Gauss Algorithm Research Articles

Modeling a poiseuille flow through a rectangular pipe in a floor slab (PSD)

This study was devoted to the modeling of a laminar fluid flow in a pipe of the rectangular section located in a floor slab. This theme was raised because of its relevance in the large business sector as well as in the areas of energy saving and storage at the residential scale. The equations of motion quantity and heat transport are the classical equations of forced convection. However, to describe the movement amount within the heating slab pipeline, Prandtl simplified model was most appropriate. In addition, this model retains the most important terms for a laminar regime flow. In addition, the modeling of fluid flow conservation in the pipeline was taken into account in the equation system. To achieve the above-mentioned objective, a numerical resolution was made for the system resolution of the Navier-Stokes equations that govern this fluid flow. These equations were discretized by an implicit finite difference method. The system of algebraic equations as well as obtained was solved by the algorithm of Gauss and the algorithm of Thomas. The results obtained such as: the evolution of the fluid velocity profile within the slab according to pipeline to the Reynolds number variation, the fluid temperature have clearly demonstrated the Poiseuille effect on fluid flow. Moreover, the stabilization of the Gauss algorithm and the Thomas algorithm in this numerical modeling was well verified against the tricks that were taken into consideration. The result of this study was that Thomas algorithm and Gauss algorithm are the best in this type of numerical modeling.

An iterative correction method for practically LPN solving

The LPN problem, lying at the core of many cryptographic constructions for lightweight and post-quantum cryptography, has recently received much attention. Accordingly, BKW, Gauss algorithm, and their improved or hybrid variants have been proposed to solve the LPN problem. In this paper, we propose an intelligent method for LPN solving from a wholly new perspective by iterative correcting the secret, which can successfully reduce the dimension of the LPN problem. While the challenge is that there are so many independent secret variables of the given checking parity equations with noise in LPN problems, a set of rules should be developed to effectively direct and correct the secret. To solve this problem, we skillfully introduce the genetic algorithm to simulate the process of iterative correction and further add vaccination technology to guide and speed up the iterative process. Owing to the small memory and data consumption of our algorithm, we conducted experiments and, for the first time, solved the largest practical LPN(256,1/8) instance in 30 days, which shows the superiority of our method. To the best of our knowledge, this is the first time the iterative correction method and the intelligent algorithm have been successfully applied to LPN problems.

Experimental Study and Modeling of a Convective Dryer for Fruits and Vegetables

The present work deals with the study of the thermal performances of a convective dryer for fruits and vegetables. This dryer, operating with energy generated from the combustion of biomass in a boiler connected to a water/air heat exchanger could be a solution to the problematic of energy related to drying. An experimental and theoretical study is carried out on the temperature profile inside the dryer. For this purpose, 10.3 kg of tomatoes were dried on the experimental setup. The operation lasted about 16 hours and reduced the moisture content from 93.8% to 12% in wet basis. The overall thermal efficiency of the convective dryer during the trial is 10.76%. For the theoretical study, the dryer components (boiler, water/air exchanger and drying chamber) are first modeled individually; the different sub-programs are then coupled to form the convective dryer program. The method of global heat balances combined with the one called “ε-NUT” is used. The set of equations is discretized using the implicit method of finite differences, then solved with the Gauss algorithm in Fortran 90. The theoretical results obtained are in good agreement with those measured.

Modeling and simulation of viscoelastic solids under large numbers of loading cycles

An efficient modeling procedure is proposed for viscoelastic (VE) solids subjected to large numbers of loading cycles. While the Laplace–Carson transform (LCT) is often used to solve VE creep or relaxation problems, the originality here is an efficient extension of the approach to a plethora of cycles, based on some key ingredients. The time history of the cyclic loading is decomposed into transient and periodic signals, leading to two subproblems. Each one is transformed into a finite number of linear elastic analyses in the L–C domain. A method to choose the number and positioning of the L–C domain sampling points for each one of the two subproblems is detailed. Specific LCT inversion methods are applied to each subproblem in order to reconstruct the displacement, strain, and stress fields in the time domain. For the transient subproblem, Schapery’s collocation method based on exponential basis functions is used, while a new LCT inversion method is proposed for the periodic subproblem based on sinusoidal basis functions and a Newton–Gauss algorithm. After a verification on well-known 1D functions, the accuracy of the proposed method is assessed on two structural problems with large numbers of cycles. Comparison with reference finite element analyses conducted directly in the time domain shows that the proposed methodology provides excellent predictions, both at local scale (displacement, strain, and stress components at various points) and macroscale (global energy indicator). The important speedup factor (e.g., 32 for 10 k cycles) will increase significantly with the number of cycles, enabling the proposed method to be extended to high cycle fatigue of thermoplastic polymer structures in future work.

