One-dimensional Solution Research Articles

Numerical calculation of dynamic models with non-power nonlinearities

The solution to the actual problem in the numerical calculation of dynamic models with nonlinearities described by non-power elementary functions is considered. The computational difficulties of using power series to solve the problem are analyzed. A procedure based on the analytical-numerical method developed by the authors is proposed to overcome these difficulties. The numerical procedure is applicable for models described by the system of nonlinear differential equations in the Cauchy normal form. The proposed procedure possesses all the advantages of power series, as well as eliminates the necessity of using power series compositions and developing special estimates. The achieved result increases the formalization level of nonlinear dynamics based on dynamic models with non-power nonlinearities. In the numerical procedure, the obtained solutions estimates are used and the boundaries of the one-dimensional solutions areas are adjusted in order to come to unknown precise solutions. As an example, the calculation of nonlinear autonomous dynamic model type “damped pendulum” is represented.

Soliton-like unipolar objects in nonequilibrium dissipative media

For electromagnetic pulses without a carrier frequency, propagating in a system of multilevel atoms with a fast irreversible relaxation of the induced dipole moment, but a slow relaxation of the populations of quantum states, the nonlinear integro-differential equations of the ‘reaction–diffusion’ type are derived. One-dimensional soliton-like solutions of these equations in the form of unipolar pulses are found and analyzed. It is shown that such pulses can be formed in a nonequilibrium medium. These pulses transfer a medium to other metastable states, which depend on the input conditions. The propagation of these soliton-like signals is accompanied by a change in the populations of quantum states of atoms in the modes of switching waves with the memory of input conditions.

3D Wavelet Finite-Element Modeling of Frequency-Domain Airborne EM Data Based on B-Spline Wavelet on the Interval Using Potentials

We present a wavelet finite-element method (WFEM) based on B-spline wavelets on the interval (BSWI) for three-dimensional (3D) frequency-domain airborne EM modeling using a secondary coupled-potential formulation. The BSWI, which is constructed on the interval (0, 1) by joining piecewise B-spline polynomials between nodes together, has proved to have excellent numerical properties of multiresolution and sparsity and thus is utilized as the basis function in our WFEM. Compared to conventional basis functions, the BSWI is able to provide higher interpolating accuracy and boundary stability. Furthermore, due to the sparsity of the wavelet, the coefficient matrix obtained by BSWI-based WFEM is sparser than that formed by general FEM, which can lead to shorter solution time for the linear equations system. To verify the accuracy and efficiency of our proposed method, we ran numerical experiments on a half-space model and a layered model and compared the results with one-dimensional (1D) semi-analytic solutions and those obtained from conventional FEM. We then studied a synthetic 3D model using different meshes and BSWI basis at different scales. The results show that our method depends less on the mesh, and the accuracy can be improved by both mesh refinement and scale enhancement.

Misinformation vs. Situational Awareness: The Art of Deception and the Need for Cross-Domain Detection.

The world has been afflicted by the rise of misinformation. The sheer volume of news produced daily necessitates the development of automated methods for separating fact from fiction. To tackle this issue, the computer science community has produced a plethora of approaches, documented in a number of surveys. However, these surveys primarily rely on one-dimensional solutions, i.e., deception detection approaches that focus on a specific aspect of misinformation, such as a particular topic, language, or source. Misinformation is considered a major obstacle for situational awareness, including cyber, both from a company and a societal point of view. This paper explores the evolving field of misinformation detection and analytics on information published in news articles, with an emphasis on methodologies that handle multiple dimensions of the fake news detection conundrum. We analyze and compare existing research on cross-dimensional methodologies. Our evaluation process is based on a set of criteria, including a predefined set of performance metrics, data pre-processing features, and domains of implementation. Furthermore, we assess the adaptability of each methodology in detecting misinformation in real-world news and thoroughly analyze our findings. Specifically, survey insights demonstrate that when a detection approach focuses on several dimensions (e.g., languages and topics, languages and sources, etc.), its performance improves, and it becomes more flexible in detecting false information across different contexts. Finally, we propose a set of research directions that could aid in furthering the development of more advanced and accurate models in this field.

