Step Pyramid Distribution for Prime Numbers

In this document, we will present a new way to visualize the distribution of Prime Numbers in the number system to spot Prime numbers in a subset of numbers using a simpler algorithm. Then we will look throw a classification algorithm to check if a number is prime using only 7 simple arithmetic operations with an algorithm complexity less than or equal to O (7) operations for any number.

Effect of Fin Number and Position on Non-linear Characteristics of Natural Convection Heat Transfer in Internally Finned Horizontal Annulus

Detailed numerical calculations are performed for investigating the effect of fin number and position on unsteady natural convection heat transfer in internally finned horizontal annulus. The SIMPLER algorithm with Quick scheme is applied for solving the Navier Stokes equations of flow and heat transfer. The results show that the heat transfer rate in annulus with fins increases with the increasing numbers of fin and Rayleigh numbers. For Ra = 2 × 105, the effect of numbers of fins and fins position at the bottom part on the unsteady solutions can be neglected, because the self-oscillation phenomenon is mainly affected by natural convection at the upper part of annulus. Although the fin positions cannot increase heat transfer rate significantly in the case of four fins, the self-oscillated solutions can be suppressed by altering fins position.

Diagnostic Strategies to Identify Patients with Genetic Salt-Losing Tubulopathies

Background: Distinguishing patients with the inherited salt-losing tubulopathies (SLT), Gitelman or Bartter syndrome (GS or BS) from wildtype (WT) patients who purge is difficult. We decided to identify clinical/biochemical characteristics which correctly classify SLT. Methods: 66 patients with possible SLT were recruited to a prospective observational cohort study at the UCL Renal Tubular Clinic (London). 31 datapoints were recorded on each patient. All patients were genotyped for pathogenic mutations in genes which cause SLT; 39 patients had pathogenic variants in genes causing SLT. We obtained similar datasets from cohorts in Taipei and Kobe; the combined dataset comprised 419 patients, 291 had genetically confirmed SLT. London and Taipei datasets were combined to train machine learning (ML) algorithms. These were then tested on the Kobe dataset to determine the best biochemical predictors of genetic confirmation of SLT. Results: Single biochemical variables (e.g. plasma renin) were significantly, but inconsistently different between SLT and WT, in the London and combined cohorts. A decision table algorithm using serum bicarbonate and urinary sodium excretion (FENa) achieved a classification accuracy of 74%. A simpler algorithm based on the FECl achieved a classification accuracy of 61%. This was superior to all of the single biochemical variables identified previously.

Pressure-Velocity Coupling Schemes for Bouyancy Driven Flow in a Differentially Heated Cavity Using F.V.M and Matlab

Numerical analysis of fluid flow is anchored on the laws of conservation. A challenge in solving the momentum equation arises due to the unavailability of an explicit pressure equation. To avoid solving the pressure term most researchers have eliminated it by cross differentiating the x and the y two dimensional momentum equations and subtracting them. This method introduces more variables to be solved in comparison to the primitive variables and is restricted to two-dimensional flows as streamlines do not exist in three-dimension. This method thus presents a serious limitation in analysis of fluid flow. In this study an equation for computing pressure has been developed using pressure - velocity coupling and used in solving the governing equations. The performance of three pressure velocity schemes namely; the Semi Implicit Method for Pressure linked Equation (SIMPLE), SIMPLE Revised (SIMPLER) and SIMPLE Consistent (SIMPLEC) for laminar buoyancy driven flow has been tested in order to establish the scheme that gives results consistent with bench mark data. The equations governing the flow are solved iteratively using finite volume method together with the central difference interpolating scheme. The solutions are presented for Rayleigh numbers of 103, 104, and 105. This resulted in the velocity profiles for the SIMPLE, SIMPLER, and SIMPLEC algorithm for a Rayleigh number of 104 and 105 converging to the same path. At a Rayleigh number of 103 however, SIMPLER algorithm undergoes a degradation in convergence with grid refinement at the baffle region. Results predicted by using the SIMPLEC algorithm are thus able to effectively compute the velocity of fluid flow in a differentially heated square enclosure with baffles for both low and higher Rayleigh numbers irrespective of the grid size.

