Approximations for traveltime, slope, curvature, and geometrical spreading of elastic waves in layered transversely isotropic media

Each seismic body wave, including quasi compressional, shear, and converted wave modes, carries useful subsurface information. For processing, imaging, amplitude analysis, and forward modeling of each wave mode, we need approximate equations of traveltime, slope (ray-parameter), and curvature as a function of offset. Considering the large offset coverage of modern seismic acquisitions, we propose new approximations designed to be accurate at zero and infinitely large offsets over layered transversely isotropic media with vertical symmetry axis (VTI). The proposed approximation for traveltime is a modified version of the extended generalized moveout approximation that comprises six parameters. The proposed direct approximations for ray-parameter and curvature use new, algebraically simple, equations with three parameters. We define these parameters for each wave mode without ray tracing so that we have similar approximate equations for all wave modes that only change based on the parameter definitions. However, our approximations are unable to reproduce S-wave triplications that may occur in some strongly anisotropic models. Using our direct approximation of traveltime derivatives, we also obtain a new expression for the relative geometrical spreading. We demonstrate the high accuracy of our approximations using numerical tests on a set of randomly generated multilayer models. Using synthetic data, we present simple applications of our approximations for normal moveout correction and relative geometrical spreading compensation of different wave modes.

Estimating computational limits on theoretical descriptions of biological cells

There has been much success recently in theoretically simulating parts of complex biological systems on the molecular level, with the goal of first-principles modeling of whole cells. However, there is the question of whether such simulations can be performed because of the enormous complexity of cells. We establish approximate equations to estimate computation times required to simulate highly simplified models of cells by either molecular dynamics calculations or by solving molecular kinetic equations. Our equations place limits on the complexity of cells that can be theoretically understood with these two methods and provide a first step in developing what can be considered biological uncertainty relations for molecular models of cells. While a molecular kinetics description of the genetically simplest bacterial cell may indeed soon be possible, neither theoretical description for a multicellular system, such as the human brain, will be possible for many decades and may never be possible even with quantum computing.

EQUATIONS FOR THE OPERATING TEMPERATURE OF THERMOSENSITIVE ELEMENTS OF FIRE DETECTORS EMBEDDED IN A CONCRETE BLOCK

Statement of the problem. Solving the problem of giving the properties of a building structure to detect fires outside buildings is one of the ways to prevent the transition of fire from one building to another. Embedding of fire automation equipment in construction products should be carried out after making the appropriate calculations. The absence of an expression for determining the temperature of the heat-sensitive element of a fire detector inside a concrete block requires detailed calculations. At the same time, it is necessary to study the influence of the distance to the object of a possible fire, the size of the heat-sensitive element, and the heat flow on the time of fire detection by a construction product included in the smart home system.Results. As part of the temperature measurement of heat-sensitive elements of fire detectors inside the concrete block, empirical data were obtained. This information allows us to describe the radiant heat exchange at an early stage of a fire. This is typical of open burning outdoors. Conclusions. Approximate equations are obtained for determining the temperature and response time of a fire detector inside a concrete block at the initial stage of a fire, depending on the distance to the fire object (radiation source), heat flow, and the size of the thermosensitive element. These values can be determined with sufficient accuracy.

On the approximations of solutions to stochastic differential equations under polynomial condition

The subject of this paper is an analytic approximate method for a class of stochastic differential equations with coefficients that do not necessarily satisfy the Lipschitz and linear growth conditions but behave like a polynomials. More precisely, equations from the observed class have unique solutions with bounded moments and their coefficients satisfy polynomial condition. Approximate equations are defined on partitions of a time interval, and their coefficients are Taylor approximations of the coefficients of the initial equation. The rate of Lp convergence increases when degrees in Taylor approximations of coefficients increase. At the end of the paper, an example is provided to support the main theoretical result.

