Dispersion of a solute in a fully developed laminar tube flow

1970 ◽  
Vol 317 (1528) ◽  
pp. 91-99 ◽  
Keyword(s):  
Initial Conditions ◽  
Experimental Studies ◽  
Local Concentration ◽  
Eigenvalues And Eigenvectors ◽  
Transient Dispersion ◽  
The Matrix ◽  
Method Of Solution ◽  
Laminar Tube Flow ◽  
Diffusion Convection ◽  
Mean Concentration

The diffusion-convection equation, which is used to model the transient dispersion of a solute in a circular tube, has been solved by the linear combination of the eigenvalues and eigenvectors of the matrix form of the equation. The solution, which is valid for all time, gives the local concentration as well as the integrated mean concentration. The results compare well with other analytical and experimental studies in the region of common validity. Comparisons with numerical results show small discrepancies. The method of solution may be applied to similar problems with different boundary and initial conditions.

scholarly journals Indirect Reconstruction of Structural Responses Based on Transmissibility Concept and Matrix Regularization

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Chudong Pan ◽  
Liwen Zhang ◽  
Zhuo Sun
Keyword(s):  
Initial Conditions ◽  
Time Windows ◽  
Experimental Studies ◽  
Physical Sensors ◽  
Norm Values ◽  
The Matrix ◽  
Structural Responses ◽  
Novel Method ◽  
Matrix Regularization ◽  
Critical Locations

A novel method is proposed based on the transmissibility concept and matrix regularization for indirectly measuring the structural responses. The inputs are some measured responses that are obtained via physical sensors. The outputs are the structural responses corresponding to some critical locations where no physical sensors are installed. Firstly, the transmissibility concept is introduced for expressing the relationship between the measured responses and the indirectly measured ones. Herein, a transmissibility matrix is formulated according to the theory of force identification under unknown initial conditions. Then, in order to reduce the size of the transmissibility matrix, structural responses are reshaped in a form of a matrix by using the concept of moving time windows. According to the matrix form of input-output relationship, indirect reconstruction of responses is boiled down to an optimization equation. Since inverse problem may be ill-conditioned, matrix regularization such as F-norm regularization is then recommended for improving the optimization problem. Herein, the penalty function is defined by using a weighted sum of two F-norm values, which correspond to the estimated responses of physical sensors and the ones of the concerned critical locations, respectively. Numerical simulations and experimental studies are finally carried out for verifying the effectiveness and feasibility of the proposed method. Some results show that the proposed method can be applied for indirectly measuring the responses with good robustness.

On Laminar Dispersion for Flow Through Round Tubes

1979 ◽  
Vol 46 (4) ◽  
pp. 750-756 ◽  
Author(s):  
J. S. Yu
Keyword(s):  
Peclet Number ◽  
Molecular Diffusion ◽  
Initial Conditions ◽  
Local Concentration ◽  
Axial Distance ◽  
Dimensionless Time ◽  
Axially Symmetric ◽  
Péclet Number ◽  
Average Flow Velocity ◽  
Diffusion Convection

A general method for the solution of the axially symmetric transient diffusion-convection equation for laminar dispersion in round tubes subject to arbitrary square-integrable initial conditions is analytically developed. The solution representing the local concentration is expressed by a series in terms of the zeroth-order Bessel function, and the order of approximation (equal to the number of terms in the series) required at a given value of the dimensionless time τ for flow with a specified Peclet number Pe is clearly established. It is shown that the approximation used by Gill, et al. [5–8], is a special case of the present analysis under certain conditional assumptions. For the case of fundamental interest with an initial input concentrated at a section of the tube, the mean concentration as a function of the axial distance measured from the origin of a coordinate moving with the average flow velocity determined by the present method at given values of the Peclet number and the dimensionless time is compared with those by Taylor [1], Lighthill [4], Chatwin [9], Gill, et al. [7], and Hunt [23]. The comparison of the concentration profiles shows that Lighthill’s solution is perhaps valid as τ → 0, Hunt’s solution obtained by first-order perturbation approximation yields too large a dispersion by molecular diffusion even at small times, and the other solutions are asymptotically correct at large values of time for flow with high Peclet numbers.

