scholarly journals An analytic expression for the ultimate intrinsic SNR in a uniform sphere

2018 ◽  
Vol 80 (5) ◽  
pp. 2256-2266 ◽  
Author(s):  
Hong‐Hsi Lee ◽  
Daniel K. Sodickson ◽  
Riccardo Lattanzi
Keyword(s):  
Analytic Expression ◽  
Uniform Sphere

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

Analytic expression for the charge carried by a locally excited Bloch state

2021 ◽  
Vol 103 (24) ◽  
Author(s):  
István Magashegyi ◽  
Katalin Oltyán ◽  
Péter Földi
Keyword(s):  
Locally Excited ◽  
Bloch State ◽  
Analytic Expression

Stability analysis of uncertain delay differential equations

2021 ◽  
pp. 1-11
Author(s):  
Jian Wang ◽  
Yuanguo Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liu Process ◽  
Uncertain Dynamical System ◽  
Analytic Expression ◽  
Functional Differential ◽  
The One ◽  
Delay Differential

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

scholarly journals Out of sight, out of mind? The impact of correlated clustering in substructure lensing

2021 ◽  
Author(s):  
Alexandres Lazar ◽  
James S Bullock ◽  
Michael Boylan-Kolchin ◽  
Robert Feldmann ◽  
Onur Çatmabacak ◽  
...  
Keyword(s):  
Dark Matter ◽  
Principal Axis ◽  
Major Axis ◽  
Line Of Sight ◽  
Gravitational Lenses ◽  
Local Clustering ◽  
Analytic Expression ◽  
Halo Masses ◽  
The Impact

Abstract A promising route for revealing the existence of dark matter structures on mass scales smaller than the faintest galaxies is through their effect on strong gravitational lenses. We examine the role of local, lens-proximate clustering in boosting the lensing probability relative to contributions from substructure and unclustered line-of-sight (LOS) haloes. Using two cosmological simulations that can resolve halo masses of Mhalo ≃ 109 M⊙ (in a simulation box of length Lbox ∼ 100 Mpc) and 107 M⊙ (Lbox ∼ 20 Mpc), we demonstrate that clustering in the vicinity of the lens host produces a clear enhancement relative to an assumption of unclustered haloes that persists to >20 Rvir. This enhancement exceeds estimates that use a two-halo term to account for clustering, particularly within 2 − 5 Rvir. We provide an analytic expression for this excess, clustered contribution. We find that local clustering boosts the expected count of 109 M⊙ perturbing haloes by ${\sim }35{{\ \rm per\ cent}}$ compared to substructure alone, a result that will significantly enhance expected signals for low-redshift (zl ≃ 0.2) lenses, where substructure contributes substantially compared to LOS haloes. We also find that the orientation of the lens with respect to the line of sight (e.g. whether the line of sight passes through the major axis of the lens) can also have a significant effect on the lensing signal, boosting counts by an additional $\sim 50{{\ \rm per\ cent}}$ compared to a random orientations. This could be important if discovered lenses are biased to be oriented along their principal axis.

scholarly journals ENERGY EXTRACTION FROM GRAVITATIONAL COLLAPSE TO STATIC BLACK HOLES

2003 ◽  
Vol 12 (01) ◽  
pp. 121-127 ◽  
Author(s):  
REMO RUFFINI ◽  
LUCA VITAGLIANO
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Extraction Process ◽  
Maximum Efficiency ◽  
Energy Extraction ◽  
Mass Energy ◽  
Classical Level ◽  
Static Black Hole ◽  
Exact Analytic Expression ◽  
Analytic Expression

The mass-energy formula of black holes implies that up to 50% of the energy can be extracted from a static black hole. Such a result is reexamined using the recently established analytic formulas for the collapse of a shell and the expression for the irreducible mass of a static black hole. It is shown that the efficiency of energy extraction process during the formation of the black hole is linked in an essential way to the gravitational binding energy, the formation of the horizon and the reduction of the kinetic energy of implosion. Here a maximum efficiency of 50% in the extraction of the mass energy is shown to be generally attainable in the collapse of a spherically symmetric shell: surprisingly this result holds as well in the two limiting cases of the Schwarzschild and extreme Reissner–Nordström space–times. Moreover, the analytic expression recently found for the implosion of a spherical shell to an already formed black hole leads to a new exact analytic expression for the energy extraction which results in an efficiency strictly less than 100% for any physical implementable process. There appears to be no incompatibility between General Relativity and Thermodynamics at this classical level.

