred covalent bonds, a sensitivity some orders of magnitude greater than that of previou…
Stringlike Cooperative Motion in a Supercooled Liquid
1998
Extensive molecular dynamics simulations are performed on a glass-forming Lennard-Jones mixture to determine the nature of the cooperative motions occurring in this model fragile liquid. We observe stringlike cooperative molecular motion (``strings'') at temperatures well above the glass transition. The mean length of the strings increases upon cooling, and the string length distribution is found to be nearly exponential.
Universal Dynamic Fragmentation inDDimensions
2004
A generic model is introduced for brittle fragmentation in $D$ dimensions, and this model is shown to lead to a fragment-size distribution with two distinct components. In the small fragment-size limit a scale-invariant size distribution results from a crack branching-merging process. At larger sizes the distribution becomes exponential as a result of a Poisson process, which introduces a large-scale cutoff. Numerical simulations are used to demonstrate the validity of the distribution for $D=2$. Data from laboratory-scale experiments and large-scale quarry blastings of granitic gneiss confirm its validity for $D=3$. In the experiments the nonzero grain size of rock causes deviation from th…
Exponential and power-law mass distributions in brittle fragmentation
2004
Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size $s…
Analytical representations for relaxation functions of glasses
2002
Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the complex frequency dependent Cole-Cole, Cole-Davidson and Havriliak-Negami susceptibilities are also represented in terms of $H$-functions. In the frequency domain the complex frequency dependent susceptibility function corresponding to the time dependent stretched exponential relaxation function is given in terms of $H$-functions. The new representations are useful for fitting to experiment.
CONSTRUCTION OF METASTABLE STATES IN QUANTUM ELECTRODYNAMICS
2004
In this paper, we construct metastable states of atoms interacting with the quantized radiation field. These states emerge from the excited bound states of the non-interacting system. We prove that these states obey an exponential time-decay law. In detail, we show that their decay is given by an exponential function in time, predicted by Fermi's Golden Rule, plus a small remainder term. The latter is proportional to the (4+β)th power of the coupling constant and decays algebraically in time. As a result, though it is small, it dominates the decay for large times. A central point of the paper is that our remainder term is significantly smaller than the one previously obtained in [1] and as…
Measurement of the differential cross sectiondσ/dtin elasticpp¯scattering ats=1.96 TeV
2012
We present a measurement of the elastic differential cross section $d\sigma(p\bar{p}\rightarrow p\bar{p})/dt$ as a function of the four-momentum-transfer squared t. The data sample corresponds to an integrated luminosity of $\approx 31 nb^{-1}$ collected with the D0 detector using dedicated Tevatron $p\bar{p} $ Collider operating conditions at sqrt(s) = 1.96 TeV and covers the range $0.26 <|t|< 1.2 GeV^2$. For $|t|<0.6 GeV^2$, d\sigma/dt is described by an exponential function of the form $Ae^{-b|t|}$ with a slope parameter $ b = 16.86 \pm 0.10(stat) \pm 0.20(syst) GeV^{-2}$. A change in slope is observed at $|t| \approx 0.6 GeV^2$, followed by a more gradual |t| dependence with increasing …