Numerical Analysis of the Influence of Buoyancy Ratio and Dufour Parameter on Thermosolutal Convection in a Square Salt Gradient Solar Pond

Revise the abstract as follows: This work aims to investigate numerically the influence of the buoyancy ratio and the Dufour parameter on thermosolutal convection in a square Salt Gradient Solar Pond (SGSP). The absorption of solar radiation by the saline water, the heat losses and the wind effects via the SGSP free surface are considered. The mathematical model is based on the Navier-Stokes equations used in synergy with the thermal energy equation. These equations are solved using the finite volume method and the Gauss algorithm. Velocity-pressure coupling is implemented through the SIMPLE algorithm. Simulations of the SGSP are performed for three values of buoyancy ratio (N = 1, 2 and 10), three values of Dufour parameter (Dƒ = 0, 0.2 and 0.8) and some sample meteorological data (Tangier, Morocco). Results show that the highest dimensionless temperature of the storage zone is found for N = 10. In the same zone and for the same value of N, the dimensionless salt concentration decreases very slightly versus time (unlike for N = 1 or 2). Moreover, increasing Df from 0 to 0.8 causes a decrease in the dimensionless temperature of the SGSP storage zone and this decrease is more pronounced for N = 1 and N = 2.

An Unbiased Symmetric Matrix Estimator for Topology Inference Under Partial Observability

Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem that only a limited part of observed nodes are available. This letter considers the problem of network topology inference under the framework of partial observability. Based on the vector autoregressive model, we propose a novel unbiased estimator for the symmetric network topology with the Gaussian noise and the Laplacian combination rule. Theoretically, we prove that it converges to the network combination matrix in probability. Furthermore, by utilizing the Gaussian mixture model algorithm, an effective algorithm called network inference Gauss algorithm is developed to infer the network structure. Finally, compared with the state-of-the-art methods, numerical experiments demonstrate the proposed algorithm enjoys better performance in the case of small sample sizes.

Modeling Heat Transfers in a Typical Roasting Oven of Burkina Faso

This work concerns a numerical study of heat transfers in a typical roasting oven in Burkina Faso. The numerical methodology is based on the nodal method and the heat transfer equations have been established by performing a heat balance on each node. The equations obtained were then discretized using an implicit finite difference scheme and solved by the Gauss algorithm. The numerical results validated by the experiment show that the heat transfers within the oven are mainly influenced by the gas flow, the ambient temperature, the flame extinction time and the wind speed. Increasing gas flow rate and increasing ambient temperature increase the oven cavity temperature. The increase in wind speed causes a significant drop in the oven cavity temperature after the first 15 minutes of operation. Beyond a wind speed of 3m/s, we observe a convergence of the oven cavity temperatures towards a limit value. Regardless of the time the flame is extinguished, the gas flow rate, the ambient temperature and the wind speed, the oven cavity temperature drops rapidly towards the ambient temperature.

Numerical Study of the Performance of a Double-Insulated Barbecue Oven: Implication for Energy Savings and Thermal Comfort

This work is devoted to a numerical study of the performance of a double insulated barbecue oven using terracotta bricks and plywood. The numerical methodology is based on the nodal method and the heat transfer equations have been established by performing an energy balance on each node. The equations obtained were then discretized using an implicit finite difference scheme and solved by the Gauss algorithm. The numerical results validated by the experiment show that this double insulation considerably reduces the energy losses through the walls of the oven. However, the addition of plywood does not significantly change the energy savings compared to simple terracotta insulation but does drop the external wall temperatures. Thus, for 4 cm of thickness of terracotta bricks and 1 cm of plywood, the energy savings (compared to the non-insulated oven) are of the order of 70% and the temperature of the outer walls of the oven does not exceed not 60°C, which ensures better thermal comfort for users.

Lattice Size and Generalized Basis Reduction in Dimension Three

The lattice size of a lattice polytope P was defined and studied by Schicho, and Castryck and Cools. They provided an “onion skins” algorithm for computing the lattice size of a lattice polygon P in $$\mathbb R^2$$ based on passing successively to the convex hull of the interior lattice points of P. We explain the connection of the lattice size to the successive minima of $$K=(P+(-P))^*$$ and to the lattice reduction with respect to the general norm that corresponds to K. It follows that the generalized Gauss algorithm of Kaib and Schnorr (which is faster than the “onion skins” algorithm) computes the lattice size of any convex body in $$\mathbb R^2$$ . We extend the work of Kaib and Schnorr to dimension three, providing a fast algorithm for lattice reduction with respect to the general norm defined by a convex origin-symmetric body $$K\subset \mathbb R^3$$ . We also explain how to recover the successive minima of K and the lattice size of P from the obtained reduced basis and therefore provide a fast algorithm for computing the lattice size of any convex body $$P\subset \mathbb R^3$$ .

