Mathematical Models of Placement Optimisation: Two- and Three-Dimensional Problems and Applications

2012 ◽  
pp. 363-388 ◽  
Author(s):  
Yuri Stoyan ◽  
Tatiana Romanova
Keyword(s):  
Mathematical Models ◽  
Three Dimensional

scholarly journals Robot Modeling for Physical Rehabilitation

Robotics ◽  
2013 ◽  
pp. 1212-1232 ◽  
Author(s):  
Rogério Sales Gonçalves ◽  
João Carlos Mendes Carvalho
Keyword(s):  
Mathematical Models ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Industrial Robots ◽  
Limb Movements ◽  
Rehabilitation Robots ◽  
Wide Range ◽  
Movable Platform ◽  
Human Limb ◽  
Robot Modeling

The science of rehabilitation shows that repeated movements of human limbs can help the patient regain function in the injured limb. There are three types of mechanical systems used for movement rehabilitation: robots, cable-based manipulators, and exoskeletons. Industrial robots can be used because they provide a three-dimensional workspace with a wide range of flexibility to execute different trajectories, which are useful for motion rehabilitation. The cable-based manipulators consist of a movable platform and a base, which are connected by multiple cables that can extend or retract. The exoskeleton is fixed around the patient's limb to provide the physiotherapy movements. This chapter presents a summary of the principal human limb movements, a review of several mechanical systems used for rehabilitation, as well as common mathematical models of such systems.

Three-Dimensional Dynamic Modeling of the Human Knee to Include Tibio-Femoral and Patello-Femoral Joints

2001 ◽  
Author(s):  
Dumitru Caruntu ◽  
Mohamed Samir Hefzy
Keyword(s):  
Knee Joint ◽  
Mathematical Models ◽  
Dynamic Modeling ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Human Knee ◽  
Two Dimensional Model ◽  
Rigid Contact ◽  
Locomotor Activities

Abstract Most of the anatomical mathematical models that have been developed to study the human knee are either for the tibio-femoral joint (TFJ) or patello-femoral joint (PFJ). Also, most of these models are static or quasistatic, and therefore do not predict the effects of dynamic inertial loads, which occur in many locomotor activities. The only dynamic anatomical model that includes both joints is a two-dimensional model by Tumer and Engin [1]. The model by Abdel-Rahman and Hefzy [2] is the only three dimensional dynamic model for the knee joint available in the literature; yet, it includes only the TFJ and allows only for rigid contact.

scholarly journals On the correctness of mathematical models of time-of-flight cathodoluminescence of direct-gap semiconductors

2019 ◽  
Vol 30 ◽  
pp. 07014
Author(s):  
Mikhail A. Stepovich ◽  
Dmitry V. Turtin ◽  
Elena V. Seregina ◽  
Veronika V. Kalmanovich
Keyword(s):  
Electron Beam ◽  
Gallium Nitride ◽  
Initial Data ◽  
Mathematical Models ◽  
Single Crystal ◽  
Three Dimensional ◽  
Time Of Flight ◽  
Semiconductor Material ◽  
Two Dimensional ◽  
Cathodoluminescence Intensity

Two-dimensional and three-dimensional mathematical models of diffusion and cathodoluminescence of excitons in single-crystal gallium nitride excited by a pulsating sharply focused electron beam in a homogeneous semiconductor material are compared. The correctness of these models has been carried out, estimates have been obtained to evaluate the effect of errors in the initial data on the distribution of the diffusing excitons and the cathodoluminescence intensity.

scholarly journals Analysis of spatial thermal field in a magnetic bearing

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 52-56
Author(s):  
Dawid Wajnert ◽  
Bronisław Tomczuk
Keyword(s):  
Temperature Field ◽  
Mathematical Models ◽  
Computer Simulations ◽  
Thermal Field ◽  
Three Dimensional ◽  
Magnetic Bearing ◽  
Field Analysis ◽  
Two Dimensional ◽  
Temperature Distributions ◽  
Dimensional Simulation

AbstractThis paper presents two mathematical models for temperature field analysis in a new hybrid magnetic bearing. Temperature distributions have been calculated using a three dimensional simulation and a two dimensional one. A physical model for temperature testing in the magnetic bearing has been developed. Some results obtained from computer simulations were compared with measurements.