A discrete scheme of the fluid motion equation based on the pore-scale SPH method

To study the phenomenon of convection diffusion and solute migration in porous media, the smoothed particle hydrodynamics method is used to solve the N–S equation describing pore water flow and the linear homogeneous second-order differential equation describing the solute diffusion process. The accuracy of the simulation method is verified by solving the one-dimensional definite solution of the convection diffusion equation at a low Peclet (Pe) number. Under the condition of a high Pe number, the simulation experiment of solute breakthrough porous media at the pore scale is simulated. Through the analysis of the velocity distribution of fluid particles in pore channels of porous media and the mechanical dispersion process of solutes in porous media, it is found that the flow velocity presents a parabolic distribution in the pore channel, and the particles with high velocity are mainly concentrated in the middle of the pore channel between the solid particles. The solute dispersion is obvious in porous media, and some fluid particles containing solutes penetrate porous media earlier along fast-flowing pore channels. Finally, the solute breakthrough curve and the motion path length of the particle are obtained through the simulation experiment. The calculation methods of the dispersion degree and tortuosity of porous media are further given, and the dispersion degree of porous media in this paper is 0.000 95 m.

Simulation study for cross-sectional absorption distribution in turbid medium using spatially resolved backscattered light with lateral scanning and one-dimensional solution of nonlinear inverse problem

For a practical technique of cross-sectional imaging of animal bodies, we developed a new method using spatially resolved backscattered light. This method is based on the solution of the one-dimensional nonlinear inverse problem, and on the lateral scan of the source–detector pair along the object surface. Using this method, unknown variables in inverse problems can be reduced more greatly than when using conventional methods. A stable solution for the inverse problem becomes possible. The possibility of using the proposed method was assessed using simulation analysis. The results verified that cross-sectional imaging from several to 10 millimeter depths is possible for animal tissue. This analysis clarified the specific spatial resolution and accuracy in the estimated absorption coefficient. Distortionless imaging was confirmed. Results suggest that the proposed method represents new options as a stable and practical method for biological cross-sectional imaging.

Pulse compression favorable frequency modulated thermal wave imaging for non-destructive testing and evaluation: an analytical study

InfraRed Thermography (IRT) is one of the non-destructive testing and evaluation (NDT&E) approach widely used for testing and evaluation of wide verity of materials such as metals, semiconductors and composites. Among the widely used Thermal NDT&E (TNDT&E) approaches for better depth resolution and sensitivity for detection of defects located at different depths inside the test specimen recently proposed correlation based approach gained importance due to its enhanced defect detection capabilities. The present paper introduces a novel one-dimensional analytical solution for the frequency modulated excitation scheme under adiabatic boundary conditions for detection of flat bottom holes as defects in a mild steel sample. The performance of the Pulse Thermography (PT), Lock-in Thermography (LT) and Frequency Modulated Thermal Wave Imaging (FMTWI) methods are highlighted their defect detection capabilities have been compared by adopting the recently introduced correlation based post-processing approach. Finally, the proposed analytical method has been validated with the results obtained from the commercially available finite element based software.

Turbulent flame-wall interactions for flames diluted by hot combustion products

Flames diluted by combustion products can reduce emissions such as Carbon Monoxide (CO) and Nitrogen Oxides (NOx) in industrial applications. In gas turbines, these flames are confined in a combustor and can interact with relatively cold walls. This interaction can quench the flame, producing incomplete combustion products. In this study, Flame-Wall Interaction (FWI) for methane/air flames diluted by hot combustion products is investigated using direct numerical simulation. A three-Dimensional (3D) turbulent V-flame in a channel with isothermal hot and cold walls is simulated.It is shown that a main reaction zone in the central region between two walls supported by periodic bulk ignition events changes the position of volumetric reaction zones where CO is formed. The cold wall leads to a longer flame, thereby having disproportionately large contribution to the exhaust CO. Near-wall turbulence-flame interaction creates wrinkled and streaky flame surfaces, and localises the near-wall CO distribution. High mean CO mass fraction develops in the free-stream while a high magnitude of the peak RMS CO mass fraction is present closer to the wall. It is also shown that one-dimensional flame solutions can reasonably describe the changes of CO mass fraction as a function of temperature in the free-stream region and some parts of the near-wall region but not close to the wall. Turbulent mixing and diffusion effects contribute to this deviation. The results highlight the complexities involved in CO modelling for diluted flames and set a benchmark for future work.

Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z-graded graphs

We consider discrete one-dimensional nonlinear equations and present the procedure of lifting them to Z-graded graphs. We identify conditions that allow one to lift one-dimensional solutions to solutions on graphs. In particular, we prove the existence of solitons for static potentials on graded fractal graphs. We also show that even for a simple example of a topologically interesting graph, the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z-graded graph.

