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.

scholarly journals Augmented Reality Chemical Reaction with User-Centered Design

2018 ◽  
Vol 218 ◽  
pp. 04012
Author(s):  
Finsa Nurpandi ◽  
Agung Gumelar
Keyword(s):  
Augmented Reality ◽  
Chemical Reactions ◽  
Periodic Table ◽  
Three Dimensional ◽  
User Centered Design ◽  
Structure Of Molecules ◽  
Level Of Activity ◽  
Chemistry Learning ◽  
Chemical Concepts ◽  
User Centered

One of chemistry is the chemical element that is represented by the symbol on the periodic table. The low level of activity, interest, and the result of chemistry learning in school is caused by the students generally having difficulty in solving problems related to chemical reactions. In addition, most of the chemical concepts are abstract so it is difficult to imagine the structure of molecules clearly. Augmented Reality can integrate digital elements with the real world in real time and follow the circumstances surrounding environment. Augmented Reality can provide a new more interactive concept in the learning process because users can directly interact naturally. By using Augmented Reality, the atoms in the periodic table will be scanned using a camera from an Android-based smartphone that has installed this app. The scan results are then compared with existing data and will show the molecular structure in three-dimensional form. Users can also observe reactions between atoms by combining multiple markers simultaneously. Augmented Reality application is built using the concept of user-centered design and Unity with personal license as development tools. By using this app, studying chemical reactions no longer requires a variety of chemicals that could be harmful to users.

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.

Electrical turbulence in three-dimensional heart muscle

Science ◽  
1994 ◽  
Vol 266 (5187) ◽  
pp. 1003-1006 ◽  
Author(s):  
A. Winfree
Keyword(s):  
Heart Muscle ◽  
Three Dimensional

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.

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