Угловые характеристики сенсора коэффициента преломления на основе отражательного интерферометра

The angular properties of sensor, implemented in Kretschmann’s scheme, where the optimized for oblique incidence of light thin-film reflection interferometer acts as a sensing element, are described in the paper. Analytical equations, defining the sensor’s properties for S and P polarization states at working wavelength in vicinity of working angle of incidence, are provided, as well as approximate equations for main parameters of sensor: sensitivity, angular full width at half maximum, contrast and figure of merit. The possibility to vary the named parameters by choosing appropriate metal and dielectric layers of the structure is shown. For an example, the numerical calculations are made for one of special cases, optimized for S polarization state, as having larger figures of merit. The dependencies of angular properties on number of layers and base thickness are demonstrated. It is shown, that angular measurements with this method are theoretically capable of infinite figures of merit, and in practice they are only limited by losses in layered structure and beam divergency. The recommendations for experimental realization of method are given.

EQUATIONS FOR THE OPERATING TEMPERATURE OF THERMOSENSITIVE ELEMENTS OF FIRE DETECTORS EMBEDDED IN A CONCRETE BLOCK

Постановка задачи. Решение проблемы придания строительной конструкции свойств, позволяющих обнаруживать пожары вне зданий, является одним из направлений предупреждения перехода огня с одного здания на другое. Встраивание средств пожарной автоматики в строительные изделия должно осуществляться после проведения соответствующих расчетов. Отсутствие выражения, позволяющего определить температуру термочувствительного элемента пожарного извещателя, встроенного в бетонный блок, вынуждает проводить детальные расчеты. Вместе с тем, необходимо исследовать влияние расстояния до объекта возможного пожара, размера термочувствительного элемента, теплового потока на время обнаружения пожара строительным изделием, входящим в систему «умный дом». Результаты. В процессе измерения температуры термочувствительных элементов пожарных извещателей, встроенных в бетонные блоки, получены эмпирические данные, позволяющие описать на ранней стадии пожара лучистый теплообмен, характерный для открытого горения вне помещений. Выводы. Получены приближенные уравнения, которые позволяют с достаточной точностью определить температуру и время срабатывания пожарного извещателя, встроенного в бетонный блок, на начальной стадии пожара в зависимости от расстояния до объекта пожара (источника излучения), теплового потока, размера термочувствительного элемента. Statement of the problem. Solving the problem of giving the properties of a building structure to detect fires outside buildings is one of the ways to prevent the transition of fire from one building to another. Embedding of fire automation equipment in construction products should be carried out after making the appropriate calculations. The absence of an expression for determining the temperature of the heat-sensitive element of a fire detector inside a concrete block requires detailed calculations. At the same time, it is necessary to study the influence of the distance to the object of a possible fire, the size of the heat-sensitive element, and the heat flow on the time of fire detection by a construction product included in the smart home system. Results. As part of the temperature measurement of heat-sensitive elements of fire detectors inside the concrete block, empirical data were obtained. This information allows us to describe the radiant heat exchange at an early stage of a fire. This is typical of open burning outdoors. Conclusions. Approximate equations are obtained for determining the temperature and response time of a fire detector inside a concrete block at the initial stage of a fire, depending on the distance to the fire object (radiation source), heat flow, and the size of the thermosensitive element. These values can be determined with sufficient accuracy.

Gravity with Higher Derivatives in D-Dimensions

The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations of motion, (3) derivation of approximate equations in the presence of a small parameter in the system, and (4) the method of test functions. Some applications are presented to illustrate each method. The unification of two necessary elements of a future theory is also kept in mind—the extra dimensions and the extended form of the gravity.

Wave-equation time migration

Time migration, as opposed to depth migration, suffers from two well-known shortcomings: (1)approximate equations are used for computing Green’s functions inside the imaging operator; (2) in case of lateral velocity variations, the transformation between the image ray coordinates andthe Cartesian coordinates is undefined in places where the image rays cross. We show that thefirst limitation can be removed entirely by formulating time migration through wave propagationin image-ray coordinates. The proposed approach constructs a time-migrated image without relyingon any kind of traveltime approximation by formulating an appropriate geometrically accurateacoustic wave equation in the time-migration domain. The advantage of this approach is that thepropagation velocity in image-ray coordinates does not require expensive model building and canbe approximated by quantities that are estimated in conventional time-domain processing. Synthetic and field data examples demonstrate the effectiveness of the proposed approach and show that theproposed imaging workflow leads to a significant uplift in terms of image quality and can bridge thegap between time and depth migrations. The image obtained by the proposed algorithm is correctlyfocused and mapped to depth coordinates it is comparable to the image obtained by depth migration.