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Addenda and Erratum to: Characteristic directions of closed planar motions
No full textIn a previous paper [2], some properties of closed planar motions were investigated. The focus was on three aspects: the area enclosed by the paths of points, the polar moment of inertia and the natural average of a path. These three mathematical objects were shown to be interrelated. For reasons of completeness, we now add some historical references which relate the problem considered to that of mechanical integrators eg. polarplanimeter. In this communication, we introduce a fourth related entity, which is analogous to the action in theoretical mechanics. The relationship of action to the entities discussed in our previous article is given by a spatial invariant. Then, we add some properties of the double hinge, in order to clarify the example given in the previous paper. Finally, we correct a sign error which appeared in [2]. In the Appendix (see Supplementary Material, Wiley online library), we present a general construction for spatial invariants. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei
Characteristic directions of closed planar motions
No full textWe investigate some properties of closed planar motions. These motions appear between two coordinate systems, fixed and moving. We focus on three aspects: The area enclosed by the paths of points belonging to each of these reference systems, the polar moment of inertia, and the natural average of a path. First, we consider a formula proposed by Jakob Steiner. It states that, for a motion with a complete turn, the points enclosing the same area lie on a circle. Moreover, all circles for different areas have a common center. We start by deriving the Steiner formula relative to both frames. We emphasize that, for practical applications such as in biomechanics, the Steiner circle reduces to a straight line. Then, the centrodes are considered in relation to the Steiner point or normal. We next consider the polar moment of inertia. Its coefficients are shown to be related to those of the Steiner point or normal. Thirdly, the natural average of a path is introduced. Its coefficients are shown to be related to those previously discussed. Finally, we show how the results can be applied to experimentally measured motions. As an example, we consider human gait in the sagittal direction. The most important part of this motion is described as a double hinge driven by the hip and knee angle, which is a simple model for a planar motion. We conclude that, for practical purposes, the Steiner line allows us to visualize a selected direction of motion under consideration
A functional renormalization group approach to non-equilibrium properties of mesoscopic interacting quantum systems
No full textWe present an extension of the concepts of the functional renormalization group approach to quantum many-body problems in non-equilibrium situations. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations. We discuss the influence of finite bias voltage and temperature on the current and conductance. (C) 2009 Elsevier B.V. All rights reserved
Effect of apple, baobab, red-chicory, and pear extracts on cellular energy expenditure and morphology of a Caco-2 cells using transepithelial electrical resistance (TEER) and scanning electron microscopy (SEM)
No full textThe present study investigated the effects of four food extracts on the Caco-2 intestinal cell line using a new transepithelial electrical resistance method (TEER) concurrent with electron microscopy (SEM). Caco-2 cells are widely used in transepithelial studies because they can be cultured to create a selective permeable interface similar to that between the intestinal lumen and the basolateral tissue. These cells absorb, secrete, and function as a barrier that limits the passive transepithelial diffusion of hydrophilic solutes from the digestive tract into the circulation. The intercellular tight junctions provide a limiting barrier to the movement of the solutes through the paracellular route. The integrity of this tissue must be maintained when studying cellular physiology. TEER provides useful information on cellular function when a tissue in chemical equilibrium is perturbed by an external compound (such as nutrient, drug, pathogenic microorganism or toxins). In order to restore this equilibrium, the cells need to expend energy that can be calculated through a mathematical TEER value. The change in energy from the equilibrium value depends on the time elapsed and the nature and concentration of the test substance. The results show that extracts of four commercial foods (with the total phenolic content shown in mg g(-1) gallic acid equivalents) - apples (3.39), baobab (130), red chicory (13.31), and pears (1.15) induced concentration-dependent changes in both the energy and histology (morphology) of the cells as well as the formation of mucopolysaccharide. These changes, reported graphically and mathematically, were altered in the presence of the free radical (oxidant) 2,2'-azobis (2-amidinepropane) dihydrochloride (AAPH). At highest concentration, measured, the food extract with the highest phenolic content (baobab) completely damage the cells. The new simple in vitro TEER assay offers a novel approach to investigate the influence of nutrients, antinutrients, food toxicants, and drugs on the physiology and morphology of the Caco-2 cells that may predict their behavior in the digestive tract