The Harmonically Coupled Admittance Matrix of the Single-Phase Diode Rectifier

The convergence of the iterative harmonic analysis (IHA) of networks with nonlinear loads can be improved if the Gauss algorithm is replaced by the modular decoupled Newton solution (M-DNS). The core of the M-DNS is the harmonically coupled admittance matrix (HCAM) of each nonlinear load. HCAM of high-power converters has received special attention. However, the HCAM of single-phase uncontrolled rectifiers (SPUR) with capacitive smoothing has only been developed under certain simplifications for the SPUR. A reference model for the SPUR is extensively accepted and a detailed analytical procedure (DAP) is the fastest way to obtain the steady state of the SPUR. The main object of this paper is to present a HCAM for the reference model of SPUR with capacitive smoothing. This HCAM is directly derived from a DAP for the converter. Convergence properties of the IHA with this HCAM are studied.

Implicit $\text{Z}_\text{bus}$ Gauss Algorithm Revisited

The implicit Z bus Gauss algorithm is revisited to empower the power flow analysis for microgrids with hierarchical control and frequency- and voltage- dependent loads. The contributions of the revisited Gauss (GRev) algorithm include: 1) a droop-based implicit Z bus Gauss microgrid algorithm which automatically incorporates the distributed energy resources (DERs)/load droop effects; 2) new formulations which accurately integrate the secondary control adjustments for power sharing and voltage regulation. Case studies verify the efficacy, robustness and excellent convergence performance of GRev for both radial and meshed microgrids.

Modeling of Energy Savings Performed by a Barbecue Oven Isolated with Terracotta Bricks

This work is devoted to a numerical study of the energy savings achieved by an oven insulated with terracotta bricks compared to an uninsulated oven. The numerical methodology is based on the nodal method and the transfer equations were obtained by making an energy balance on each node. The equations were then discretized using an implicit scheme with finite differences and solved by the Gauss algorithm. Numerical results validated by the experiment show that the insulation of the oven with terracotta bricks considerably reduces the energy losses through the walls, but the reduction level varies according to the thickness of the bricks. The optimal thicknesses of the bricks are between 3 and 4 cm, which corresponds to energy savings of between 60 to 70% compared to the uninsulated oven. The energy saved increases the energy efficiency of the oven from 15-17% to 25-29%.

Lattice Reduction Over Imaginary Quadratic Fields

Complex bases, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices. In this work, we study such lattices and their reduction algorithms. Firstly, when the lattice is spanned over a two dimensional basis, we show that the algebraic variant of Gauss's algorithm returns a basis that corresponds to the successive minima of the lattice if the chosen ring is Euclidean. Secondly, we extend the celebrated Lenstra-Lenstra-Lovász (LLL) reduction from over real bases to over complex bases. Properties and implementations of the algorithm are examined. In particular, satisfying Lovász's condition requires the ring to be Euclidean. Lastly, we numerically show the time-advantage of using algebraic LLL by considering lattice bases generated from wireless communications and cryptography.

Modeling and Numerical Simulation of Heat Transfers in a Metallic Pressure Cooker Isolated with Kapok Wool

In this work, a numerical study of heat transfers in a metallic pressure cooker isolated with kapok wool was carried out. This equipment works like a thermos, allowing finishing cooking meals only thanks to the heat stored at the beginning of cooking, which generates energy savings. Cooked meals are also kept hot for long hours. In our previous work, we have highlighted the performances of the pressure cooker when making common dishes in Burkina Faso. Also, the parameters (thickness and density) of the insulating matrix allowing having such performances as well as the influence of the climatic conditions on the pressure cooker operation were analyzed in detail in this present work. The numerical methodology is based on the nodal method and the transfer equations obtained by making an energy balance on each node have been discretized using an implicit scheme with finite differences and resolved by the Gauss algorithm. Numerical results validated experimentally show that the thickness of the kapok wool as well as its density play an important role in the pressure cooker operation. In addition, equipment performances are very little influenced by the weather conditions of the city of Ouagadougou (Burkina Faso).

Parametric Optimization of Thermal Comfort in Extreme Weather Conditions

This work focuses on the numerical investigation of different modes of heat exchangebetween the habitat and its environment in an extremely hot climate to optimize thermal comfort.Notably, to optimize habitable comfort, it is essential to model the solar flux and the temperatureabsorbed by the habitat walls. In this context, we have developed an analytical model to predict heatexchange for a habitat in the Adrar region. The heat transfer equations have been established in eachwall of the habitat. These equations were discretized by the finite difference method and solvedusing the Gauss algorithm. The models developed were validated with climatic data measured in theresearch unit ''URER'MS'' in Adrar. The results obtained showed that building materials andextreme weather conditions were the decisive parameters of unwanted overheating.