Computational studies of the mitochondrial carrier family SLC25. Present status and future perspectives

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrea Pasquadibisceglie ◽  
Fabio Polticelli
Keyword(s):  
Transport Mechanism ◽  
Experimental Studies ◽  
Intermembrane Space ◽  
Mitochondrial Carrier ◽  
Mitochondrial Homeostasis ◽  
The Matrix ◽  
Mitochondrial Carrier Family ◽  
Mitochondrial Intermembrane Space ◽  
Computational Analyses

Abstract The members of the mitochondrial carrier family, also known as solute carrier family 25 (SLC25), are transmembrane proteins involved in the translocation of a plethora of small molecules between the mitochondrial intermembrane space and the matrix. These transporters are characterized by three homologous domains structure and a transport mechanism that involves the transition between different conformations. Mutations in regions critical for these transporters’ function often cause several diseases, given the crucial role of these proteins in the mitochondrial homeostasis. Experimental studies can be problematic in the case of membrane proteins, in particular concerning the characterization of the structure–function relationships. For this reason, computational methods are often applied in order to develop new hypotheses or to support/explain experimental evidence. Here the computational analyses carried out on the SLC25 members are reviewed, describing the main techniques used and the outcome in terms of improved knowledge of the transport mechanism. Potential future applications on this protein family of more recent and advanced in silico methods are also suggested.

scholarly journals Theoretical and experimental studies of a gas stamping device with a piston pressure multiplier

2019 ◽  
Vol 18 (1) ◽  
pp. 163-173
Author(s):  
A. Yu. Botashev ◽  
R. A. Bayramukov
Keyword(s):  
Theoretical Analysis ◽  
Experimental Studies ◽  
Fuel Mixture ◽  
Small Scale ◽  
Scale Production ◽  
Pressure Treatment ◽  
Energy Of Combustion ◽  
Stamping Process ◽  
Pressure Multiplier ◽  
The Matrix

In many industries, the share of small-scale production plants is significant. In these conditions, compared with traditional methods of pressure treatment, pulse pressure treatment methods, one of the varieties of which is gas stamping, are more efficient. However, the known devices of gas stamping provide mainly stamping of thin-walled parts. To expand the technological capabilities of gas stamping, the authors developed a gas stamping device with a piston pressure multiplier, in which heating and deformation of the stamping workpiece is carried out using the energy of combustion of fuel mixtures in the combustion chamber, in the working cylinder and in the cavity of the matrix. This article is devoted to the study of the workflow of this device. Theoretical analysis of the workflow was carried out, and, as a result, a pattern was determined for the variation of the pressure that performs the stamping process in the working cylinder. In particular, it was found that at the final stage of the stamping process, due to the energy of combustion of the fuel mixture, the pressure in the working cylinder increases 1.5...2 times, which allows a significant increase in the thickness of the parts to be stamped. An experimental gas stamping device with a piston pressure multiplier was developed, and experimental studies were carried out. The studies confirmed the main results of the theoretical analysis: the discrepancy between the theoretical and experimental values of the degree of pressure multiplication in the working cylinder does not exceed 11%.

Micromechanical Analysis of Nonlinear Response of Unidirectional Composites: A Fundamental Approach

2001 ◽  
Author(s):  
Virendra R. Jadhav ◽  
Srinivasan Sridharan
Keyword(s):  
Mechanical Model ◽  
Nonlinear Response ◽  
Experimental Studies ◽  
Matrix Cracking ◽  
Type Model ◽  
Unidirectional Composites ◽  
The Matrix ◽  
Experimental Response ◽  
Square Cells ◽  
Experimental Comparisons

Abstract Micromechanical models with different representative volume elements have been developed to study their ability to predict nonlinear response of unidirectional composites. A simple, square cells type micro-mechanical model similar to those widely used by other researchers is compared with a more advanced 3-phase finite element based micro-mechanical model. The models utilize the “bulk” properties of the matrix without attempting to “tune” the model to fit with experimental response of laminae. This is a more fundamental approach and constitutes a departure from current practice. The models account for shear softening, matrix cracking and the presence of residual stresses. A smeared cracking approach was used to characterize the micro-cracking in matrix. Experimental studies were performed on laminae, laminates and cylinders made from carbon epoxy composites. Experimental comparisons show that the more accurate micro-mechanical model with proper partial cracking options provides good bounds on experimental response with consistent accuracy. A square cells type model however is not consistent in its predictions, thus raising questions about its applicability in any general micro-mechanics based analysis.

Entrainment and growth of vortical disturbances in the channel-entrance region

2021 ◽  
Vol 927 ◽  
Author(s):  
Pierre Ricco ◽  
Claudia Alvarenga
Keyword(s):  
Initial Conditions ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Analytical Description ◽  
Reynolds Numbers ◽  
Boundary Region ◽  
Shear Layers ◽  
Base Flow ◽  
Open Boundary ◽  
Classical Stability

The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.

scholarly journals Symmetries of the quaternionic Ginibre ensemble

2020 ◽  
Vol 10 (01) ◽  
pp. 2150013 ◽  
Author(s):  
Guillaume Dubach
Keyword(s):  
Radial Symmetry ◽  
Complex Case ◽  
Proof Technique ◽  
Eigenvalues And Eigenvectors ◽  
Unitary Matrices ◽  
Ginibre Ensemble ◽  
The Matrix ◽  
De Bruijn ◽  
Gaussian Case

