On Functions with Zero Integral Moments over Balls of Fixed Radius

AbstractWe consider a space-time random field on ${{\mathbb{R}^d} \times {\mathbb{R}}}$ given as an integral of a kernel function with respect to a Lévy basis with a convolution equivalent Lévy measure. The field obeys causality in time and is thereby not continuous along the time axis. For a large class of such random fields we study the tail behaviour of certain functionals of the field. It turns out that the tail is asymptotically equivalent to the right tail of the underlying Lévy measure. Particular examples are the asymptotic probability that there is a time point and a rotation of a spatial object with fixed radius, in which the field exceeds the level x, and that there is a time interval and a rotation of a spatial object with fixed radius, in which the average of the field exceeds the level x.

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Data-Driven Additive Manufacturing Constraints for Topology Optimization

Volume 2A: 44th Design Automation Conference ◽

10.1115/detc2018-85391 ◽

2018 ◽

Cited By ~ 3

Author(s):

Benjamin M. Weiss ◽

Joshua M. Hamel ◽

Mark A. Ganter ◽

Duane W. Storti

Keyword(s):

Topology Optimization ◽

Additive Manufacturing ◽

Optimal Designs ◽

Data Driven ◽

Constraint Function ◽

Manufacturing Constraint ◽

Gradient Based ◽

Fixed Radius ◽

Different Shapes ◽

Moving Morphable Components

The topology optimization (TO) of structures to be produced using additive manufacturing (AM) is explored using a data-driven constraint function that predicts the minimum producible size of small features in different shapes and orientations. This shape- and orientation-dependent manufacturing constraint, derived from experimental data, is implemented within a TO framework using a modified version of the Moving Morphable Components (MMC) approach. Because the analytic constraint function is fully differentiable, gradient-based optimization can be used. The MMC approach is extended in this work to include a “bootstrapping” step, which provides initial component layouts to the MMC algorithm based on intermediate Solid Isotropic Material with Penalization (SIMP) topology optimization results. This “bootstrapping” approach improves convergence compared to reference MMC implementations. Results from two compliance design optimization example problems demonstrate the successful integration of the manufacturability constraint in the MMC approach, and the optimal designs produced show minor changes in topology and shape compared to designs produced using fixed-radius filters in the traditional SIMP approach. The use of this data-driven manufacturability constraint makes it possible to take better advantage of the achievable complexity in additive manufacturing processes, while resulting in typical penalties to the design objective function of around only 2% when compared to the unconstrained case.

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Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

Journal of Applied Probability ◽

10.1017/jpr.2017.37 ◽

2017 ◽

Vol 54 (3) ◽

pp. 833-851 ◽

Cited By ~ 1

Author(s):

Anders Rønn-Nielsen ◽

Eva B. Vedel Jensen

Keyword(s):

Random Field ◽

Large Class ◽

Random Fields ◽

Lévy Measure ◽

Infinitely Divisible ◽

Excursion Sets ◽

Excursion Set ◽

Fixed Radius ◽

Asymptotic Probability ◽

The Right

Abstract We consider a continuous, infinitely divisible random field in ℝd, d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

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Effect of an internal nonlinear rotational dissipative element on vortex shedding and vortex-induced vibration of a sprung circular cylinder

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.504 ◽

2017 ◽

Vol 828 ◽

pp. 196-235 ◽

Cited By ~ 15

Author(s):

Ravi Kumar R. Tumkur ◽

Arne J. Pearlstein ◽

Arif Masud ◽

Oleg V. Gendelman ◽

Antoine B. Blanchard ◽

...

