scholarly journals On the Stability of Reconstruction of Irregularly Sampled Diffraction Fields

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Vladislav Uzunov ◽  
Atanas Gotchev ◽  
Karen Egiazarian
Keyword(s):  
Degrees Of Freedom ◽  
Light Field ◽  
Monochromatic Light ◽  
Three Dimensional ◽  
Regularized Inversion ◽  
Volume Of Interest ◽  
Wide Range ◽  
Data Points ◽  
Data Point ◽  
The Stability

This paper addresses the problem of reconstruction of a monochromatic light field from data points, irregularly distributed within a volume of interest. Such setting is relevant for a wide range of three-dimensional display and beam shaping applications, which deal with physically inconsistent data. Two finite-dimensional models of monochromatic light fields are used to state the reconstruction problem as regularized matrix inversion. The Tikhonov method, implemented by the iterative algorithm of conjugate gradients, is used for regularization. Estimates of the model dimensionality are related to the number of degrees of freedom of the light field as to show how to control the data redundancy. Experiments demonstrate that various data point distributions lead to ill-poseness and that regularized inversion is able to compensate for the data point inconsistencies with good numerical performance.

Do Arm Postures Vary With the Speed of Reaching?

1999 ◽  
Vol 81 (5) ◽  
pp. 2582-2586 ◽  
Author(s):  
Kiisa C. Nishikawa ◽  
Sara T. Murray ◽  
Martha Flanders
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Reaching Movements ◽  
Total Force ◽  
Joint Torques ◽  
Dynamic Factors ◽  
Human Arm ◽  
Wide Range ◽  
Dynamic Forces

Do arm postures vary with the speed of reaching? For reaching movements in one plane, the hand has been observed to follow a similar path regardless of speed. Recent work on the control of more complex reaching movements raises the question of whether a similar “speed invariance” also holds for the additional degrees of freedom. Therefore we examined human arm movements involving initial and final hand locations distributed throughout the three-dimensional (3D) workspace of the arm. Despite this added complexity, arm kinematics (summarized by the spatial orientation of the “plane of the arm” and the 3D curvature of the hand path) changed very little for movements performed over a wide range of speeds. If the total force (dynamic + quasistatic) had been optimized by the control system (e.g., as in a minimization of the change in joint torques or the change in muscular forces), the optimal solution would change with speed; slow movements would reflect the minimal antigravity torques, whereas fast movements would be more strongly influenced by dynamic factors. The speed-invariant postures observed in this study are instead consistent with a hypothesized optimization of only the dynamic forces.

scholarly journals Periodic orbits relevant for the formation of inner rings in barred galaxies

1985 ◽  
Vol 106 ◽  
pp. 543-544
Author(s):  
M. Michalodimitrakis ◽  
Ch. Terzides
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Particle Trapping ◽  
Barred Galaxies ◽  
Future Paper ◽  
Stability Of Periodic Orbits ◽  
Wide Range ◽  
The Galaxy ◽  
Stable Periodic ◽  
The Stability

The study of orbits of a test particle in the gravitational field of a model barred galaxy is a first step toward the understanding of the origin of the morphological characterstics observed in real barred galaxies. In this paper we confine our attention to the inner rings. Inner rings are a very common characteristic of barred galaxies. They are narrow, round or slightly elongated along the bar (with typical axial ratios from 0.7 to near 1.0), and of the same size as the bar. A first step to test the old hypothesis that inner rings consist of stars trapped near stable periodic orbits would be a study of particle trapping around periodic orbits encircling the bar. Such a study is contained in the work of several authors (Danby 1965, de Vaucouleurs and Freeman 1972, Michalodimitrakis 1975, Contopoulos and Papayannopoulos 1980, Athanassoula et al. 1983). In the above works the stability of periodic orbits was studied with respect to perturbations which lie on the plane of motion z = 0 (planar stability). To ensure the possibility of formation of rings, a study of stability with respect to perturbations perpendicular to the plane of motion (vertical stability) is necessary. In this paper we investigate the properties of periodic orbits which we believe to be relevant for the inner-ring problem using a sufficiently general model for the galaxy and sets of values for the parameters which cover a wide range of different possible cases. We also study the stability, planar and vertical, with respect to large perturbations in order to estimate the extent of particle trapping. A detailed numerical investigation of three-dimensional periodic orbits will be given in a future paper.