We establish a few properties of eigenvalues and eigenvectors of the quaternionic Ginibre ensemble (QGE), analogous to what is known in the complex Ginibre case (see [7, 11, 14]). We first recover a version of Kostlan’s theorem that was already at the heart of an argument by Rider [1], namely, that the set of the squared radii of the eigenvalues is distributed as a set of independent gamma variables. Our proof technique uses the De Bruijn identity and properties of Pfaffians; it also allows to prove that the high powers of these eigenvalues are independent. These results extend to any potential beyond the Gaussian case, as long as radial symmetry holds; this includes for instance truncations of quaternionic unitary matrices, products of quaternionic Ginibre matrices, and the quaternionic spherical ensemble. We then study the eigenvectors of quaternionic Ginibre matrices. Angles between eigenvectors and the matrix of overlaps both exhibit some specific features that can be compared to the complex case. In particular, we compute the distribution and the limit of the diagonal overlap associated to an eigenvalue that is conditioned to be at the origin. This complements a recent study of overlaps in quaternionic ensembles by Akemann, Förster and Kieburg [1, 2].

COEXISTENCE OF LOW- AND HIGH-DIMENSIONAL SPATIOTEMPORAL CHAOS IN A CHAIN OF DISSIPATIVELY COUPLED CHUA’S CIRCUITS

1994 ◽  
Vol 04 (03) ◽  
pp. 639-674 ◽  
Author(s):  
A.L. ZHELEZNYAK ◽  
L.O. CHUA
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
Spatiotemporal Chaos ◽  
Matrix Phase ◽  
High Dimensional ◽  
The Matrix ◽  
A Chain

Spatiotemporal dynamics of a one-dimensional cellular neural network (CNN) made of Chua’s circuits which mimics a reaction-diffusion medium is considered. An approach is presented to analyse the properties of this reaction-diffusion CNN through the characteristics of the attractors of an associated infinite-dimensional dynamical system with a matrix phase space. Using this approach, the spatiotemporal correlation dimension of the CNN’s spatiotemporal patterns is computed over various ranges of the diffusion coupling parameter, length of the chain, and initial conditions. It is shown that in a finite-dimensional projection of the matrix phase space of the CNN, both low- and high-dimensional attractors corresponding to different initial conditions coexist.

The Effect of Nearfield Constraints on the Corrosion Behavior of High Burnup Spent Fuel

2006 ◽  
Vol 932 ◽  
Author(s):  
Andreas Loida ◽  
Manfred Kelm ◽  
Bernhard Kienzler ◽  
Horst Geckeis ◽  
Andreas Bauer
Keyword(s):  
Host Rock ◽  
Near Field ◽  
Experimental Studies ◽  
Spent Fuel ◽  
Mutual Support ◽  
Significant Extent ◽  
Dissolution Rates ◽  
The Matrix ◽  
Container Material

ABSTRACTThe long-term immobilization for individual radioelements released from the waste form “spent fuel” in solid phases upon groundwater contact depends strongly on the (geo)chemical constraints prevailing in the repository. Related experimental studies comprise effects induced by the presence of Fe based container material, and near field materials other than Fe for a rock salt environment. The effect of the presence of an argillaceous host rock containing organic matter and pyrite on fuel alteration was studied in addition. The results have shown that oxidative radio-lysis products were found to be consumed at a significant extent by the metallic Fe and by the argillaceous host rock. Under these conditions a decrease at a factor of ca.100 for both the matrix dissolution rates and the solution concentrations of U and Pu was found. There is mutual support between the matrix dissolution rates, the solution concentrations and the amounts of oxygen encountered during the experiments under various conditions controlled by the presence of near field materials under study.

On a Numerical Method for Solution of the Mathieu-Hill Type Equations

1980 ◽  
Vol 102 (3) ◽  
pp. 619-626 ◽  
Author(s):  
A. Midha ◽  
M. L. Badlani
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Initial Conditions ◽  
Linear Equations ◽  
Solution Process ◽  
Constraint Equations ◽  
Step Functions ◽  
The Matrix ◽  
Constant Coefficients ◽  
Simultaneous Linear Equations

This paper presents a computer-programmable numerical method for the solution of a class of linear, second order differential equations with periodic coefficients of the Mathieu-Hill type. The method is applicable only when the initial conditions are prescribed and the solution is not requiried to be periodic. The solution is facilitated by representing the coefficient functions as a sum of step functions over corresponding sub-intervals of the fundamental interval. During each sub-interval, the solution form is assumed to be that of the differential equations with “constant” coefficients. Constraint equations are derived from imposing the conditions of “compatibility” of response at the end nodes of the intermediate sub-intervals. This set of simultaneous linear equations is expressed in matrix form. The matrix of coefficients may be represented as a triangular one. This form greatly simplifies the solution process for simultaneous equations. The method is illustrated by its application to some specific problems.

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