Secrecy coverage in two dimensions

2016 ◽  
Vol 48 (1) ◽  
pp. 1-12
Author(s):  
Amites Sarkar
Keyword(s):  
Poisson Process ◽  
Two Dimensions ◽  
Infinite Plane ◽  
Black Point ◽  
Wide Range ◽  
Independent Poisson Process ◽  
Random Configuration

Abstract Working in the infinite plane R2, consider a Poisson process of black points with intensity 1, and an independent Poisson process of red points with intensity λ. We grow a disc around each black point until it hits the nearest red point, resulting in a random configuration Aλ, which is the union of discs centered at the black points. Next, consider a fixed disc of area n in the plane. What is the probability pλ(n) that this disc is covered by Aλ? We prove that if λ3nlogn = y then, for sufficiently large n, e-8π2y ≤ pλ(n) ≤ e-2π2y/3. The proofs reveal a new and surprising phenomenon, namely, that the obstructions to coverage occur on a wide range of scales.

scholarly journals Adjustment models for multivariate geodetic time series with vector-autoregressive errors

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Boris Kargoll ◽  
Alexander Dorndorf ◽  
Mohammad Omidalizarandi ◽  
Jens-André Paffenholz ◽  
Hamza Alkhatib
Keyword(s):  
Least Squares Method ◽  
Functional Model ◽  
Expectation Maximization Algorithm ◽  
Two Dimensions ◽  
Vector Autoregressive ◽  
Wide Range ◽  
Engineering Geodesy ◽  
Cross Correlations ◽  
T Distribution ◽  
Multivariate T

Abstract In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals Is contact angle a cause or an effect? – A cautionary tale

2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Angles ◽  
Two Dimensions ◽  
Experimental Results ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Wide Range ◽  
Fluid Drop ◽  
Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

Study of Method for Determination of Thermal Conductivity of Automotive Interior Materials

2014 ◽  
Vol 526 ◽  
pp. 46-51
Author(s):  
Li Xiong Zhang ◽  
Rong Gang Gao
Keyword(s):  
Thermal Conductivity ◽  
Conductivity Measurement ◽  
Transient Heat Conduction ◽  
Traditional Theory ◽  
Infinite Plane ◽  
Plane Source ◽  
Transient Plane Source ◽  
Wide Range ◽  
Automotive Interior

Based on the traditional theory of transient plane source for thermal conductivity measurement, this paper designed and developed a new pattern of heating and temperature sensing probe, presented the study of transient heat conduction of half-infinite plane while being heated, established a modified mathematical model of transient plane source method, and achieved the measurement of thermal conductivity of automotive interior material sample by the data processing method of mathematical iteration and liner regression using the modified transient plane source probe. According to the data of experiments, the instrument which this paper designed has a high precision of 5% and a wide range of 0.003-1W/(mK).This paper provides a practicable way for heat capacity determination of automotive interior materials.

scholarly journals Woody species do not differ in dormancy progression: differences in time to budbreak due to forcing and cold hardiness

2021 ◽  
Author(s):  
Al Kovaleski
Keyword(s):  
Maximum Rate ◽  
Path Length ◽  
Cold Hardiness ◽  
Woody Species ◽  
Two Dimensions ◽  
Spring Phenology ◽  
Wide Range ◽  
The Difference ◽  
Response To Temperature ◽  
Phenological Phases

