scholarly journals A theoretical verification of the integral fluctuation theorem for accelerated colloidal systems in the long-time limit

2021 ◽  
Author(s):  
Yash Lokare
Keyword(s):  
Steady State ◽  
Time Scales ◽  
Numerical Study ◽  
Quantitative Description ◽  
Experimental Studies ◽  
Fluctuation Theorem ◽  
Nonequilibrium Steady States ◽  
Small Scale ◽  
Colloidal Systems ◽  
Long Time

A quantitative description of the violation of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem. It has been well established both theoretically and experimentally, the validity of the fluctuation theorem to small scale systems that are disturbed from their initial equilibrium states. Some experimental studies in the past have also explored the validity of the fluctuation theorem to nonequilibrium steady states at long time scales in the asymptotic limit. To this end, a theoretical and/or purely numerical model of the integral fluctuation theorem has been presented. An approximate general expression for the dissipation function has been derived for accelerated colloidal systems trapped/confined in power-law traps. Thereafter, a colloidal particle trapped in a harmonic potential (generated by an accelerating one-dimensional optical trap) and undergoing Brownian motion has been considered for the numerical study. A toy model of a quartic potential trap in addition to the harmonic trap has also been considered for the numerical study. The results presented herein show that the integral fluctuation theorem applies not only to equilibrium steady state distributions but also to nonequilibrium steady state distributions of colloidal systems in accelerated frames of reference over long time scales.

On the analysis of the integral fluctuation theorem for accelerated colloidal systems in the long-time limit

2021 ◽  
Author(s):  
Yash Lokare
Keyword(s):  
Steady State ◽  
Time Scales ◽  
Numerical Study ◽  
Quantitative Description ◽  
Experimental Studies ◽  
Fluctuation Theorem ◽  
Nonequilibrium Steady States ◽  
Small Scale ◽  
Colloidal Systems ◽  
Long Time

Abstract A quantitative description of the violation of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem. It has been well established both theoretically and experimentally, the validity of the fluctuation theorem to small scale systems that are disturbed from their initial equilibrium states. Some experimental studies in the past have also explored the validity of the fluctuation theorem to nonequilibrium steady states at long time scales in the asymptotic limit. To this end, a theoretical and/or purely numerical model of the integral fluctuation theorem has been presented. An approximate general expression for the dissipation function has been derived for accelerated colloidal systems trapped/confined in power-law traps. Thereafter, a colloidal particle trapped in a harmonic potential (generated by an accelerating one-dimensional optical trap) and undergoing Brownian motion has been considered for the numerical study. A toy model of a quartic potential trap in addition to the harmonic trap has also been considered for the numerical study. The results presented herein show that the integral fluctuation theorem applies not only to equilibrium steady state distributions but also to nonequilibrium steady state distributions of colloidal systems in accelerated frames of reference over long time scales.

scholarly journals A Theoretical Analysis of the Integral Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit

2021 ◽  
Author(s):  
Yash Lokare
Keyword(s):  
Steady State ◽  
Time Scales ◽  
Numerical Study ◽  
Quantitative Description ◽  
Experimental Studies ◽  
Fluctuation Theorem ◽  
Nonequilibrium Steady States ◽  
Small Scale ◽  
Colloidal Systems ◽  
Long Time

A quantitative description of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem. It has been well established both theoretically and experimentally, the validity of the fluctuation theorem to small scale systems that are disturbed from their initial equilibrium states. Some experimental studies in the past have also explored the validity of the fluctuation theorem to nonequilibrium steady states at long time scales in the asymptotic limit. To this end, a theoretical and/or purely numerical model of the integral fluctuation theorem has been presented. An approximate general expression for the dissipation function has been derived for accelerated colloidal systems trapped/confined in power-law traps. Thereafter, a colloidal particle trapped in a harmonic potential (generated by an accelerating one-dimensional optical trap) and undergoing Brownian motion has been considered for the numerical study. A toy model of a quartic potential trap in addition to the harmonic trap has also been considered for the numerical study. The results presented herein show that the integral fluctuation theorem applies not only to equilibrium steady state distributions but also to nonequilibrium steady state distributions of ideal colloidal systems in accelerated frames of reference over long time scales.