Keyword(s):

Circular Cylinder ◽

Nonlinear Energy Sink ◽

Stream Velocity ◽

Rectilinear Motion ◽

Mean Flow ◽

Number Range ◽

Vortex Induced Vibration ◽

Concomitant Reduction ◽

Fixed Radius ◽

Lift And Drag

We computationally investigate coupling of a nonlinear rotational dissipative element to a sprung circular cylinder allowed to undergo transverse vortex-induced vibration (VIV) in an incompressible flow. The dissipative element is a ‘nonlinear energy sink’ (NES), consisting of a mass rotating at fixed radius about the cylinder axis and a linear viscous damper that dissipates energy from the motion of the rotating mass. We consider the Reynolds number range $20\leqslant Re\leqslant 120$, with $Re$ based on cylinder diameter and free-stream velocity, and the cylinder restricted to rectilinear motion transverse to the mean flow. Interaction of this NES with the flow is mediated by the cylinder, whose rectilinear motion is mechanically linked to rotational motion of the NES mass through nonlinear inertial coupling. The rotational NES provides significant ‘passive’ suppression of VIV. Beyond suppression however, the rotational NES gives rise to a range of qualitatively new behaviours not found in transverse VIV of a sprung cylinder without an NES, or one with a ‘rectilinear NES’, considered previously. Specifically, the NES can either stabilize or destabilize the steady, symmetric, motionless-cylinder solution and can induce conditions under which suppression of VIV (and concomitant reduction in lift and drag) is accompanied by a greatly elongated region of attached vorticity in the wake, as well as conditions in which the cylinder motion and flow are temporally chaotic at relatively low $Re$.

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RINGS: Almost a ring, semiring, zero, integral domain

10.31219/osf.io/bzugr ◽

2021 ◽

Author(s):

Matheus Pereira Lobo

Keyword(s):

Knowledge Base ◽

Commutative Ring ◽

Integral Domain ◽

White Paper ◽

Zero Divisors ◽

Domain Integral ◽

Zero Integral

RING, commutative ring, almost a ring, semiring, zero ring, zero property, zero divisors, domain, integral domain, and their underlying definitions are presented in this white paper (knowledge base).

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Neural Processing of Gravito-Inertial Cues in Humans. II. Influence of the Semicircular Canals During Eccentric Rotation

Journal of Neurophysiology ◽

10.1152/jn.2001.85.4.1648 ◽

2001 ◽

Vol 85 (4) ◽

pp. 1648-1660 ◽

Cited By ~ 65

Author(s):

D. M. Merfeld ◽

L. H. Zupan ◽

C. A. Gifford

Keyword(s):

Nervous System ◽

Time Course ◽

Rotation Speed ◽

Linear Acceleration ◽

Otolith Organs ◽

Centripetal Acceleration ◽

Variable Radius ◽

Fixed Radius ◽

The Subject ◽

Roll Tilt

All linear accelerometers, including the otolith organs, respond equivalently to gravity and linear acceleration. To investigate how the nervous system resolves this ambiguity, we measured perceived roll tilt and reflexive eye movements in humans in the dark using two different centrifugation motion paradigms (fixed radius and variable radius) combined with two different subject orientations (facing-motion and back-to-motion). In the fixed radius trials, the radius at which the subject was seated was held constant while the rotation speed was changed to yield changes in the centrifugal force. In variable radius trials, the rotation speed was held constant while the radius was varied to yield a centrifugal force that nearly duplicated that measured during the fixed radius condition. The total gravito-inertial force (GIF) measured by the otolith organs was nearly identical in the two paradigms; the primary difference was the presence (fixed radius) or absence (variable radius) of yaw rotational cues. We found that the yaw rotational cues had a large statistically significant effect on the time course of perceived tilt, demonstrating that yaw rotational cues contribute substantially to the neural processing of roll tilt. We also found that the orientation of the subject relative to the centripetal acceleration had a dramatic influence on the eye movements measured during fixed radius centrifugation. Specifically, the horizontal vestibuloocular reflex (VOR) measured in our human subjects was always greater when the subject faced the direction of motion than when the subjects had their backs toward the motion during fixed radius rotation. This difference was consistent with the presence of a horizontal translational VOR response induced by the centripetal acceleration. Most importantly, by comparing the perceptual tilt responses to the eye movement responses, we found that the translational VOR component decayed as the subjective tilt indication aligned with the tilt of the GIF. This was true for both the fixed radius and variable radius conditions even though the time course of the responses was significantly different for these two conditions. These findings are consistent with the hypothesis that the nervous system resolves the ambiguous measurements of GIF into neural estimates of gravity and linear acceleration. More generally, these findings are consistent with the hypothesis that the nervous system uses internal models to process and interpret sensory motor cues.

