Transport in the Critical Region

2005 ◽  
Author(s):  
Eldred H. Chimowitz
Keyword(s):  
Random Walk ◽  
Critical Region ◽  
Diffusion Processes ◽  
Dynamic Properties ◽  
Relaxation Times ◽  
Two Dimensions ◽  
Thermally Induced ◽  
Self Diffusion ◽  
Slowing Down ◽  
Definition Of

The behavior of dynamic properties in the critical region is important in many engineering applications, and in this chapter we investigate this topic, focusing upon diffusion. In the literature, the term critical slowing down is used to describe the long relaxation times that occur when criticality is approached. Does this mean that diffusion processes per se come to a halt and, if not, how does slowing down manifest itself in fluids? We see that, in spite of the nonequilibrium nature of this topic, equilibrium concepts still play a key role in describing dynamics in the critical region. To begin this discussion, we investigate the dynamic behavior of a tagged fluid molecule as it experiences random fluctuations in its position in the fluid. These fluctuations would be induced by random thermally induced collisions between the tagged species and other fluid molecules. This type of dynamics is referred to as Brownian motion or a random walk. A schematic showing two 10-step trajectories depicting a random walk in two dimensions is shown in figure 12.1, and its analysis leads naturally to the definition of the self-diffusion coefficient.

The Nature of Point Defects and their Influence on Diffusion Processes in Silicon at High Temperatures

1982 ◽  
Vol 14 ◽  
Author(s):  
U. GÖsele ◽  
T.Y. Tan
Keyword(s):  
Diffusion Processes ◽  
Surface Oxidation ◽  
Group V ◽  
Group Iii ◽  
Self Diffusion ◽  
Slowing Down ◽  
Silicon Crystals ◽  
Order Of Magnitude ◽  
Theoretical Results

ABSTRACTThe paper highlights recent progress in understanding the role of vacancies and self-interstitials in self- and impurity diffusion in silicon above about 700°C. How surface oxidation of silicon leads to a perturbation of the pointdefect population is described. An analysis of the resulting oxidationenhanced or -retarded diffusion of group III and group V dopants shows that under thermal equilibrium as well as under oxidation conditions both vacancies and self-interstitials are present. For sufficiently long times vacancies and self-interstitials attain dynamical equilibrium which involves their recombination and spontaneous thermal creation in the bulk of silicon crystals. The existence and the nature of a recombination barrier slowing down the recombination process are discussed in this context. Recent experimental and theoretical results on the diffusion of gold in silicon enable us to determine the selfinterstitial component of silicon self-diffusion and to obtain an estimate of the respective vacancy contribution. The two components turn out to be of the same order of magnitude from 700°C up to the melting point.

scholarly journals Non-Exponential 1H and 2H NMR Relaxation and Self-Diffusion in Asphaltene-Maltene Solutions

Molecules ◽  
2021 ◽  
Vol 26 (17) ◽  
pp. 5218
Author(s):  
Kevin Lindt ◽  
Bulat Gizatullin ◽  
Carlos Mattea ◽  
Siegfried Stapf
Keyword(s):  
Diffusion Coefficients ◽  
Relaxation Times ◽  
Chemical Species ◽  
Nmr Relaxation ◽  
Molecular Size ◽  
Relaxation Rates ◽  
Vast Number ◽  
Self Diffusion ◽  
Slowing Down ◽  
The Individual

The distribution of NMR relaxation times and diffusion coefficients in crude oils results from the vast number of different chemical species. In addition, the presence of asphaltenes provides different relaxation environments for the maltenes, generated by steric hindrance in the asphaltene aggregates and possibly by the spatial distribution of radicals. Since the dynamics of the maltenes is further modified by the interactions between maltenes and asphaltenes, these interactions—either through steric hindrances or promoted by aromatic-aromatic interactions—are of particular interest. Here, we aim at investigating the interaction between individual protonic and deuterated maltene species of different molecular size and aromaticity and the asphaltene macroaggregates by comparing the maltenes’ NMR relaxation (T1 and T2) and translational diffusion (D) properties in the absence and presence of the asphaltene in model solutions. The ratio of the average transverse and longitudinal relaxation rates, describing the non-exponential relaxation of the maltenes in the presence of the asphaltene, and its variation with respect to the asphaltene-free solutions are discussed. The relaxation experiments reveal an apparent slowing down of the maltenes’ dynamics in the presence of asphaltenes, which differs between the individual maltenes. While for single-chained alkylbenzenes, a plateau of the relaxation rate ratio was found for long aliphatic chains, no impact of the maltenes’ aromaticity on the maltene–asphaltene interaction was unambiguously found. In contrast, the reduced diffusion coefficients of the maltenes in presence of the asphaltenes differ little and are attributed to the overall increased viscosity.

scholarly journals A FUZZY FRONT-END PRODUCT DEVELOPMENT FRAMEWORK FOR START-UPS

2021 ◽  
Vol 1 ◽  
pp. 111-120
Author(s):  
Nuno Miguel Martins Pacheco ◽  
Anand Vazhapilli Sureshbabu ◽  
Masaru Charles Nürnberger ◽  
Laura Isabel Durán Noy ◽  
Markus Zimmermann
Keyword(s):  
Two Dimensions ◽  
Fuzzy Front End ◽  
Development Framework ◽  
Front End ◽  
Start Up ◽  
Extended Approach ◽  
Role Based ◽  
Definition Of ◽  
Clear Idea ◽  
Start Ups

AbstractStart-ups tend to form with a central idea that differentiates them from their competitors in the market. It is crucial for them to efficiently transform the idea into a marketable product. Prototyping helps to iteratively achieve a minimum viable product and plays a crucial role by enabling teams to test their ideas with limited resources early on. However, the prototyping process may have wrong focus leading to a suboptimal allocation of resources. Previously, we proposed role-based prototyping for fuzzy front-end development in small teams. It supports (1) resource allocation, (2) the definition of responsibilities, and (3) structuring the development process with milestones. In recent research this was a promising yet incomplete approach. We extend the previous work by refining the prototyping process by adding a prototyping matrix with two dimensions (purpose and lens), a prototyping cycle (plan, execute, test, reflect, assimilate), and a modified Kanban board (Protoban) for planning, managing, and reflecting cycles. This process, named PETRA was tested with a start-up developing an autonomous trash picking robot. The extended approach supported the team significantly in providing a clear idea of what to do at what time.