Maximin: a direct approach to sustainability

2006 ◽  
Vol 11 (3) ◽  
pp. 275-300 ◽  
Author(s):  
ROBERT D. CAIRNS ◽  
NGO VAN LONG
Keyword(s):  
Precautionary Principle ◽  
Direct Approach ◽  
Necessary Condition ◽  
Hyperbolic Discount ◽  
Discount Factors ◽  
Discounted Utility ◽  
Special Cases ◽  
Analytic Expression ◽  
Hotelling's Rule ◽  
Competitive Economy

We solve directly a general maximin (sustainment, intergenerational-equity) problem. Because the shadow values of a maximin problem do not correspond to the shadow values from a general discounted-utility solution, they correspond to the prices of only a very special competitive economy. Virtual discount factors for the economy arise. They do not correspond to hyperbolic discount factors. Hartwick's rule is derived and generalized naturally to take into account non-autonomous and non-deterministic features of the economy. Under uncertainty, Hartwick's rule is the analytic expression of a form of precautionary principle. Hotelling's rule is a necessary condition, but may be more complex than has been appreciated in simple models. Some interpretations of strong sustainment are special cases of weak sustainment but, paradoxically, may be more difficult to solve.

Statics Analysis of the Mechanical Model of Nucleosome

2011 ◽  
Vol 343-344 ◽  
pp. 661-667 ◽  
Author(s):  
Yun Xue ◽  
De Wei Weng ◽  
Gang Ming Gong
Keyword(s):  
Mechanical Model ◽  
The Other ◽  
Elastic Rod ◽  
Equilibrium Equations ◽  
Constraint Force ◽  
Precession Angle ◽  
Nutation Angle ◽  
Analytic Expression ◽  
Set Up ◽  
Calculated Analysis

Mechanical model of nucleoside and its equilibrium equations are set up, and the mechanical properties on the equilibrium position are analyzed. In the case constraint force and electrostatic attraction between cylinder OH and elastic rod are balanced, the analytic expression of nutation angle of the section and its conditions of existence are given. It is show that the cylinder OH can maintain equilibrium at any range of the precession angle. In the other case when unbanced, there is phenomenon of separation of elastic rod from cylinder OH in the spiral wound 2 circles, and numerical solution of the precession angle at separation points are calculated. Analysis of equilibrium of cylinder H1 illustrates that the generatrix of cylinder H1 and OH are not parallel, and the angle between them is obtained

Optimal Control of Arrays of Microcantilevers

1999 ◽  
Vol 121 (4) ◽  
pp. 686-690 ◽  
Author(s):  
Mariateresa Napoli ◽  
Bassam Bamieh ◽  
Mohammed Dahleh
Keyword(s):  
Optimal Control ◽  
Atomic Force Microscopy ◽  
Optimal Controller ◽  
Invariant System ◽  
Sensors And Actuators ◽  
Force Microscopy ◽  
Atomic Force ◽  
Distributed Array ◽  
Spatial Invariance ◽  
Analytic Expression

In this paper we will present a model for an array of microcantilevers that are used in Atomic Force Microscopy and nano-scale manufacturing. The microcantilevers are connected to each other through a common base, and are individually actuated. The sensors are also integrated on each microcantilever. We consider the problem of controlling a tightly packed array of identical microcantilevers that are dynamically coupled. This system is an example of a spatially-invariant system with a distributed array of sensors and actuators. We exploit the spatial invariance of the problem to design optimal ℋ2 controllers for this array. An analytic expression for the optimal controller is derived in the transformed domain, and estimates of the coupling range of the controller is obtained.

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