scholarly journals Spin Waves in Two and Three Dimensional Magnetic Materials

2015 ◽  
Vol 49 ◽  
pp. 35-47 ◽  
Author(s):  
H.S. Wijesinhe ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Spin Waves ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Second Order ◽  
Three Dimensions ◽  
Operator Representation ◽  
Computer Based ◽  
Canonical Ensembles

The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.

scholarly journals Spin Waves in One Dimensional Magnetic Material

2015 ◽  
Vol 47 ◽  
pp. 24-39
Author(s):  
H.S. Wijesinhe ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Spin Wave ◽  
Numerical Solutions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Spin Waves ◽  
Dynamic Structure ◽  
Three Dimensions ◽  
Spin Interaction ◽  
Operator Representation ◽  
One Dimensional

Using Heisenberg model, the equations of motion for the dynamic properties of spin waves in three dimensions were obtained and solved analytically up to an exponential operator representation. Second order Suzuki Trotter decomposition method with evolution operator solution was applied to obtain the numerical solutions by making it closer to real spin systems. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for one dimensional lattice by investigating the occurrence, temperature dependence and spin-spin interaction dependence of the spin waves. A visualization technique was used to show the existence of many spin wave components below the Curie temperature of the system. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor. Energy conservation of the algorithm is also shown.

The Brain Stem Saccadic Burst Generator Encodes Gaze in Three-Dimensional Space

2008 ◽  
Vol 99 (5) ◽  
pp. 2602-2616 ◽  
Author(s):  
Marion R. Van Horn ◽  
Pierre A. Sylvestre ◽  
Kathleen E. Cullen
Keyword(s):  
Eye Movements ◽  
Brain Stem ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Saccadic Eye Movements ◽  
Three Dimensions ◽  
Related Information ◽  
Computer Based ◽  
Different Depths ◽  
The Brain

When we look between objects located at different depths the horizontal movement of each eye is different from that of the other, yet temporally synchronized. Traditionally, a vergence-specific neuronal subsystem, independent from other oculomotor subsystems, has been thought to generate all eye movements in depth. However, recent studies have challenged this view by unmasking interactions between vergence and saccadic eye movements during disconjugate saccades. Here, we combined experimental and modeling approaches to address whether the premotor command to generate disconjugate saccades originates exclusively in “vergence centers.” We found that the brain stem burst generator, which is commonly assumed to drive only the conjugate component of eye movements, carries substantial vergence-related information during disconjugate saccades. Notably, facilitated vergence velocities during disconjugate saccades were synchronized with the burst onset of excitatory and inhibitory brain stem saccadic burst neurons (SBNs). Furthermore, the time-varying discharge properties of the majority of SBNs (>70%) preferentially encoded the dynamics of an individual eye during disconjugate saccades. When these experimental results were implemented into a computer-based simulation, to further evaluate the contribution of the saccadic burst generator in generating disconjugate saccades, we found that it carries all the vergence drive that is necessary to shape the activity of the abducens motoneurons to which it projects. Taken together, our results provide evidence that the premotor commands from the brain stem saccadic circuitry, to the target motoneurons, are sufficient to ensure the accurate control shifts of gaze in three dimensions.

scholarly journals Re-Evaluating the Classical Falling Body Problem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 553 ◽  
Author(s):  
Essam R. El-Zahar ◽  
Abdelhalim Ebaid ◽  
Abdulrahman F. Aljohani ◽  
José Tenreiro Machado ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Inertial Frame ◽  
Analytic Solution ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Rotating Frame ◽  
Dimensional Model ◽  
Three Dimensional Model

This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.

High Velocity Impact Calculations in Three Dimensions

1977 ◽  
Vol 44 (1) ◽  
pp. 95-100 ◽  
Author(s):  
G. R. Johnson
Keyword(s):  
High Velocity ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Material Strength ◽  
Large Strains ◽  
Strain Rates ◽  
High Velocity Impact ◽  
Velocity Impact ◽  
Elastic Stresses

A three-dimensional analysis is presented for high velocity impact problems. A Lagrangian finite-element technique is formulated for tetrahedron elements subjected to large strains and displacements. The effects of material strength and compressibility are included to account for elastic-plastic flow and wave propagation. The strains and strain rates in each element are determined from the displacements and velocities of the nodes. The strains, strain rates, and material properties are used to determine the elastic stresses, plastic deviator stresses, hydrostatic pressure, and artificial viscosity. The stresses are equated to concentrated forces acting on concentrated masses at the nodes, and the nodal equations of motion are numerically integrated. Illustrative examples are also included.

scholarly journals Vibration Isolation: Use and Characterization

1980 ◽  
Vol 53 (5) ◽  
pp. 1041-1087 ◽  
Author(s):  
J. C. Snowdon
Keyword(s):  
Vibration Isolation ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Second Order ◽  
Two Stage ◽  
General Terms ◽  
Pole Parameter ◽  
Wave Effects ◽  
Compressive Loads ◽  
Rubberlike Materials