The Influence of Combined Turbulators on the Hydraulic-Thermal Performance and Exergy Efficiency of MWCNT-Cu/Water Nanofluid in a Parabolic Solar Collector: A Numerical Approach

The present research benefits from the finite volume method in investigating the influence of combined turbulators on the thermal and hydraulic exergy of a parabolic solar collector with two-phase hybrid MWCNT-Cu/water nanofluid. All parabolic geometries are produced using DesignModeler software. Furthermore, FLUENT software, equipped with a SIMPLER algorithm, is applied for analyzing the performance of thermal and hydraulic, and exergy efficiency. The Eulerian–Eulerian multiphase model and k-ε were opted for simulating the two-phase hybrid MWCNT-Cu/water nanofluid and turbulence model in the collector. The research was analyzed in torsion ratios from 1 to 4, Re numbers from 6,000 to 18,000 (turbulent flow), and the nanofluid volume fraction of 3%. The numerical outcomes confirm that the heat transfer and lowest pressure drop are relevant to the Re number of 18,000, nanofluid volume fraction of 3%, and torsion ratio of 4. Furthermore, in all torsion ratios, rising Re numbers and volume fraction lead to more exergy efficiency. The maximum value of 26.32% in the exergy efficiency was obtained at a volume fraction of 3% and a torsion ratio of 3, as the Re number goes from 60,000 to 18,000.

Testing the Magnetohydrodynamic Analysis Software with Natural Convection and Geodynamo Problems

В рамках метода контрольного объема разработан программный код для численного решения задач неидеальной магнитной гидродинамики вязкой несжимаемой жидкости на структурированных разнесенных сетках в сферических координатах. При дискретизации уравнения индукции магнитного поля использован алгоритм ограниченного переноса (Сonstrained Transport Algorithm) и схема QUICK с методом отложенной коррекции для аппроксимации конвективных членов. Для решения уравнений гидродинамики использован алгоритм SIMPLER. Программный код разработан для моделирования естественной конвекции и гидромагнитного динамо во вращающемся шаре или сферическом слое. Представлены результаты решения тестовых задач естественной конвекции и геодинамо с вакуумными граничными условиями, демонстрирующие достаточно точное соответствие результатам эталонных расчетов. Программное обеспечение разработано для ускорителей вычислений, поддерживающих технологию CUDA, с использованием набора расширений к языку программирования Фортран.   Using the control volume method we developed the software for the numerical solution of viscous incompressible fluid resistive magnetohydrodynamics problems on structured staggered meshes in spherical coordinates. The constrained transport algorithm and the QUICK method with delayed correction for the approximation of the convective terms were used for the discretization of the magnetic field induction equation. The SIMPLER algorithm was applied to solving the hydrodynamic equations. We developed software for modeling natural convection and the hydromagnetic dynamo in a rotating sphere or spherical shell. We proposed an algorithm for the numerical solution of the geodynamo problem with vacuum boundary conditions. The results of solving natural convection and geodynamo benchmark problems with vacuum boundary conditions are presented; they demonstrate a fairly accurate agreement with the reference calculations. The software supports CUDA-enabled accelerators and uses a set of extensions to the Fortran programming language.

Optimization of Inclination Angle of Cavity and Characteristics of Attached Fins on the Absorber for Performance Enhancement of Solar Collectors

This research investigation was undertaken in ANDUAT, Kumarganj, Ayodhya, Uttar Pradesh, India to study the numerical optimization of natural convection heat suppression in a solar flat plate collector with straight fins. Optimal characteristics of an array of thin fins attached on the absorber plat were obtained by Particle Swarm Optimization algorithm (PSOA). Free convection considered dominant in the cavity. Governing equations contained continuity; momentum and energy are discretized by finite volume method. The medium is considered incompressible, whose free convection is dominant and Boussinesq approximation is applied. A simplified model of real systems is applied with free convection. Free convection problem is solved by SIMPLER algorithm. Two confined cavities with aspect ratios 30 and 60 are considered as flat plate solar collectors. The results indicate that significant reduction on the free convection heat loss can be obtained from solar flat plate collector by using plate fins, and an optimal plate fins configuration exit for minimal natural convection heat loss for a given range of Rayleigh number. Reduction of up to a maximum of 25% at 0 inclination angle was observed in aspect ratio 30. Results showed PSOA is able to obtain characteristics of attached adiabatic fins on the absorber plate also it can obtain optimal inclination angle of cavity to decrease heat losses from solar collectors. The results obtained provide a novel approach for improving design of flat plate solar collectors for optimal performance.

