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The evolution of universal systems has been of great interest to computer scientists. In particular, the role of Turing machines in the study of computational universality is widely recognized. Even though the patterns emerging from the evolution of this kind of dynamical system have been studied in much detail, the transition functions themselves have received less attention. In the present paper, the iota-delta function is used to encode the transition function of one-head Turing machines. In order to illustrate the methodology, we describe the transition functions of two universal Turing machines in terms of the latter function. By using the iota-delta function in this setting, Turing machines can be represented as a system of transition functions. This new representation allows us to write the transition functions as a linear combination of evolution variables wrapped by the iota-delta function. Thus, the nonlinear part of the evolution is totally described by the iota-delta function. [ABSTRACT FROM AUTHOR]

To learn, humans observe and experience the world, collect data, and establish patterns through repetition. In scientific discovery, these patterns and relationships are expressed as laws and equations, data as properties and variables, and observations as events. Data-driven techniques aim to provide an impartial approach to learning using raw data from actual or simulated observations. In soil science, parametric models known as constitutive models are used to represent the behavior of natural and artificial materials. Creating data-driven constitutive models using deep learning techniques requires large and consistent datasets, which are challenging to acquire through experiments. Synthetic data can be generated using a theoretical function, but there is a lack of literature on high-volume and robust datasets of this kind. Digital soil models can be utilized to conduct numerical simulations that produce synthetic results of triaxial tests, which are regarded as the preferred tests for assessing soil's constitutive behavior. Due to its limitations for modeling real sands, the Modified Cam Clay model has been replaced by the NorSand model in some situations where sand-like materials need to be modelled. Therefore, for a material following the NorSand model, the present paper presents a first-of-its-kind database that addresses the size and complexity issues of creating synthetic datasets for nonlinear constitutive modeling of soils by simulating both drained and undrained triaxial tests of 2000 soil types, each subjected to 40 initial test configurations, resulting in a total of 160000 triaxial test results. Each simulation dataset comprises a 4000×10 matrix that can be used for general multivariate forecasting benchmarks, in addition to direct geotechnical and soil science applications. [ABSTRACT FROM AUTHOR]

Mudflow is often associated with seismic activities. The present study applied a seismic based detection of the surface waves generated by the mudflow of Brumadinho dam collapse using records of Brazilian Seismographic Network. The signal envelope and time-frequency spectrograms of the mudflow signals were used in the analysis. As a result, the mudflow signals were successfully detected from the data recorded at a nearby seismic station. The findings of this study provide a good basis for future research to develop a flood early warning system based on cost-effective, remote and contentious seismic monitoring approaches. [ABSTRACT FROM AUTHOR]

This paper describes a methodology based on the Rosenblueth point estimate method to analyze the active earth pressure developed on retaining walls for c-ɸ soil backfill under seismic loading conditions. The fundamentals of this methodology are to use two point estimates to examine a variable in the safety analysis: the mean value and the standard deviation. When the horizontal seismic acceleration coefficient increases, the overturning factor of safety decreases, whereas the probability of failure increases, particularly for coefficients greater than 0.2. In addition, the mean factor of safety increases when the vertical seismic acceleration coefficient increases, but the probability of failure remains practically identical for the considered critical factor of safety (1.15). [ABSTRACT FROM AUTHOR]

Although the finite-difference method (FDM) has been commonly used to numerically solve Richard's equation, numerical diffi- culties are often encountered, even for comparatively simple problems. To minimize convergence problems, comparatively small discretization and time steps have often been adopted to solve this highly nonlinear equation, resulting in significant computational costs. To overcome these difficulties, this paper presents an efficient approach to solving Richard's equation that combines two numerical techniques: the FDM and the cubic interpolated pseudoparticle (CIP) method. The FDM is used to solving the diffusive flow component of Richard's equation, the convergence of which can be controlled by adopting time steps corresponding to Neumann's number under 0.5. In contrast, the CIP method is used to solve the advective flow component of the equation. The CIP method is found to be particularly suitable for facilitating convergence and eliminating the presence of spurious results when the Courant number is under 1.0. Analytical solutions for transient unsaturated flow problems, developed in a companion paper, allow comparison between the predictions obtained using the proposed numerical approach and the exact solutions. Use of the newly developed algorithm is found to be particularly accurate and stable for solving Richard's equation, being clearly superior to the use of the traditional FDM. After validating the new numerical approach using the boundary conditions and hydraulic functions for which analytical solutions have been developed, the new numerical scheme was subsequently implemented to address more general unsaturated flow problems. In particular, the new numerical approach was extended to solve unsaturated flow problems involving complex soil hydraulic functions as well as different boundary conditions. Comparisons are presented to illustrate the accuracy of the new numerical approach even when extended to incorporate the use of complex hydraulic functions for which there are no analytical solutions. The efficient, validated numerical schemes presented in this paper are found to be well suited for solving complex unsaturated flow problems. [ABSTRACT FROM AUTHOR]