Theoretical and Experimental Estimation of Soil Temperature Distribution in Arid Region

In this work, the one-dimensional finite element solution of the transient heat equation was used to calculate the temperature distribution through the soil in the arid region. As an example, Baghdad city was chosen due to the dryness of its weather which can be regarded as an arid region. The solar radiation, ambient temperature, relative humidity, soil thermal properties, soil water content, and wind speed were used as input parameters to the solution to obtain the surface and in-depth temperature distribution in the soil. The solar light components that hit the soil have been obtained theoretically and measured experimentally with good nearby results. The obtained temperature distributions were compared with experimental data and good nearby results could verify the used methodology.

A 1-D Search Approach for Single Sensor Passive Localization Based on Signal Periodicity

An efficient one-dimensional search solution is proposed for single-sensor emitter localization based on signal periodicity. By introducing an intermediate variable, this single-sensor localization problem can be solved by solving a set of equations for classic multi-sensor time difference of arrival localization, whose algebraic solutions can be obtained by the well-known two-stage weighted least squares (TSWLS) algorithm. In this manner, the two-dimensional or three-dimensional search for the emitter location can be replaced by a one-dimensional search for the intermediate variable. Simulations indicate that, at the expense of a small loss of localization accuracy, the proposed method achieves a significant advantage in computation time, compared with the conventional maximum likelihood technique.

The Method of Rotated Solutions: A Highly Efficient Procedure for Code Verification

Abstract Code verification provides mathematical evidence that the source code of a scientific computing software platform is free of bugs and that the numerical algorithms are consistent. The most stringent form of code verification requires the user to demonstrate agreement between the formal and observed orders of accuracy. The observed order is based on a determination of the discretization error, and therefore requires the existence of an analytical solution. One drawback of analytical solutions based on traditional engineering problems is that most derivatives appearing in the related governing equations (or mathematical model) are identically zero, which limits their scope during code verification. The method of rotated solutions (MRS) is introduced herein as a methodology that utilizes coordinate transformations to generate additional nonzero derivatives in the governing equations and numerical solutions. These transformations extend the utility of even the simplest one-dimensional solutions to be able to perform more thorough evaluations. This paper outlines the rotated solutions methodology and provides an example that demonstrates and confirms the usefulness of this new technique.

A variational approach to three-phase traveling waves for a gradient system

<p style='text-indent:20px;'>In this paper, we use a variational approach to study traveling wave solutions of a gradient system in an infinite strip. As the even-symmetric potential of the system has three local minima, we prove the existence of a traveling wave that propagates from one phase to the other two phases, where these phases corresponds to the three local minima of the potential. To control the asymptotic behavior of the wave at minus infinity, we successfully find a certain convexity condition on the potential, which guarantees the convergence of the wave to a constant state but not to a one-dimensional homoclinic solution or other equilibria. In addition, a non-trivial steady state in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb R^2 $\end{document}</tex-math></inline-formula> is established by taking a limit of the traveling wave solutions in the strip as the width of the strip tends to infinity.

Spreadsheet Tools for Quantifying Seepage Flux Across the GW-SW Interface.

Identifying the spatial distribution and magnitude of seepage flux across the groundwater-surface water (GW-SW) interface is critical for assessing potential impairments and restoration alternatives for water bodies adjacent to sites with groundwater contamination. Measurement of the vertical distribution and time-varying characteristics of temperature in sediments provides an indirect way to map out spatial and temporal patterns of seepage flux into surface water. Two spreadsheet-based calculation tools are introduced that implement four one-dimensional analytical solutions to calculate the magnitude and direction of seepage flux based on measurement of steady-state vertical temperature profiles or transient diel temperature signals at two depths within sediment. Performance of these calculation tools is demonstrated for a pond receiving contaminated groundwater discharge from an adjacent landfill. Transient versus steady-state model performance is compared, and limitations of transient modelsare illustrated for a situation with unfavorable sediment characteristics and inadequate sensor spacing. The availability of a range of analytical solutions implemented within Microsoft Excel® is intended to encourage practitioners to explore use of this seepage flux characterization method and develop greater insight into best practices for model selection and use.

Measurement of the will to live in older adults: Transcultural adaptation, validity and reliability of the Will-to-Live Scale.