A Design Study of a Supersonic Air Intake Device in a Wide Range of Main Flow Parameters

2020 ◽  
pp. 44-53
Author(s):  
E.S. Studennikov ◽  
R.S. Ayupov
Keyword(s):  
Boundary Layer ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Stability Margin ◽  
Aircraft Design ◽  
Software Systems ◽  
Flow Parameters ◽  
Wide Range ◽  
Air Intake ◽  
The Stability

This paper examines operation modes of a mixed compression air intake with a rectangular cross-section at Mach number 2.0. The perfect gas model was used for the calculation. Calculations were performed for three values of Mach numbers: 1.8, 2.0 and 3.0. k–ε turbulence model was chosen for describing flows with large adverse pressure gradients. Two-dimensional and three-dimensional configurations of the air intake device were examined. Versions of geometry with and without the boundary layer drain system were considered. The influence of the boundary layer drain system on the flow in the air intake and its characteristics was established. Throttle characteristic curves were formed for all the considered modes with regard to the averaged flow parameters. A comparison of the calculation and experimental data showed a good agreement of the results. The obtained results can serve as a basis for further optimization and improvement of the efficiency of the aircraft design layout, increase in the stability margin of air intakes, as well as development of software systems for regulating supersonic input devices.

On a Leray–α model of turbulence

2005 ◽  
Vol 461 (2055) ◽  
pp. 629-649 ◽  
Author(s):  
Alexey Cheskidov ◽  
Darryl D. Holm ◽  
Eric Olson ◽  
Edriss S. Titi
Keyword(s):  
Power Law ◽  
Upper Bound ◽  
Empirical Data ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Large Eddy Simulation Model ◽  
Eddy Simulation ◽  
Wide Range ◽  
Three Dimensional Models

In this paper we introduce and study a new model for three–dimensional turbulence, the Leray– α model. This model is inspired by the Lagrangian averaged Navier–Stokes– α model of turbulence (also known Navier–Stokes– α model or the viscous Camassa–Holm equations). As in the case of the Lagrangian averaged Navier–Stokes– α model, the Leray– α model compares successfully with empirical data from turbulent channel and pipe flows, for a wide range of Reynolds numbers. We establish here an upper bound for the dimension of the global attractor (the number of degrees of freedom) of the Leray– α model of the order of ( L / l d ) 12/7 , where L is the size of the domain and l d is the dissipation length–scale. This upper bound is much smaller than what one would expect for three–dimensional models, i.e. ( L / l d ) 3 . This remarkable result suggests that the Leray– α model has a great potential to become a good sub–grid–scale large–eddy simulation model of turbulence. We support this observation by studying, analytically and computationally, the energy spectrum and show that in addition to the usual k −5/3 Kolmogorov power law the inertial range has a steeper power–law spectrum for wavenumbers larger than 1/ α . Finally, we propose a Prandtl–like boundary–layer model, induced by the Leray– α model, and show a very good agreement of this model with empirical data for turbulent boundary layers.

Stabilizing Passive Dynamic Walk Under Wide Range of Environments by Constraint Mechanism Fitted to Sole of Foot

2009 ◽  
Vol 21 (3) ◽  
pp. 403-411 ◽  
Author(s):  
Kazuyuki Hyodo ◽  
◽  
Takeshi Oshimura ◽  
Sadayoshi Mikami ◽  
Sho'ji Suzuki ◽  
...  
Keyword(s):  
Sagittal Plane ◽  
Three Dimensional ◽  
Sharp Edge ◽  
Shape Design ◽  
Geometrical Analysis ◽  
Forward Movement ◽  
Wide Range ◽  
Outdoor Environments ◽  
Lateral Plane ◽  
The Stability

This paper proposes a foot shape design to enhance the stability of passive dynamic walk by constraining fall down phenomenon in both sagittal and lateral planes. We focus on excessive side-to-side and forward leg swinging that causes a passive dynamic biped walker to fall over. Geometrical analysis showed that stability under a wide range of slope inclinations is achievable by limiting the swinging leg spatially to within a certain angle. Such a limit, or constraint, on swinging effectively prevents falling down on the lateral plane, while stable walking is maintained on the sagittal plane by constraining forward movement using a sharp edge at the head of a foot. We propose a foot prototype realizing these two constraints using a three-dimensional (3D) sole design and show that the proposed constraint is more effective for walking than an arctic foot shape. In verification experiments, the constraint stabilized the passive dynamic walker in a wide range of outdoor environments.