AbstractBudbreak is one of the most observed and studied phenological phases in perennial plants. Two dimensions of exposure to temperature are generally used to model budbreak: accumulation of time spent at low temperatures (chilling); and accumulation of heat units (forcing). These two effects have a well-established negative correlation: the more chilling, the less forcing required for budbreak. Furthermore, temperate plant species are assumed to vary in amount of chilling required to complete endodormancy and begin the transition to breaking bud. Still, prediction of budbreak remains a challenge. The present work demonstrates across a wide range of species how bud cold hardiness must be accounted for to study dormancy and accurately predict time to budbreak. Cold hardiness defines the path length to budbreak, meaning the difference between the cold hardiness buds attain during the winter, and the cold hardiness at which deacclimated buds are predicted to open. This distance varies among species and throughout winter within a species. Increases in rate of cold hardiness loss (deacclimation) measured throughout winter show that chilling controls deacclimation potential – the proportion of the maximum rate response attained at high chill accumulation – which has a sigmoid relationship to chilling accumulation. For forcing, rates of deacclimation increase non-linearly in response to temperature. Comparisons of deacclimation potential show a dormancy progresses similarly for all species. This observation suggests that comparisons of physiologic and genetic control of dormancy requires an understanding of cold hardiness dynamics and the necessity for an update of the framework for studying dormancy and its effects on spring phenology.

The reflexion of a spherical acoustic pulse by an absorbent infinite plane and related problems

1952 ◽  
Vol 215 (1121) ◽  
pp. 233-254 ◽  
Keyword(s):  
Acoustic Waves ◽  
Acoustic Pulse ◽  
Practical Interest ◽  
Exact Result ◽  
Integral Solution ◽  
Blast Waves ◽  
Angle Of Incidence ◽  
Infinite Plane ◽  
Formal Integral ◽  
Wide Range

A formal integral solution is given for the problem of the reflexion of a spherical acoustic pulse by an infinite plane interface having an impedance of arbitrary dependence on frequency and angle of incidence. In many cases of practical interest the impedance may be assumed to be independent of angle of incidence, and under this assumption the integral solution is relatively easy to evaluate. A simple exact expression for the reflected pulse, in closed form, is obtained when the wall impedance is purely resistive (i.e. independent of frequency). This solution is a special case of a general type of solution of the wave equation when it is reduced to a rotationally symmetric Laplace’s equation in the ‘spherical polar’ co-ordinates [√{( ct / r ) 2 - sin 2 θ}, ( ct cos θ/ r )/ √{( ct / r ) 2 - sin 2 θ}]. To illustrate the relatively wide range of validity of the assumption of an impedance independent of angle of incidence, when applied to real materials, this exact result is compared with an approximate solution for the case where the interface separates two homogeneous isotropic lossless materials. The formal integral solution is evaluated approximately for wall impedances of the following types: (i) resistance and mass, (ii) resistance and stiffness, (iii) resistance, mass and stiffness. The solutions are compared with corresponding solutions for plane incident waves, and the behaviour of the scattered wave, distinguishing between the spherical and the plane wave, is discussed. Possible applications of the results for acoustic waves to problems in the reflexion of blast waves and of transient radiation by an electric dipole are indicated briefly.

Motherhood

2016 ◽  
Author(s):  
Marcia Yonemoto
Keyword(s):  
Family Planning ◽  
Early Modern ◽  
Lived Experience ◽  
Early Modern Period ◽  
Two Dimensions ◽  
Low Fertility ◽  
Primary Sources ◽  
Modern World ◽  
The Social ◽  
Wide Range

The chapter explores the discourse and experience of motherhood within Japan’s low-fertility regime in the early modern period. In a manner rarely seen elsewhere in the early modern world, Japanese families used various means, from infanticide to adoption, to correlate family size with income. The chapter examines a wide range of primary sources to explore the effects of family planning on motherhood in two dimensions, the biological and the social. It also examines motherhood as a lived experience through the writings of Inoue Tsūjo, Kuroda Tosako, and Sekiguchi Chie.

scholarly journals Digital laser micro- and nanoprinting

Nanophotonics ◽  
2018 ◽  
Vol 8 (1) ◽  
pp. 27-44 ◽  
Author(s):  
Qingfeng Li ◽  
David Grojo ◽  
Anne-Patricia Alloncle ◽  
Boris Chichkov ◽  
Philippe Delaporte
Keyword(s):  
Three Dimensional ◽  
Digital Fabrication ◽  
Two Dimensions ◽  
Minimum Size ◽  
Direct Writing ◽  
3D Objects ◽  
Wide Range ◽  
Macro Scale ◽  
Forward Transfer ◽  
Pros And Cons