Functional renormalization group for nonequilibrium quantum many-body problems
No full textWe extend the concept of the functional renormalization for quantum many-body problems to nonequilibrium situations. Using a suitable generating functional based on the Keldysh approach, we derive a system of coupled differential equations for the m-particle vertex functions. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations at finite bias voltage employing two different truncation schemes for the infinite hierarchy of equations arising in the functional renormalization group scheme
Non-equilibrium properties of mesoscopic systems - functional renormalization group approach
No full textUsing the Keldysh technique for non-equilibrium interacting many-particle systems, the concept of the functional renormalization is extended to non-equilibrium situations. The approach is completely general and thus allows calculations for both stationary and time-dependent situations. As a specific example we present results for the stationary state transport through a quantum dot with finite bias voltage. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Variational cluster approach to superconductivity and magnetism in the Kondo lattice model
No full textThe description of the human knee as four-bar linkage
No full textPurpose: We investigate the dependence of the kinematics of the human knee on its anatomy. The idea of describing the kinematics of the knee in the sagittal plane using four-bar linkage is almost as old as kinematics as an independent discipline. We start with a comparison of known four-bar linkage constructions. We then focus on the model by H. Nagerl which is applicable under form closure. Methods: We use geometry and analysis as the mathematical methods. The relevant geometrical parameters of the knee will be determined on the basis of the dimensions of the four-bar linkage. This leads to a system of nonlinear equations. Results: The four-bar linkage will be calculated from the limits of the constructively accessible parameters by means of a quadratic approximation. Conclusions: By adapting these requirements to the dimensions of the human knee, it will be possible to obtain valuable indications for the design of an endoprosthesis which imitates the kinematics of the natural knee
Mathematical study on the guidance of the tibiofemoral joint as theoretical background for total knee replacements
No full textThe mathematical approach presented allows main features of kinematics and force transfer in the loaded natural tibiofemoral joint (TFJ) or in loaded knee endoprostheses with asymmetric condyles to be deduced from the spatial curvature morphology of the articulating surfaces. The mathematical considerations provide the theoretical background for the development of total knee replacements (TKR) which closely reproduce biomechanical features of the natural TFJ. The model demonstrates that in flexion/extension such kinematic features as centrodes or slip ratios can be implemented in distinct curvature designs of the contact trajectories in such a way that they conform to the kinematics of the natural TFJ in close approximation. Especially the natural roll back in the stance phase during gait can be reproduced. Any external compressive force system, applied to the TFJ or the TKR, produces two joint reaction forces which - when applying screw theory - represent a force wrench. It consists of a force featuring a distinct spatial location of its line and a torque parallel to it. The dependence of the geometrical configuration of the force wrench on flexion angle, lateral/medial distribution of the joint forces, and design of the slopes of the tuberculum intercondylare is calculated. The mathematical considerations give strong hints about TKR design and show how main biomechanical features of the natural TFJ can be reproduced
Mathematical study on the guidance of the tibiofemoral joint as theoretical background for total knee replacements
No full textThe mathematical approach presented allows main features of kinematics and force transfer in the loaded natural tibiofemoral joint (TFJ) or in loaded knee endoprostheses with asymmetric condyles to be deduced from the spatial curvature morphology of the articulating surfaces. The mathematical considerations provide the theoretical background for the development of total knee replacements (TKR) which closely reproduce biomechanical features of the natural TFJ. The model demonstrates that in flexion/extension such kinematic features as centrodes or slip ratios can be implemented in distinct curvature designs of the contact trajectories in such a way that they conform to the kinematics of the natural TFJ in close approximation. Especially the natural roll back in the stance phase during gait can be reproduced. Any external compressive force system, applied to the TFJ or the TKR, produces two joint reaction forces which - when applying screw theory - represent a force wrench. It consists of a force featuring a distinct spatial location of its line and a torque parallel to it. The dependence of the geometrical configuration of the force wrench on flexion angle, lateral/medial distribution of the joint forces, and design of the slopes of the tuberculum intercondylare is calculated. The mathematical considerations give strong hints about TKR design and show how main biomechanical features of the natural TFJ can be reproduced
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