Investigation of the Effect of Incomplete Droplet Prevaporization on NOx Emissions in LDI Combustion Systems

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Christian H. Beck ◽  
Rainer Koch ◽  
Hans-Jörg Bauer
Keyword(s):  
Reaction Zone ◽  
Liquid Fuel ◽  
Laser Doppler Anemometry ◽  
Numerical Study ◽  
Experimental Studies ◽  
Peak Temperature ◽  
Small Scale ◽  
Nitric Oxides ◽  
Transition Range ◽  
Combustion Systems

The influence of incomplete liquid fuel prevaporization on the emissions of nitric oxides in a swirl stabilized model gas turbine combustor is investigated experimentally and numerically. The design of the model combustor enables the variation of the degree of prevaporization. This is achieved by using two liquid fuel injectors. One injector is located far upstream of the combustor and generates a fully prevaporized and premixed air fuel mixture. The second injector is located at the combustor inlet. Consequently, the liquid fuel mass flow split between the two injectors determines the fraction of nonprevaporized fuel present in the reaction zone. The NO∕NO2 measurements were performed with a chemoluminescence analyzer. In accordance to the findings of other researchers, the present experimental study revealed that the influence of prevaporization on nitric oxide emissions is of significance for practical applications. The experimental studies were accompanied by numerical studies of partially prevaporized lean combustion in an abstracted configuration. The purpose of this numerical study is to gain a detailed understanding of the influence of droplet slip on droplet flame position and peak temperature. The droplet slip velocity was found to have a significant impact on the peak temperature of the droplet flame and, therefore, NO formation rates within the droplet flame. The combustion system used for the experimental investigation was characterized regarding droplet slip velocities with an extended laser Doppler anemometry technique. The comparison between numerical and experimental results shows that the droplet slip velocities in the macroscopic reaction zone are within the transition range from an envelope to a wake flame. It is concluded that small-scale mixing effects play a significant role in the formation of nitric oxides in spray combustion systems with incomplete prevaporization.

scholarly journals Irradiance Effects of Small-Scale Magnetic Fields on the Sun

1994 ◽  
Vol 143 ◽  
pp. 226-235 ◽  
Author(s):  
Sami K. Solanki
Keyword(s):  
Magnetic Fields ◽  
Time Scales ◽  
Magnetic Feature ◽  
Small Scale ◽  
The Sun ◽  
Theoretical Understanding ◽  
Flux Tubes ◽  
Solar Luminosity ◽  
Long Time ◽  
Observational Knowledge

Small-scale magnetic fields affect the solar luminosity mainly on long time scales. To understand their contribution to solar luminosity variations we must know and understand the contribution of a typical small-scale magnetic feature. In this review I briefly outline our theoretical understanding of the processes leading to the enhancement (or reduction) of the brightness of flux tubes. I also present a brief overview of our observational knowledge.

Molecular Tagging Velocimetry and Its Application to In-Cylinder Flow Measurements

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Ravi Vedula ◽  
Mayank Mittal ◽  
Harold J. Schock
Keyword(s):  
Internal Combustion Engines ◽  
Measurement Techniques ◽  
Quantitative Description ◽  
Experimental Studies ◽  
Small Scale ◽  
Flow Measurements ◽  
Molecular Tagging Velocimetry ◽  
Molecular Tagging ◽  
Intake Stroke ◽  
Cylinder Flows

This review article provides an overview of the experimental studies of in-cylinder flows using various flow measurement techniques with a focus on molecular tagging velocimetry. It is necessary to understand the evolution of large-scale and small-scale turbulence as prepared during the intake stroke with a cycle resolved quantitative description. Due to the difficulty in obtaining these descriptions, either by modeling or experimentally, they are often characterized with somewhat ambiguous notions of bulk swirl and tumble measurement methods. During the intake stroke, in-cylinder flows are formed in such a manner as to provide advantageous spatial and temporal behavior for mixture formation later during the compression stroke. Understanding the details of how these flows influence fuel-air mixing, the initiation of ignition, combustion, and subsequent flame propagation processes is the primary motivation for the development of the methods described in this paper. The authors provide an introduction to fundamental flow motion inside the engine cylinder and measurement techniques, e.g., hot-wire anemometry, laser Doppler anemometry, and particle image velocimetry. Furthermore, molecular tagging velocimetry is discussed in detail in terms of (i) different mechanisms, (ii) procedure and data reduction methods to obtain the desired flow properties such as velocity, vorticity, and turbulent intensities, and (iii) applications to flow studies in internal combustion engines. Finally, the significance of experimental investigations of in-cylinder flows is discussed along with possible future applications.

scholarly journals An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number

2007 ◽  
Vol 574 ◽  
pp. 405-427 ◽  
Author(s):  
MICHELE GUALA ◽  
ALEXANDER LIBERZON ◽  
ARKADY TSINOBER ◽  
WOLFGANG KINZELBACH
Keyword(s):  
Reynolds Number ◽  
Time Scales ◽  
Correlation Functions ◽  
Time Scale ◽  
Cross Correlation ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Small Scale ◽  
Production Term ◽  
Long Time

Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.