Vortices in Motionless Media

1990 ◽  
Vol 43 (12) ◽  
pp. 297-309 ◽  
Author(s):  
A. T. Winfree
Keyword(s):  
Mathematical Models ◽  
Chemical Reactions ◽  
Heart Muscle ◽  
Local Reaction ◽  
Three Dimensional ◽  
Vortex Filament ◽  
Local Geometry ◽  
Lateral Motion ◽  
Local Activation ◽  
Vortex Lines

Three-dimensional continua capable of recurrent local activation are observed—both in the laboratory and in mathematical models—to support persistent self-organizing patterns of activity most conveniently described in terms of vortex lines. These lines generally close in rings, which may be linked and knotted. In some cases they adopt stable configurations resembling tiny dynamos of millimeter dimensions. The dynamics of these “organizing centers” has been investigated in certain chemical reactions, in heart muscle, and numerically in digital computers. The pertinent mathematical principles appear to entail consequences of local reaction and neighborhood diffusion, in the form of a dependency of the vortex filament’s lateral motion upon its local geometry and, when too closely approached by another segment of vortex filament, upon the distance and orientation involved.

Illustrating Mathematical Connections: Two Proofs That Only Five Regular Polyhedra Exist

1993 ◽  
Vol 86 (8) ◽  
pp. 657-661
Author(s):  
Peter L. Glidden ◽  
Erin K. Fry
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Mathematics Curriculum ◽  
Three Dimensional ◽  
Discrete Mathematics ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Regular Polyhedra ◽  
Real World Problems

The reforms proposed in the NCTM's Curriculum and Evaluation Standards (1989) call for specific changes in the grades 9-12 mathematics curriculum, as well as for general themes that should be emphasized throughout the curriculum. In particular, the standards document calls for including topics from discrete mathematics and three-dimensional geometry, and it calls for increased emphasis on paragraph-style proofs. Overall, these and other topics should be taught with the ultimate goals of illustrating mathematical connections and constructing mathematical models to solve real-world problems.

Tumor Volumes in Choroidal Melanoma: Agreement Between Three-Dimensional Ultrasound and Two Mathematical Models

2016 ◽  
Vol 166 ◽  
pp. 181-188 ◽  
Author(s):  
Josep M. Caminal ◽  
Karol Mejía ◽  
Luis Arias ◽  
Cristina Masuet-Aumatell ◽  
Jon Larrucea-Maseda ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Three Dimensional ◽  
Choroidal Melanoma

scholarly journals Influence of the Moment in Mathematical Models for Open Systems

2021 ◽  
Vol 16 ◽  
pp. 250-260
Author(s):  
Evelina Prozorova
Keyword(s):  
Mathematical Models ◽  
Stress Tensor ◽  
Open Systems ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Collective Effects ◽  
Physical Parameters ◽  
Potential Flows ◽  
The Moment ◽  
Definition Of

Article is proposed, built taking into account the influence of the angular momentum (force) in mathematical models of open mechanics. The speeds of various processes at the time of writing the equations were relatively small compared to modern ones. Theories have generally been developed for closed systems. As a result, in continuum mechanics, the theory developed for potential flows was expanded on flows with significant gradients of physical parameters without taking into account the combined action of force and moment. The paper substantiates the vector definition of pressure and the no symmetry of the stress tensor based on consideration of potential flows and on the basis of kinetic theory. It is proved that for structureless particles the symmetry condition for the stress tensor is one of the possible conditions for closing the system of equations. The influence of the moment is also traced in the formation of fluctuations in a liquid and in a plasma in the study of Brownian motion, Landau damping, and in the formation of nanostructures. The nature of some effects in nanostructures is discussed. The action of the moment leads to three-dimensional effects even for initially flat structures. It is confirmed that the action of the moment of force is the main source of the collective effects observed in nature. Examples of solving problems of the theory of elasticity are given.

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