Richard's equation governs the migration of moisture in the soil under unsaturated conditions. Although this differential equation provides a rigorous approach to simulating important infiltration problems, obtaining analytical and numerical solutions to this equation has been a particularly challenging task. This is largely due to the highly nonlinear nature of the soil hydraulic properties, including the moisture retention curve and the hydraulic conductivity function. Whereas analytical solutions of Richard's equation have been reported for problems involving steady-state conditions and simple hydraulic models, solutions for transient conditions have rarely been obtained. However, such analytical solutions would be particularly valuable, for example, to validate the accuracy of numerical schemes, as well as to facilitate parametric evaluations. A series of analytical solutions of Richard's equation for unsaturated flow under transient conditions have been developed as part of this study. The solutions involve a variety of initial and boundary conditions. The analytical solutions in this study could be obtained after expressing the governing equation as the addition of advective and diffusive flow components. The solutions consider logarithmic and linear models to represent the soil moisture retention and the hydraulic conductivity functions, respectively. Solutions are also provided for special cases in which either the advective or the diffusive components dominate the flow process, as well as for the steady-state cases. A parametric evaluation was found to provide insight into important characteristics of infiltration problems. In particular, relevant features of an unsaturated flow problem can be explained by evaluating the trends in its advective and diffusive flow components. [ABSTRACT FROM AUTHOR]

Problems involving fluid flow in porous media are of great interest in many scientific and technological areas. The development of numericalmethods at the pore level allows simulating such phenomena considering characteristics and heterogeneities of the mediumnormally ignored in themacroscopic approach. To achieve thecomputational implementation of thosenumericalmethods, it is necessary to initially define the domain (porous media) inwhich the simulations will be held. In this study, a simple, yet powerful methodology of representing a porous medium by means of cellular automata (CA) and microcomputed tomography is presented. Two parameters are proposed to link the tomographic images with those generated by CA. The first one considers the porosity, whereas the second one takes into account void alignment inside the image. The methodology computes the parameters in every automata image generated in a time range and compares themwith the parameters of the tomographic image until certain user-controlled precision is achieved. As an application example, two tomographic experiments with different resolutions were carried out on a soil sample. Two-dimensional (2D) outer totalistic CA rules whose evolution in time exhibits variation between theamount of black andwhite cells, independently fromthe initial condition, are considered. The calculations showeda gain of accuracy with the resolution increase. Although the implementation is presented for the 2D case, the methodology proposed is easily extendible to threedimensional analysis. [ABSTRACT FROM AUTHOR]

Consolidation is one of the most important concepts in geotechnics. The pioneer ideas of both Terzaghi and Biot, and its attendant phenomena have been shown to be widely applicable to a wide variety of soils. However, when structured and collapsible soils are taken into account, the standard consolidation theory ultimately requires complementary considerations to correctly predict a soil's behavior. In particular, indirect determination of permeability by means of the consolidation coefficient, cv, tends to highly underestimate the real hydraulic behavior for these types of soil. In the present paper, a modification in the understanding of the consolidation process is proposed to adjust the prevailing theory to the reality of both structured and collapsible soils. In short, it is considered that every soil may suffer microcollapses that increase porewater pressure momentarily during the consolidation process. The mathematical basis for the new theory is developed and a new parameter, the collapsibility index η, is introduced. The new understanding provides an alternative explanation to the apparent low permeability observed in consolidation tests. Also, an experimental data set is analyzed in light of the concepts hereby developed. The latter analysis reveals that the alternative approach proposed predicts well the behavior of the experimental data considered. [ABSTRACT FROM AUTHOR]