Abstract This article is concerned with vibration isolation, with antivibration mountings (resilient isolators), and with the static and dynamic properties of rubberlike materials that are suited for use in antivibration mountings. The design of practical antivibration mounts incorporating rubber or coiled-steel springs is described in Refs. 1–27; pneumatic isolators (air mounts, etc.) are described in Refs. 5, 28–35. Throughout the literature, as here, attention is focussed predominantly on the translational (vertical) effectiveness of antivibration mountings. However, the two- and three-dimensional vibration of one- or two-stage mounting systems is addressed in Refs. 4, 10, 12, 36–56. Following a description of the static and dynamic properties of rubberlike materials, the performance of the simple or one-stage mounting system is analyzed, account being taken of the occurrence of second-order resonances in the isolator and in the mounted item. In the latter case, as likely in practice, the bulk of the mounted item is assumed to remain masslike, whereas the feet of the item are assumed to be nonrigid (multiresonant). Discussion is then given to the two-stage or compound mounting system, which affords superior vibration isolation at high frequencies. Subsequently, the powerful four-pole parameter technique is employed to analyze, in general terms, the performance of an antivibration mounting with second-order resonances (wave effects) when both the foundation that supports the mounting system and the machine are nonrigid. The universally adopted method of measuring mount transmissibility is then described, followed by an explanation of how transmissibility can also be determined by four-pole parameter techniques based on an apparatus used by Schloss. The four-pole measurement approach has not been exploited hitherto, but it is apparently feasible and valuable because it enables mounts to be tested under compressive loads equal to those routinely encountered in service.

scholarly journals Simulation of angiogenesis in three dimensions: Application to cerebral cortex

2021 ◽  
Vol 17 (6) ◽  
pp. e1009164
Author(s):  
Jonathan P. Alberding ◽  
Timothy W. Secomb
Keyword(s):  
Cerebral Cortex ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Three Dimensions ◽  
Vascular Response ◽  
Biological Responses ◽  
Dimensional Network ◽  
Partial Pressures ◽  
Essential Components ◽  
Mouse Cerebral Cortex

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

Spray Car Workbench Racks of Modal Analysis

2015 ◽  
Vol 1094 ◽  
pp. 469-474
Author(s):  
Yu Jing He ◽  
Jiang Feng Shen ◽  
Xiang Fu Li
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Support Frame

The author designed a intelligential spray car of fruit tree, this support frame of worktable support the whole spraying arm in the course, its dynamic properties is important to determine the product quality and life. On the basis of three-dimensional modeling, The modal of dynamic that support frame was analysis and the first ten modal parameters (natural frequencies and mode shapes) was calculated by using ANSYS finite element of analysis software. Compared with Modal parameters by method and experimental modal analysis obtained, summarizes the higher modes of dynamic structure, and proposed modifications for the structure.

scholarly journals Overall dynamic properties of three-dimensional periodic elastic composites

2011 ◽  
Vol 468 (2137) ◽  
pp. 269-287 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Effective Properties ◽  
Dynamic Properties ◽  
Mass Density ◽  
Three Dimensional ◽  
Linear Momentum ◽  
Three Dimensions ◽  
Theoretical Treatment ◽  
Periodic Composite ◽  
Constitutive Parameters ◽  
Elastic Composites

This article presents a method for the homogenization of three-dimensional periodic elastic composites. It allows for the evaluation of the averaged overall frequency-dependent dynamic material constitutive tensors relating the averaged dynamic field variable tensors of velocity, strain, stress and linear momentum. Although the form of the dynamic constitutive relation for three-dimensional elastodynamic wave propagation has been known, this is the first time that explicit calculations of the effective parameters (for three dimensions) are presented. We show that for three-dimensional periodic composites, the overall compliance (stiffness) tensor, as produced directly by our formulation, is Hermitian, regardless of whether the corresponding unit cell is geometrically or materially symmetric. Overall, mass density is shown to be a tensor and, like the overall compliance tensor, always Hermitian. The average strain and linear momentum tensors are, however, coupled, and the coupling tensors are shown to be each others' Hermitian transpose. Finally, we present a numerical example of a three-dimensional periodic composite composed of elastic cubes periodically distributed in an elastic matrix. The presented results corroborate the predictions of the theoretical treatment illustrating the frequency dependence of the constitutive parameters. We also show that the effective properties calculated in this paper satisfy the dispersion relation of the composite.

The method of characteristics for steady supersonic rotational flow in three dimensions

1956 ◽  
Vol 1 (4) ◽  
pp. 409-423 ◽  
Author(s):  
Maurice Holt
Keyword(s):  
Supersonic Flow ◽  
Method Of Characteristics ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Rotational Flow ◽  
Conical Flow ◽  
Plane Flow ◽  
Flow Problems ◽  
The Method Of Characteristics

The method of characteristics for steady supersonic flow problems in three dimensions, due to Coburn & Dolph (1949), is extended so that flow with shocks and entropy changes may be treated. Equations of motion based on Coburn & Dolph's characteristic coordinate system are derived and a scheme is described for solving these by finite differences.A linearized method of characteristics is developed for calculating perturbations of a given three-dimensional field of flow. This is a generalization of the method evolved by Ferri (1952) for perturbations of plane flow and conical flow.

VARIATIONAL DESCRIPTION OF WEAKLY INTERACTING BOSE GASES IN 3 DIMENSIONS

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5061-5070
Author(s):  
F. MAZZANTI ◽  
M. SAARELA ◽  
V. APAJA
Keyword(s):  
Structure Function ◽  
Excited States ◽  
Hard Spheres ◽  
Dynamic Properties ◽  
Dynamic Structure ◽  
Basis Functions ◽  
Three Dimensions ◽  
Bose Gases ◽  
Weakly Interacting ◽  
Good Agreement

Static and dynamic properties of a weakly interacting Bose gas of Hard Spheres in three dimensions are studied in the framework of the Correlated Basis Functions (CBF) approximation. Results are compared with explicit expressions for the same quantities derived within the Bogoliubov model. Despite the good agreement in the energy of the groundstate and the excited states, other quantities such as the dynamic structure function present important differences that become more significant when the density is raised.

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