Exterior Stationary Navier–Stokes Flows in 3D with Nonzero Velocity at Infinity: Asymptotic Behavior of the Second Derivatives of the Velocity

2005 ◽  
Vol 30 (7) ◽  
pp. 987-1020 ◽  
Author(s):  
Paul Deuring
Keyword(s):  
Asymptotic Behavior ◽  
Navier Stokes ◽  
Stokes Flows ◽  
Second Derivatives ◽  
Derivatives Of

scholarly journals Self-Aware Distributed Consensus Building for Sensor Networks

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Lei Chen ◽  
Jeff Frolik
Keyword(s):  
Asymptotic Behavior ◽  
Sensor Networks ◽  
Extensive Study ◽  
Practical Implementation ◽  
Consensus Building ◽  
Optimal Parameters ◽  
Distributed Consensus ◽  
Systematic Analysis ◽  
Second Derivatives ◽  
Derivatives Of

Distributed consensus building promises to improve the robustness and reliability of sensor networks and thus is an active topic of research. Whereas extensive study has been done on the theoretical analysis of the asymptotic behavior of consensus building, one important issue that is crucial to the practical implementation of sensor networks was rarely explored, namely, the criteria to determine whether consensus has been attained. In this paper, we propose an approach that allows each node in a network to make the decision by itself, based on the second derivatives of its own state. The approach does not rely on the states of other nodes, leads to substantial saving of communication resources, and is resilient to connection failure. We perform a systematic analysis of the approach and, as a consequence, derive the optimal parameters that minimize the upper bound of the number of required iterations to reach consensus.

Weighted spatial decay rates for the Navier–Stokes flows in a half-space

2014 ◽  
Vol 144 (3) ◽  
pp. 491-510 ◽  
Author(s):  
Pigong Han
Keyword(s):  
Half Space ◽  
Stokes Flow ◽  
Projection Operator ◽  
Decay Rates ◽  
Navier Stokes ◽  
Convection Term ◽  
Spatial Decay ◽  
Stokes Flows ◽  
Spatial Derivatives ◽  
Derivatives Of

The weighted Lq − Lr-estimates for the Stokes flow are given in half-spaces. Furthermore, the weighted decays for the first and second spatial derivatives of the Navier-Stokes flows are also established, where the unboundedness of the projection operator is overcome by employing a decomposition for the convection term. The main results in this paper are inspired by the works of Bae and Jin.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

A State-Space Approach to the Synthesis of Random Vertical and Crosslevel Rail Irregularities

1990 ◽  
Vol 112 (1) ◽  
pp. 83-87 ◽  
Author(s):  
R. H. Fries ◽  
B. M. Coffey
Keyword(s):  
Numerical Simulation ◽  
White Noise ◽  
State Space ◽  
Spectral Characteristics ◽  
The State ◽  
Second Derivatives ◽  
Time Histories ◽  
Sample Interval ◽  
Rail Irregularities ◽  
Derivatives Of

Solution of rail vehicle dynamics models by means of numerical simulation has become more prevalent and more sophisticated in recent years. At the same time, analysts and designers are increasingly interested in the response of vehicles to random rail irregularities. The work described in this paper provides a convenient method to generate random vertical and crosslevel irregularities when their time histories are required as inputs to a numerical simulation. The solution begins with mathematical models of vertical and crosslevel power spectral densities (PSDs) representing PSDs of track classes 4, 5, and 6. The method implements state-space models of shape filters whose frequency response magnitude squared matches the desired PSDs. The shape filters give time histories possessing the proper spectral content when driven by white noise inputs. The state equations are solved directly under the assumption that the white noise inputs are constant between time steps. Thus, the state transition matrix and the forcing matrix are obtained in closed form. Some simulations require not only vertical and crosslevel alignments, but also the first and occasionally the second derivatives of these signals. To accommodate these requirements, the first and second derivatives of the signals are also generated. The responses of the random vertical and crosslevel generators depend upon vehicle speed, sample interval, and track class. They possess the desired PSDs over wide ranges of speed and sample interval. The paper includes a comparison between synthetic and measured spectral characteristics of class 4 track. The agreement is very good.

Investigation of a Technique for the Differentiation of Empirical Data

1983 ◽  
Vol 105 (3) ◽  
pp. 200-202 ◽  
Author(s):  
D. M. Trujillo ◽  
H. R. Busby
Keyword(s):  
Dynamic Programming ◽  
Differentiable Function ◽  
Empirical Data ◽  
Numerical Experiments ◽  
Random Noise ◽  
Second Derivatives ◽  
Derivatives Of

A dynamic programming filter is derived to estimate the first and second derivatives of empirical data. A series of numerical experiments are conducted using a known differentiable function with various amounts of added random noise.

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