Sensing and Manipulation Problems in Endoscopic Surgery: Experiment, Analysis, and Observation

1993 ◽  
Vol 2 (1) ◽  
pp. 66-81 ◽  
Author(s):  
Frank Tendick ◽  
Russell W. Jennings ◽  
Gregory Tharp ◽  
Lawrence Stark
Keyword(s):  
Endoscopic Surgery ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Direct Vision ◽  
Human Hand ◽  
Endoscopic Techniques ◽  
Surgery Patient ◽  
Wide Range ◽  
Recovery Times ◽  
Conventional Open Surgery

The minimally invasive nature of endoscopic surgery allows operations to be performed through small incisions, producing significantly less damage to good tissue than in conventional open surgery. Patient recovery times are thus greatly reduced. This major advantage has driven a dramatic growth of endoscopic techniques in a wide range of surgical applications. Unfortunately, the surgeon's abilities are severely hampered by the limitations of current endoscopic technology. In many ways endoscopic surgery is similar to teleoperation of a remote manipulator. Although the surgeon is physically close to the patient, the surgical environment is effectively “remote,” with sensing and manipulation transmitted through the endoscope and long instruments. Existing solutions from teleoperation applications could likely be applied to endoscopic surgery. This paper attempts to identify the major problems of current endoscopic technology, particularly in vision and manipulation. Vision issues are discussed in the first half, motivated by an experiment comparing surgeons' performance under different visual conditions. Surgeon subjects perform a three-dimensional positioning task with binocular direct vision, monocular direct vision, and a video endoscope. The lack of a stereoscopic view through the endoscope significantly slows performance of the tasks, but there are additional factors that make endoscopic viewing worse than monocular direct viewing. Relevant previous results which demonstrate the significance of interocular spacing in stereo viewing and the effect of display-control axes misalignment are also discussed. Issues of endoscopic manipulation are discussed in the second half of this paper, motivated by a suturing task comparing surgeons' performance with hand and endoscopic instruments. The constraint of endoscopic instruments' passing through the skin reduces their usable degrees of freedom and significantly increases the time to tie a suture knot. Kinematics of endoscopic instruments are compared to the human hand and arm. A model of the surgeon's precision grasp demonstrates the role of stiffness in fine motion control as an example of an advantage of the hand which is lost in the use of endoscopic instruments. The work described in this paper represents an initial effort in identifying problems and evaluating solutions in endoscopic surgery based on objective measurement of performance.

On Instability Pockets and Influence of Damping in Parametrically Excited Systems

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Ashu Sharma ◽  
S. C. Sinha
Keyword(s):  
Degrees Of Freedom ◽  
State Transition ◽  
Degree Of Freedom ◽  
Transition Matrices ◽  
Stability Boundaries ◽  
Parametrically Excited ◽  
Parametric Space ◽  
Stability Diagrams ◽  
Wide Range ◽  
The Stability

In most parametrically excited systems, stability boundaries cross each other at several points to form closed unstable subregions commonly known as “instability pockets.” The first aspect of this study explores some general characteristics of these instability pockets and their structural modifications in the parametric space as damping is induced in the system. Second, the possible destabilization of undamped systems due to addition of damping in parametrically excited systems has been investigated. The study is restricted to single degree-of-freedom systems that can be modeled by Hill and quasi-periodic (QP) Hill equations. Three typical cases of Hill equation, e.g., Mathieu, Meissner, and three-frequency Hill equations, are analyzed. State transition matrices of these equations are computed symbolically/analytically over a wide range of system parameters and instability pockets are observed in the stability diagrams of Meissner, three-frequency Hill, and QP Hill equations. Locations of the intersections of stability boundaries (commonly known as coexistence points) are determined using the property that two linearly independent solutions coexist at these intersections. For Meissner equation, with a square wave coefficient, analytical expressions are constructed to compute the number and locations of the instability pockets. In the second part of the study, the symbolic/analytic forms of state transition matrices are used to compute the minimum values of damping coefficients required for instability pockets to vanish from the parametric space. The phenomenon of destabilization due to damping, previously observed in systems with two degrees-of-freedom or higher, is also demonstrated in systems with one degree-of-freedom.