Emergence of transverse size in electric streamers

<p>The accurate determination of parameters of electric streamer propagation in air, such as their velocity, transverse size (radius) and the maximum field at the tip, is extremely important, e.g., for the studies of further lightning development and acceleration of electrons at the tip, which may lead to generation of x-rays. Relations between these parameters produce a family of streamer-shaped solutions, while the radius remains undetermined. We hypothesize that all these solutions are, in fact, valid solutions of hydrodynamic equations, but the physical radius emerges when one solution is selected by the condition of being maximally unstable, i.e., having the highest velocity.</p><p>Direct verification of this hypothesis by hydrodynamic simulations is complicated by the fact that the streamer length is one of the background conditions which determine its parameters, and in a propagating streamer the length is constantly changing. To circumvent this, we simulate a `steady-state' streamer, such that its length is kept constant by synchronizing the motion of the electrode to which it is attached. We show that the predicted maximally-unstable selected solution does, in fact, emerge in the infinite time limit of the simulation. We note, however, that we were yet unable to test the first part of the hypothesis, i.e. to produce the non-selected solutions in the predicted family, as they are quickly replaced by the selected one.</p><p>We present the calculated streamer parameter dependence on external uniform field and streamer length for an isolated streamer and streamers propagating parallel to each other. In the latter case, the field of neighboring streamers makes the streamer propagation independent of its length when it exceeds the inter-streamer distance. We draw parallels of this situation to the selected solution for a viscous Saffman-Taylor finger of infinite length in a narrow channel [Luque et al, 2008, doi:10.1103/PhysRevE.78.016206].</p><p>The practical interest of this work lies in reducing the complexity of streamer propagation modeling, by avoiding detailed simulation of the streamer head, if we can calculate the parameters by a simpler algorithm.</p>

An Efficient Broadband Adaptive Beamformer without Presteering Delays

Broadband adaptive beamformers have been widely used in many areas due to their ability of filtering signals in space domain as well as in frequency domain. However, the space-time array employed in broadband beamformers requires presteering delays to align the signals coming from a specific direction. Because the presteering delays are direction dependent, it is difficult to make precise delays in practice. A common way to eliminate the presteering delays is imposing constraints on the weight vector of the space-time array. However, the structure of the constraint matrix is not taken into account in the existing methods, leading to a computational complexity of O(N2) when updating the weight vector. In this paper, we describe a new kind of constraint method in time domain that preserves the block diagonal structure of the constraint matrix. Based on this structure, we design an efficient weight vector update algorithm that has a computational complexity of O(N). In addition, the proposed algorithm does not contain matrix operations (only scalar and vector operations are involved), making it easy to be implemented in chips such as FPGA. Moreover, the constraint accuracy of the proposed method is as high as the frequency constraint method when the fractional bandwidth of the signal is smaller than 10%. Numerical experiments show that our method achieves the same performance of the state-of-the-art methods while keeping a simpler algorithm structure and a lower computational cost.

Numerical Study of the Effect of the Location of Baffles on the Flow and Heat Transfer of A Newtonian Fluid in A Ventilated Enclosure

Flow and heat transfer analysis in ventilated cavities is one of the most widely studied problems in thermo-fluids area. Two-dimensional mixed convection in a ventilated rectangular cavity with baffles is studied numerically and the fluid considered in this study is hot air (Pr = 0.71). The horizontal walls are maintained at a constant temperature, higher than that imposed on the vertical ones. Two very thin heat-conducting baffles are inserted inside the enclosure, on its horizontal walls, to control the flow of convective fluid. The governing equations are discretized using the finite volume method and the SIMPLER algorithm to treat the coupling velocity–pressure. Line by line method is used to solve iteratively the algebraic equations. The effect of the Richardson number Ri (0.01- 100) and the location of the baffles within the cavity on the isothermal lines, streamlines distributions and the average Nusselt number (Nu) has been investigated. The result shows that the location opposite the baffles, close to the fluid outlet, is the optimal choice to be considered for industrial applications.