Notes on the Derivation of Sedimentation Equilibrium Equations

1994 ◽  
pp. 3-14 ◽  
Author(s):  
Hiroshi Fujita
Keyword(s):  
Sedimentation Equilibrium ◽  
Equilibrium Equations

Preparation and Properties of Human Prothrombin Complex

1970 ◽  
Vol 24 (03/04) ◽  
pp. 325-333 ◽  
Author(s):  
G. H Tishkoff ◽  
L. C Williams ◽  
D. M Brown
Keyword(s):  
Molecular Weight ◽  
Proteolytic Enzyme ◽  
Enzyme Inhibitor ◽  
Specific Activity ◽  
Crystalline Form ◽  
Sedimentation Equilibrium ◽  
Crystalline Complex ◽  
Interaction Product ◽  
Proteolytic Enzyme Inhibitor ◽  
Purification Scheme

SummaryAs a corollary to our previous studies with bovine prothrombin, we have initiated a study of human prothrombin complex. This product has been isolated in crystalline form as a barium glycoprotein interaction product. Product yields were reduced compared to bovine product due to the increased solubility of the barium glycoprotein interaction product. On occasion the crystalline complex exhibited good yields. The specific activity of the crystalline complex was 1851 Iowa u/mg. Further purification of human prothrombin complex was made by removal of barium and by chromatography on Sephadex G-100 gels. The final product evidenced multiple procoagulant activities (II, VII, IX and X). The monomeric molecular weight determined by sedimentation equilibrium in a solvent of 6 M guanidine-HCl and 0.5% mercaptoethanol was 70,191 ± 3,057 and was homogeneous with respect to molecular weight. This product was characterized in regard to physical constants and chemical composition. In general, the molecular properties of human prothrombin complex are very similar to the comparable bovine product. In some preparations a reversible proteolytic enzyme inhibitor (p-aminophenylarsonic acid) was employed in the ultrafiltration step of the purification scheme to inhibit protein degradation.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

Determination and prediction of the stress-strain state of pipeline, taking into account soil changes during operation

2020 ◽  
Vol 10 (4) ◽  
pp. 372-378
Author(s):  
Aydar К. Gumerov ◽  
◽  
Rinat M. Karimov ◽  
Robert М. Askarov ◽  
Khiramagomed Sh. Shamilov ◽  
...  
Keyword(s):  
Strain State ◽  
Mathematical Framework ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Optimal Method ◽  
Initial Stress State ◽  
Soil Response ◽  
Stress Strain State ◽  
Support Reaction ◽  
Key Factor

The key factor determining the strength, reliability, service life and fail-safe operation of the main pipeline is its stress-strain state. The purpose of this article is to develop a mathematical framework and methodology for calculating the stress-strain state of a pipeline section laid in complex geotechnical conditions, taking into account all planned and altitude changes and impacts at various points of operation, as well as during repair and after its completion. The mathematical framework is based on differential equations reflecting the equilibrium state of the pipeline, taking into account the features of the sections (configuration, size, initial stress state, acting forces, temperature conditions, interaction with soil, supports, and pipe layers). The equilibrium equations are drawn up in a curvilinear coordinate system – the same one that is used for in-pipe diagnostics. According to the results of the solution, all stress components are determined at each point both along the length of the pipeline and along the circumference of any section. At the same time, transverse and longitudinal forces, bending moments, shearing forces, pipeline displacements relative to the ground and soil response to displacements are determined. As an example, a solution is given using the developed mathematical framework. During the course of calculation, the places where the lower form of the pipe does not touch the ground and the places where the support reaction becomes higher than a predetermined limit are determined. A comparative analysis was accomplished, and the optimal method for section repair has been selected.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

scholarly journals Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment

2021 ◽  
Vol 43 (5) ◽  
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Thin Plate ◽  
Strain Gradient ◽  
Plate Theory ◽  
Laminated Composite ◽  
Equilibrium Equations ◽  
Thin Plate Theory ◽  
Bending Behavior ◽  
Hygrothermal Environment ◽  
Load Types ◽  
Novel Applications

AbstractIn this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory is based on the classical laminated thin plate theory with strain gradient effect to take into account the nonlocality present in the nanostructures. The equilibrium equations have been carried out by using the principle of virtual works and a system of partial differential equations of the sixth order has been carried out, in contrast to the classical thin plate theory system of the fourth order. The solution has been obtained using a trigonometric expansion (e.g., Navier method) which is applicable to simply supported boundary conditions and limited lamination schemes. The solution is exact for sinusoidal loads; nevertheless, convergence has to be proved for other load types such as the uniform one. Both the effect of the hygrothermal loads and lamination schemes (cross-ply and angle-ply nanoplates) on the bending behavior of thin nanoplates are studied. Results are reported in dimensionless form and validity of the present methodology has been proven, when possible, by comparing the results to the ones from the literature (available only for cross-ply laminates). Novel applications are shown both for cross- and angle-ply laminated which can be considered for further developments in the same topic.

scholarly journals Terpene polyacrylate TPA5 shows favorable molecular hydrodynamic properties as a potential bioinspired archaeological wood consolidant

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michelle Cutajar ◽  
Fabrizio Andriulo ◽  
Megan R. Thomsett ◽  
Jonathan C. Moore ◽  
Benoit Couturaud ◽  
...  
Keyword(s):  
Molar Mass ◽  
Analytical Ultracentrifugation ◽  
Gel Filtration ◽  
Axial Ratio ◽  
Sedimentation Equilibrium ◽  
Archaeological Wood ◽  
Molecular Hydrodynamic ◽  
Pine Trees ◽  
Minimal Concentration ◽  
Hydrogen Bonding Potential

AbstractThere is currently a pressing need for the development of novel bioinspired consolidants for waterlogged, archaeological wood. Bioinspired materials possess many advantages, such as biocompatibility and sustainability, which makes them ideal to use in this capacity. Based on this, a polyhydroxylated monomer was synthesised from α-pinene, a sustainable terpene feedstock derived from pine trees, and used to prepare a low molar mass polymer TPA5 through free radical polymerisation. This polymer was extensively characterised by NMR spectroscopy (chemical composition) and molecular hydrodynamics, primarily using analytical ultracentrifugation reinforced by gel filtration chromatography and viscometry, in order to investigate whether it would be suitable for wood consolidation purposes. Sedimentation equilibrium indicated a weight average molar mass Mw of (4.3 ± 0.2) kDa, with minimal concentration dependence. Further analysis with MULTISIG revealed a broad distribution of molar masses and this heterogeneity was further confirmed by sedimentation velocity. Conformation analyses with the Perrin P and viscosity increment ν universal hydrodynamic parameters indicated that the polymer had an elongated shape, with both factors giving consistent results and a consensus axial ratio of ~ 4.5. These collective properties—hydrogen bonding potential enhanced by an elongated shape, together with a small injectable molar mass—suggest this polymer is worthy of further consideration as a potential consolidant.

scholarly journals Dynamic Equilibrium Equations in Unified Mechanics Theory

2021 ◽  
Vol 2 (1) ◽  
pp. 63-80
Author(s):  
Noushad Bin Jamal Bin Jamal M ◽  
Hsiao Wei Lee ◽  
Chebolu Lakshmana Rao ◽  
Cemal Basaran
Keyword(s):  
Energy Loss ◽  
Entropy Generation ◽  
Equilibrium Equation ◽  
Dynamic Equilibrium ◽  
Free Vibration Analysis ◽  
Newtonian Mechanics ◽  
Equilibrium Equations ◽  
Time Coordinate ◽  
Proposed Model ◽  
Laws Of Thermodynamics

Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

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