BORDER COLLISION BIFURCATIONS IN THREE-DIMENSIONAL PIECEWISE SMOOTH SYSTEMS

2008 ◽  
Vol 18 (02) ◽  
pp. 577-586 ◽  
Author(s):  
INDRAVA ROY ◽  
A. R. ROY
Keyword(s):  
Three Dimensional ◽  
Piecewise Smooth ◽  
Smooth Maps ◽  
Research Fields ◽  
Border Collision Bifurcations ◽  
Period 2 ◽  
Wide Range ◽  
Different Types ◽  
Piecewise Smooth Maps ◽  
The Stability

Piecewise smooth maps have been a focus of study for scientists in a wide range of research fields. These maps show qualitatively different types of bifurcations than those exhibited by generic smooth maps. We present a theoretical framework for analyzing three-dimensional piecewise smooth maps by deriving a suitable normal form and then finding the stability criteria for periodic orbits. We also show by numerical simulation different types of border collision bifurcations that can occur in such a map. We have also been able to observe a border collision bifurcation from a period-2 to a quasiperiodic orbit.

scholarly journals Ultrafast-laser-inscribed 3D integrated photonics: challenges and emerging applications

Nanophotonics ◽  
2015 ◽  
Vol 4 (3) ◽  
pp. 332-352 ◽  
Author(s):  
S. Gross ◽  
M. J. Withford
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Laser Pulses ◽  
Femtosecond Laser Pulses ◽  
Ultrafast Laser ◽  
Integrated Photonics ◽  
Transparent Dielectrics ◽  
Wide Range ◽  
The Many ◽  
Quantum Photonics

AbstractSince the discovery that tightly focused femtosecond laser pulses can induce a highly localised and permanent refractive index modification in a large number of transparent dielectrics, the technique of ultrafast laser inscription has received great attention from a wide range of applications. In particular, the capability to create three-dimensional optical waveguide circuits has opened up new opportunities for integrated photonics that would not have been possible with traditional planar fabrication techniques because it enables full access to the many degrees of freedom in a photon. This paper reviews the basic techniques and technological challenges of 3D integrated photonics fabricated using ultrafast laser inscription as well as reviews the most recent progress in the fields of astrophotonics, optical communication, quantum photonics, emulation of quantum systems, optofluidics and sensing.

scholarly journals Internal Variability of the Winter Stratosphere. Part I: Time-Independent Forcing

2006 ◽  
Vol 63 (11) ◽  
pp. 2758-2776 ◽  
Author(s):  
R. K. Scott ◽  
L. M. Polvani
Keyword(s):  
Radiative Forcing ◽  
Degrees Of Freedom ◽  
Planetary Wave ◽  
Three Dimensional ◽  
Polar Vortex ◽  
Internal Variability ◽  
Wave Forcing ◽  
Wide Range ◽  
External Sources ◽  
Stratospheric Variability

Abstract This paper examines the nature and robustness of internal stratospheric variability, namely the variability resulting from the internal dynamics of the stratosphere itself, as opposed to that forced by external sources such as the natural variability of the free troposphere. Internal stratospheric variability arises from the competing actions of radiative forcing, which under perpetual winter conditions strengthens the polar vortex, and planetary wave breaking, which weakens it. The results from a stratosphere-only model demonstrate that strong internal stratospheric variability, consisting of repeated sudden warming-type events, exists over a wide range of realistic radiative and wave forcing conditions, and is largely independent of other physical and numerical parameters. In particular, the coherent form of the variability persists as the number of degrees of freedom is increased, and is therefore not an artifact of severe model truncation. Various diagnostics, including three-dimensional representations of the potential vorticity, illustrate that the variability is determined by the vertical structure of the vortex and the extent to which upward wave propagation is favored or inhibited. In this paper, the variability arising from purely internal stratosphere dynamics is isolated by specifying thermal and wave forcings that are completely time independent. In a second paper, the authors investigate the relative importance of internal and external variability by considering time-dependent wave forcing as a simple representation of tropospheric variability.

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