Parallel real-world LU decomposition: Gauss vs. Crout algorithm

Abstract This paper presents numerical experiments with assorted versions of parallel LU matrix decomposition algorithms (Gauss and Crout algorithm). The tests have been carried out on the hardware platform with fourcore Skylake processor featuring hyperthreading technology doubling virtually core number. Parallelization algorithms have been implemented with the aid of classic POSIX threads library. Experiments have shown that basic 4-thread acceleration of all parallel implementations is almost equal to the number of threads/processors. Both algorithms are worth considering in real-world applications (Florida University collection). Gauss algorithm is a better performer, with respect to timing, in the case of matrices with lower density of nonzeros, as opposed to higher density matrices. The latter are processed more efficiently with the aid of Crout algorithm implementation.

Volumes and distributions for random unimodular complex and quaternion lattices

Two themes associated with invariant measures on the matrix groups SLN(F), with F=R,C or H, and their corresponding lattices parametrised by SLN(F)/SLN(O), O being an appropriate Euclidean ring of integers, are considered. The first is the computation of the volume of the subset of SLN(F) with bounded 2-norm or Frobenius norm. Key here is the decomposition of measure in terms of the singular values. The form of the volume, for large values of the bound, is relevant to asymptotic counting problems in SLN(O). The second is the problem of lattice reduction in the case N=2. A unified proof of the validity of the appropriate analogue of the Lagrange–Gauss algorithm for computing the shortest basis is given. A decomposition of measure corresponding to the QR decomposition is used to specify the invariant measure in the coordinates of the shortest basis vectors. With F=C this allows for the exact computation of the PDF of the first minimum (for O=Z[i] and Z[(1+−3)/2]), and the PDF of the second minimum and that of the angle between the minimal basis vectors (for O=Z[i]). It also encodes the specification of fundamental domains of the corresponding quotient spaces. Integration over the latter gives rise to certain number theoretic constants, which are also present in the asymptotic forms of the PDFs of the lengths of the shortest basis vectors. Siegel's mean value gives an alternative method to compute the arithmetic constants, allowing in particular the computation of the leading form of the PDF of the first minimum for F=H and O the Hurwitz integers, for which direct integration was not possible.

Research on Magnetic Field Measurement System Based on Distributed Magnetic Field Sensing and Numerical Integration Method

Magnetic field measurement is one of the key contents in the field of electromagnetic protection. In this paper, a magnetic field measurement system based on distributed magnetic sensing and a high-accuracy numerical integration method is proposed. And a magnetic field sensor with simple structure, small size, and wide measurement band is designed, which includes three magnetic field measurement coils that can realize the accurate measurement of a three-dimensional magnetic field. The output of the magnetic field measurement coil is a differential signal that needs to be reduced by the integrator. To solve the problems of traditional analog integrator and common digital integrator, this paper proposes a high-precision digital integral algorithm based on Gauss algorithm, which can effectively improve the accuracy of the integrator. Test results indicate that the error of the magnetic field measurement system is less than 5% in the range of 0.05–5T.

Gaseous Fuel Level Measurement of Ultrasonic Wave based on Gauss Algorithm

Gaseous Fuel Level Measurement of Ultrasonic Wave based on Gauss Algorithm

Numerical Simulation of Heat Exchanges for a Desert House Type ADRAR

The main objective of this work is to study the thermal exchanges in a habitable enclosure located in a desert region of Algeria (Adrar). This latter is considered as an air volume of parallelepiped shape limited by horizontal and vertical flat walls. The walls are the only capacitive elements of the enclosure. They are thermally coupled by convection and radiation and are the seat of conductive flux. The external facades of the enclosure are the seat of a convective flux with the external air and radiative exchanges with the environment (ground and sky). Openings (cracks, sealing defects, infiltration orifices, renewal orifices, etc.) allow the air to circulate inside the habitable enclosure and between the inside and the outside. Thermal exchanges are studied using the balance equations established at each wall of the enclosure. These equations have been discretized by an implicit finite difference method. The systems of algebraic equations thus obtained have been solved by the Gauss algorithm using the nodal method. The effects of the outdoor ambient temperature, the density of the incident solar flux on the facades and the orientation of the habitable enclosure in the meridian plane on the temperature distributions of the internal walls and the filled air in the enclosure havec been analyzed on the basis of recent climate data measured at the ADRAR Saharan Renewable Energy Research Unit. An analysis of the evolution of the internal ambient temperature as a function of the wind exposure factor of the heated space and of the degree of leaktightness of the doors and windows was also carried out at the end of this work. An acceptable agreement was found between the numerical results and those measured by the radiometric station. Moreover, the results obtained show that the building material used in this region causes undesirable overheating due to its thermal inertia.