Experimental and numerical study of friction and .giffness characteristics of small rolling tires

2011 ◽  
Vol 39 (1) ◽  
pp. 5-19 ◽  
Author(s):  
R. van der Steen ◽  
I. Lopez ◽  
H. Nijmeijer
Keyword(s):  
Steady State ◽  
Numerical Study ◽  
Complex Structure ◽  
Element Model ◽  
Steady State Solution ◽  
Experimental Results ◽  
Small Scale ◽  
The Road ◽  
Rubber Compounds ◽  
Complex Measurement

Abstract Virtual testing is nowadays the standard in the design process of new tires. Besides modeling the static response of the tire itself, the dynamics of a rolling tire in contact with the road needs to be incorporated. Due to the uncontrollable environmental conditions and the complex structure of the tires, it is advantageous to use small-scale testing under more controlled conditions. Experimental characterization of frictional properties of rubber compounds is, however, limited due to the necessity of complex measurement systems. In this paper a commercially available laboratory abrasion and skid tester is used to ide.gify both friction and .giffness characteristics of the same rubber compound. The obtained friction properties are implemented in a finite element model of the setup, and different validation steps are presented. Finally, a steady-state transport approach is used to efficiently compute a steady-state solution, which is compared with the experimental results. The numerical results show a good qualitative agreement with the experimental results.

A New Method for Fast Simulation of Adsorbate Dynamics

1995 ◽  
Vol 399 ◽  
Author(s):  
P.V. Kumar ◽  
Steven J. Warakomski ◽  
Kristen A. Fichthorn
Keyword(s):  
Time Scales ◽  
Film Growth ◽  
Experimental Studies ◽  
Simulation Method ◽  
Umbrella Sampling ◽  
Thin Film Growth ◽  
Atomic Scale ◽  
Lennard Jones ◽  
Diffusion Dynamics ◽  
Long Time

ABSTRACTWe present a dynamical version of the Smart Monte Carlo method to model the diffusion dynamics of a metal atom on a metal surface. This method, in conjunction with umbrella sampling, can be used to simulate the dynamics of metal thin film growth, including all relevant atomic-scale phenomenon, over long time scales, characteristic of experimental studies. To demonstrate the accuracy of this method we simulate the dynamics of Rh on Rh(111) and Cu on Cu(100). Interatomic forces are modeled with Lennard-Jones and Corrective-Effective-Medium potentials for the Rh and Cu systems, respectively. We show that this new simulation method correctly reproduces the diffusion dynamics and, with some modification, allows us to reach experimental time scales.

Numerical Evaluation of Splitting Performance of Prestressed Concrete Prisms With Larger Diameter Prestressing Wires

2019 ◽  
Author(s):  
Moochul Shin ◽  
Hailing Yu
Keyword(s):  
Prestressed Concrete ◽  
Structural Damage ◽  
Numerical Study ◽  
Experimental Studies ◽  
Concrete Cover ◽  
Small Scale ◽  
Slip Model ◽  
Cohesive Elements ◽  
Bond Slip ◽  
Pull Out

This numerical study focuses on evaluating the structural performance of prestressed concrete prisms with larger diameter (0.315 in) prestressing wires. More commonly used prestressing wires are the 0.209 in (5.32 mm) diameter wires for prestressed concrete crossties. However, there has been an interest to adopt larger diameter prestressing wires in order to provide higher prestress forces with the aim of mitigating the structural damage of prestressed concrete crossties. Previous experimental studies demonstrated that small-scale pretensioned concrete prisms had excellent correlation in bonding performance of concrete ties pretensioned with 0.209 in (5.32 mm) wires or three- or seven-wire strands. Using a finite element (FE) modeling approach, this study investigates the effects of 8 mm diameter prestressing wires on the splitting/bursting performance of prisms at the onset of de-tensioning of the wires. The studied parameters include geometrical/mechanical parameters such as thickness of the concrete cover, spacing between the wires, level of prestress forces, and concrete release strength in compression. Cohesive elements with a newly developed nonlinear bond-slip model are assigned to the interface between the prestressing wires and the surrounding concrete. The parameters for the bond-slip model are calibrated based on a simple pull-out test on concrete cylinders with the 0.315 in (8 mm) diameter wires. The simulation results are compared with the predicted splitting performance of prisms pretensioned with 0.209 in (5.32 mm) wires or seven-wire strands. Based on the FE analysis results, recommendations are made on the minimum concrete cover thickness and wire spacing required to achieve acceptable splitting/bursting performance in prestressed concrete prisms.

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