The Will-to-Live Scale (WTLS) is used to measure the will to live in older adults; however, there is no Spanish version. The objective of the study was to translate the WTLS into Spanish, assess its internal structure, reliability, and the correlates between WTLS and life satisfaction, resilience, and depression in older Peruvian adults. The participants were 235 Peruvian older adults (M=72.69, SD=6.68), evaluated between March to May 2019, selected through non-probability sampling. The WTLS, the Satisfaction with Life Scale (SWLS), the Brief Resilient Coping Scale (BRCS) and the Patient Health Questionnaire-2 (PHQ-2) were administered. Data analysis included reliability by internal consistency and structural equation models, specifically confirmatory factor analysis (AFC), to test the one-dimensional solution of the WTLS and the convergent validity of the WTLS at the latent level, by specifying a four-factor model (will to live, life satisfaction, resilience and depression). Cronbach's alpha coefficient and the composite reliability index obtain values of .93 and .94, respectively. The one-dimensional structure of the WTLS was fitted to the data (χ2(5)=10,067, P=.073, CFI=.999, RMSEA=.066, SRMR=.014) and showed positive associations with the SWLS (ρ=.82), and BRCS (ρ=.86), as well as negative associations with the PHQ-2 (ρ=-.66). The WTLS in Spanish presents evidence of validity and reliability to measure the will to live in Peruvian older adults.

Versão brasileira da Tuckman Procrastination Scale: adaptação e evidências psicométricas

Objetivou-se reunir evidências de validade e precisão da Tuckman Procrastination Scale (TPS) em contexto brasileiro. Para tanto, foram realizados dois estudos. No Estudo 1, participaram 210 universitários, com idade média de 23,21 (DP = 7,08). Responderam a TPS e questões demográficas. A análise fatorial exploratória sugeriu uma solução unidimensional, com alfa de Cronbach (α) e ômega de McDonald (ω) iguais a 0,88. No Estudo 2, participaram 274 universitários, com idade média de 23,72 (DP = 7,61). Uma análise fatorial confirmatória apontou indicadores adequados (CFI = 0,97; TLI = 0,96; RMSEA= 0,06; Pclose = 0,28). Ademais, a confiabilidade foi satisfatória (α = 0,86; ω = 0,70). Foram encontradas evidências psicométricas para a realidade brasileira, podendo a TPS ser uma ferramenta útil para interessados na temática.

Measurement of the will to live in older adults: Transcultural adaptation, validity and reliability of the Will-to-Live Scale

ObjectiveThe Will-to-Live Scale (WTLS) is used to measure the will to live in older adults; however, there is no Spanish version. The objective of the study was to translate the WTLS into Spanish, assess its internal structure, reliability, and the correlates between WTLS and life satisfaction, resilience, and depression in older Peruvian adults. MethodThe participants were 235 Peruvian older adults (M = 72.69, SD = 6.68), evaluated between March to May 2019, selected through non-probability sampling. The WTLS, the Satisfaction with Life Scale (SWLS), the Brief Resilient Coping Scale (BRCS) and the Patient Health Questionnaire-2 (PHQ-2) were administered. Data analysis included reliability by internal consistency and structural equation models, specifically confirmatory factor analysis (AFC), to test the one-dimensional solution of the WTLS and the convergent validity of the WTLS at the latent level, by specifying a four-factor model (will to live, life satisfaction, resilience and depression). ResultsCronbach's alpha coefficient and the composite reliability index obtain values ​​of .93 and .94 respectively. The one-dimensional structure of the WTLS was fitted to the data (χ2 (5) = 10,067, p = .073, CFI = .999, RMSEA = .066, SRMR = .014) and showed positive associations with the SWLS (ρ = .82), and BRCS (ρ = .86), as well as negative associations with the PHQ-2 (ρ = −.66). ConclusionThe WTLS in Spanish presents evidence of validity and reliability to measure the will to live in Peruvian older adults.

Experimental Study on Chloride Ion Diffusion in Concrete under Uniaxial and Biaxial Sustained Stress.

The existence of axial and lateral compressive stress affect the diffusion of chloride ions in concrete will lead to the performance degradation of concrete structure. This paper experimentally studied the chloride diffusivity properties of uniaxial and biaxial sustained compressive stress under one-dimensional chloride solution erosion. The influence of different sustained compressive stress states on chloride ion diffusivity is evaluated by testing chloride concentration in concrete. The experiment results show that the existence of sustained compressive stress does not always inhibit the diffusion of chloride ions in concrete, and the numerical value of sustained compressive stress level can affect the diffusion law of chloride ions in concrete. It is found that the chloride concentration decreases most when the lateral compressive stress level is close to 0.15 times the compressive strength of concrete. In addition, the sustained compressive stress has a significant effect on chloride ion diffusion of concrete with high water/cement ratio. Then, the chloride diffusion coefficient model under uniaxial and biaxial sustained compressive stress is established based on the apparent chloride diffusion coefficient. Finally, the results demonstrate that the chloride diffusion coefficient model is reasonable and feasible by comparing the experimental data in the opening literature with the calculated values from the developed model.