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A Method for Evaluating Fixed-Radius Plot Size When Sampling Western Juniper Seedlings and Saplings

Western Journal of Applied Forestry ◽

10.1093/wjaf/17.4.207 ◽

2002 ◽

Vol 17 (4) ◽

pp. 207-208

Author(s):

David L. Azuma ◽

Larry Bednar

Keyword(s):

Forest Inventory ◽

Forest Service ◽

Usda Forest Service ◽

Forest Inventory And Analysis ◽

Size Selection ◽

Western Juniper ◽

Plot Size ◽

Fixed Radius ◽

Selection For

Abstract This note outlines a method for evaluating plot size selection for an inventory of western juniper woodlands in eastern Oregon. The Forest Inventory and Analysis (FIA) program of the USDA Forest Service in Portland, Oregon, used this method to evaluate several plot sizes to measure seedlings and saplings in the 1998 inventory of eastern Oregon. By choosing a 5 m radius plot, the probability of tallying no seedlings or saplings on four subplots is less than 10% for the three sample densities (0.01, 0.02, and 0.03 trees/m2) used. West. J. Appl. For. 17(4):207–208.

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Competition Indexes to Evaluate Tree Growth in a Semi-Deciduous Seasonal Forest

Floresta e Ambiente ◽

10.1590/2179-8087.010716 ◽

2019 ◽

Vol 26 (4) ◽

Author(s):

Ilvan Medeiros Lustosa Junior ◽

Renato Vinícius Oliveira Castro ◽

Ricardo de Oliveira Gaspar ◽

Juliana Baldan Costa Neves Araújo ◽

Fabiana de Gois Aquino

Keyword(s):

Tree Growth ◽

Basal Area ◽

Natural Forests ◽

Competition Index ◽

Radius Of Influence ◽

Fixed Radius ◽

The Subject

ABSTRACT Most of the studies that analyze the behavior of tree competition approach even-aged plantations. Therefore, it is possible to notice a lack of this kind of information regarding natural forests with high biodiversity. The objective of this study was to evaluate the competition in a fragment of Semi-Deciduous Seasonal Forest, according to the ecologic group, light depending and non-depending groups for all species sampled in the fragment. The Distance Independent Competition Index and Semi-Distance Independent Competition Index were applied in this study. The basal area in larger trees index, without the radius of influence, was the most efficient to analyze how the competition affects the growth of the specimens in the studied fragment. It was stated that evaluating the competition per ecologic group is more efficient. The results confirm that the forest competition cannot be determined by considering only a fixed radius of influence that embraces the neighbors and the subject tree.

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A Fixed-radius Point Count Method for Nonbreeding and Breeding Season Use

The Auk ◽

10.1093/auk/103.3.593 ◽

1986 ◽

Vol 103 (3) ◽

pp. 593-602 ◽

Cited By ~ 306

Author(s):

Richard L. Hutto ◽

Sandra M. Pletschet ◽

Paul Hendricks

Keyword(s):

Bird Species ◽

Common Species ◽

Bird Abundance ◽

Point Count ◽

Bird Density ◽

Count Method ◽

Species Abundances ◽

Fixed Radius ◽

Point Count Method ◽

A Site

Abstract We provide a detailed description of a fixed-radius point count method that carries fewer assumptions than most of the currently popular methods of estimating bird density and that can be used during both the nonbreeding and breeding seasons. The method results in three indices of bird abundance, any of which can be used to test for differences in community composition among sites, or for differences in the abundance of a given bird species among sites. These indices are (1) the mean number of detections within 25 m of the observer, (2) the frequency of detections within 25 m of the observer, and (3) the frequency of detections regardless of distance from the observer. The overall ranking of species abundances from a site is similar among the three indices, but discrepancies occur with either rare species that are highly detectable at great distances or common species that are repulsed by, or inconspicuous when near, the observer. We argue that differences in the behavior among species will preclude an accurate ranking of species by abundance through use of this or any other counting method in current use.

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