AbstractLaser direct writing is a well-established ablation technology for high-resolution patterning of surfaces, and since the development of additive manufacturing, laser processes have also appeared very attractive for the digital fabrication of three-dimensional (3D) objects at the macro-scale, from few millimeters to meters. On the other hand, laser-induced forward transfer (LIFT) has demonstrated its ability to print a wide range of materials and to build functional micro-devices. For many years, the minimum size of laser-printed pixels was few tens of micrometers and is usually organized in two dimensions. Recently, new approaches have been investigated, and the potential of LIFT technology for printing 2D and 3D sub-micrometer structures has become real. After a brief description of the LIFT process, this review presents the pros and cons of the different digital laser printing technologies in the aim of the additive nanomanufacturing application. The transfer of micro- and nano-dots in the liquid phase from a solid donor film appears to be the most promising approach to reach the goal of 3D nanofabrication, and the latest achievements obtained with this method are presented and discussed.

Equilibrium probability distributions for low density highway traffic

1966 ◽  
Vol 3 (1) ◽  
pp. 247-260 ◽  
Author(s):  
G. F. Newell
Keyword(s):  
Poisson Process ◽  
Probability Distributions ◽  
Initial Distribution ◽  
Order Effects ◽  
Highway Traffic ◽  
Wide Range ◽  
Headway Distribution ◽  
Equilibrium Distributions ◽  
Initial Distributions ◽  
Special Case

If on a long homogeneous highway there is no interaction between cars, then, under a wide range of conditions, an initial distribution of cars will in the course of time tend toward that of a Poisson process with statistically independent velocities for the cars in any finite interval of highway. Here we will generalize this known property to obtain the following. Suppose cars do interact in such a way as to delay a car when it passes another, but the density of cars is so low that we can neglect simultaneous interactions between three or more cars. There will again be equilibrium distributions of cars to which general classes of initial distributions will converge. These equilibrium distributions are superpositions of two statistically independent processes, one a Poisson process of single free cars with statistically independent velocities, and the other a Poisson process of interacting pairs of cars with various velocities. In the limit of zero interaction, the density of pairs vanishes leaving only the Poisson process of single cars as a special case. To the same order of approximation, including the first order effects of interactions, the headway distribution between consecutive cars will still have exponential tail outside the range of interaction.

Minimizing manoeuvre advantage requirements for a hit-to-kill interceptor

2005 ◽  
Vol 219 (2) ◽  
pp. 113-129
Author(s):  
T L Vincent ◽  
R G Cottrell ◽  
R W Morgan
Keyword(s):  
Time Constant ◽  
Flight Control ◽  
Initial Conditions ◽  
Estimation Error ◽  
Two Dimensions ◽  
Lateral Acceleration ◽  
Proportional Navigation ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Wide Range

Hit-to-kill requires extremely high intercept accuracies. Such performance places severe demands on interceptor manoeuvrability and flight control response time constant when engaging targets that are intentionally or unintentionally manoeuvring. A well-known guidance law for use against a manoeuvring target is augmented proportional navigation (APN). It is an optimal guidance law under various assumptions including a constant-lateral-acceleration target. It is also effective when used against other target manoeuvres provided that the lateral acceleration capabilities of the interceptor is significantly greater than the lateral acceleration capabilities of the target, and if the time constant of the interceptor flight control system is small. The advantage of using a new guidance algorithm for a hit-to-kill interceptor against a manoeuvring target in two dimensions is demonstrated in this paper. A large manoeuvre advantage is not required, and it is effective with time constants that would otherwise degrade the performance of APN. Results are based on a two-dimensional non-linear model with the target performing a weave manoeuvre. The new algorithm can achieve increased intercept accuracy under minimal manoeuvre advantage requirements over a wide range of initial conditions with reasonable levels of angle noise and target manoeuvre estimation error.

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