Design of Highly Uniform Magnetic Field Coils With Wolf Pack Algorithm

Uniform magnetic fields are widely used in atomic magnetometers, MRI and other fields. The traditional method of solving closed-form equations is usually used to design highly uniform magnetic field coils. In this paper, a new intelligent algorithm, wolf pack algorithm (WPA), is proposed to design the coil structure of a highly uniform magnetic field. This method can replace the traditional method to obtain the coil parameters. We additionally use a discrete optimization method to solve the rounding error. According to the investigation, compared with particle swarm optimization (PSO) algorithm, WPA has stronger global optimization ability, faster convergence speed and multiple optimization strategies. We set appropriate coil constraints (structural and process constraints) and simplify the multi-dimensional solutions to one-dimensional solutions to reduce the difficulty of operation. The distribution of magnetic field intensity of three axes of coils is analyzed by the finite element analysis method, and the 1%, 0.1%, and 0.01% uniform regions are studied. Under the same conditions, the uniform magnetic field regions of the coils designed by the PSO and WPA, as well as a single pair of axial and radial coils are compared. The performance results of multiple pairs of coils are superior to those of a single pair of coils. In general, the uniformity of the axial and radial magnetic field coils designed by the WPA is better than that designed by the PSO. Finally, the experimental value of the magnetic field uniformity is nearly consistent with the theoretical value.

Cognitive test anxiety scale: Propriedades psicométricas no contexto brasileiro

Antecendentes: A ansiedade cognitiva refere-se a preocupações excessivas, antes, durante e depois das avaliações, interferindo no desempenho e ocasionando o fracasso acadêmico, além de estar associada positivamente o com neuroticismo e a depressão. Objetivou: Objetivou-se reunir evidências de qualidade psicométrica da Cognitive Test Anxiety Scale(CTAS) no Brasil. Método: Foram realizados dois estudos: No estudo 1 participaram 210 universitários da cidade de Parnaíba, Piauí, Brasil (Medade=21,7; DP=3,73), a maioria cursando Psicologia (60%) e mulheres (58,6%).Responderam a CTAS e questões demográficas. RESULTADOS: A análise fatorial exploratória sugeriu uma solução unidimensional, que explicou 46,94% da variância total dos itens. A confiabilidade foi avaliada pelos indicadores alfa de Cronbach (α) e ômega de McDonald (ω) iguais a 0,92. No Estudo 2, participaram 274 universitários de diferentes regiões brasileiras (Miedad=21,7; DP=3,73), a maioria do estado do Piauí (60%), cursando Psicologia (60,4%). Uma análise fatorial confirmatória apontou indicadores adequados (CFI=0,96; TLI=0,95; RMSEA=0,06). A confiabilidade foi satisfatória: (α) e (ω) iguais a 0,94. Conclusão: Foram encontradas evidências psicométricas para o Brasil, podendo a CTAS serútil para interessados em investigar a temática e seus correlatos. Objetivou: Objetivou-se reunir evidências de qualidade psicométrica da Cognitive Test Anxiety Scale(CTAS) no Brasil. Método: Foram realizados dois estudos: No estudo 1 participaram 210 universitários da cidade de Parnaíba, Piauí, Brasil (Medade=21,7; DP=3,73), a maioria cursando Psicologia (60%) e mulheres (58,6%).Responderam a CTAS e questões demográficas. RESULTADOS: A análise fatorial exploratória sugeriu uma solução unidimensional, que explicou 46,94% da variância total dos itens. A confiabilidade foi avaliada pelos indicadores alfa de Cronbach (α) e ômega de McDonald (ω) iguais a 0,92. No Estudo 2, participaram 274 universitários de diferentes regiões brasileiras (Miedad=21,7; DP=3,73), a maioria do estado do Piauí (60%), cursando Psicologia (60,4%). Uma análise fatorial confirmatória apontou indicadores adequados (CFI=0,96; TLI=0,95; RMSEA=0,06). A confiabilidade foi satisfatória: (α) e (ω) iguais a 0,94. Conclusão: Foram encontradas evidências psicométricas para o Brasil, podendo a CTAS serútil para interessados em investigar a temática e seus correlatos.