Temperature Dependence of Dynamic Properties of Elastomers. Relaxation Distributions

1952 ◽  
Vol 25 (4) ◽  
pp. 720-729 ◽  
Author(s):  
John D. Ferry ◽  
Edwin R. Fitzgerald ◽  
Lester D. Grandine ◽  
Malcolm L. Williams
Keyword(s):  
Distribution Function ◽  
Temperature Dependence ◽  
Dynamic Properties ◽  
Relaxation Times ◽  
Dynamic Mechanical Properties ◽  
Relaxation Processes ◽  
The Real ◽  
Reduced Frequency ◽  
Dynamic Rigidity ◽  
Composite Curve

Abstract By the use of reduced variables, the temperature dependence and frequency dependence of dynamic mechanical properties of rubberlike materials can be interrelated without any arbitrary assumptions about the functional form of either The definitions of the reduced variables are based on some simple assumptions regarding the nature of relaxation processes. The real part of the reduced dynamic rigidity, plotted against the reduced frequency, gives a single composite curve for data over wide ranges of frequency and temperature; this is true also for the imaginary part of the rigidity or the dynamic viscosity. The real and imaginary parts of the rigidity, although independent measurements, are interrelated through the distribution function of relaxation times, and this relation provides a check on experimental results. First and second approximation methods of calculating the distribution function from dynamic data are given. The use of the distribution function to predict various types of time-dependent mechanical behavior is illustrated.

Diffusion Mechanisms in Sige Alloys

1999 ◽  
Vol 568 ◽  
Author(s):  
Arthur F.W. Willoughby ◽  
Janet M. Bonar ◽  
Andrew D.N. Paine
Keyword(s):  
Diffusion Processes ◽  
Dopant Diffusion ◽  
Elemental Silicon ◽  
Self Diffusion ◽  
Si Substrates ◽  
Marker Layer ◽  
Diffusion Mechanisms ◽  
Silicon And Germanium ◽  
Charged Defects

ABSTRACTInterest in diffusion processes in SiGe alloys arises from their potential in HBT's, HFET's, and optoelectronics devices, where migration over distances as small as a few nanometres can be significant. Successful modelling of these processes requires a much improved understanding of the mechanisms of self- and dopant diffusion in the alloy, although recent progress has been made. It is the purpose of this review to set this in the context of diffusion processes in elemental silicon and germanium, and to identify how this can help to elucidate behaviour in the alloy. Firstly, self diffusion processes are reviewed, from general agreement that self-diffusion in germanium is dominated by neutral and acceptor vacancies, to the position in silicon which is still uncertain. Germanium diffusion in silicon, however, appears to be via both vacancy and interstitial processes, and in the bulk alloy there is evidence for a change in dominant mechanism at around 35 percent germanium. Next, a review of dopant diffusion begins with Sb, which appears to diffuse in germanium by a mechanism similar to self-diffusion, and in silicon via monovacancies also, from marker layer evidence. In SiGe, the effects of composition and strain in epitaxial layers on Si substrates are also consistent with diffusion via vacancies, but questions still remain on the role of charged defects. The use of Sb to monitor vacancy effects such as grown-in defects by low temperature MBE, are discussed. Lastly, progress in assessing the role of vacancies and interstitials in the diffusion of boron is reviewed, which is dominated by interstitials in silicon-rich alloys, but appears to change to domination by vacancies at around 40 percent germanium, although studies in pure germanium are greatly needed.

scholarly journals Three-dimensional quantification of twisting in the Arabidopsis petiole

2021 ◽  
Author(s):  
Yuta Otsuka ◽  
Hirokazu Tsukaya
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Light Sheet ◽  
Underlying Mechanism ◽  
Two Dimensions ◽  
Observation Angle ◽  
Differential Growth ◽  
Light Sheet Microscopy ◽  
Definition Of ◽  
Twisting Angle

AbstractOrganisms have a variety of three-dimensional (3D) structures that change over time. These changes include twisting, which is 3D deformation that cannot happen in two dimensions. Twisting is linked to important adaptive functions of organs, such as adjusting the orientation of leaves and flowers in plants to align with environmental stimuli (e.g. light, gravity). Despite its importance, the underlying mechanism for twisting remains to be determined, partly because there is no rigorous method for quantifying the twisting of plant organs. Conventional studies have relied on approximate measurements of the twisting angle in 2D, with arbitrary choices of observation angle. Here, we present the first rigorous quantification of the 3D twisting angles of Arabidopsis petioles based on light sheet microscopy. Mathematical separation of bending and twisting with strict definition of petiole cross-sections were implemented; differences in the spatial distribution of bending and twisting were detected via the quantification of angles along the petiole. Based on the measured values, we discuss that minute degrees of differential growth can result in pronounced twisting in petioles.

Sign in / Sign up

Export Citation Format

Share Document