Two-block Model Research Articles

Complex dynamic of two-block model for earthquake induced by periodic stress disturbances

Complex dynamic of two-block model for earthquake induced by periodic stress disturbances

Transmission–propagation–diffraction operator theory for an arbitrary acoustic two-block model

By applying the transmission–propagation–diffraction​ operator theory (TPDOT; in earlier publications abbreviated as TPOT) we have derived an analytical representation of the wavefield in two 3D inhomogeneous acoustic half-spaces separated by a piecewise-smooth interface. We scrutinize the conventional approach and reformulate the mechanical particle motion forward problem in terms of a novel wave amplitude form of counter-propagating wave events. The new wave motion statement is composed of two systems of integral equations describing propagation and transmission of the seismic wavefields. The first system represents the propagation–diffraction operator equation. We express the propagation–diffraction operator as the feasible Kirchhoff-type surface integral with a feasible fundamental solution in the kernel. The feasible fundamental solution generalizes the conventional free space Green’s function for an arbitrary domain case. The second system represents the transmission (refraction/reflection) operator equation. This convolutional interface equation generalizes the Sommerfeld–Weyl spatial-frequency plane wave decomposition in an infinitesimally thin interface layer. We transform the wave amplitude formulation by Neumann iteration into infinite series of counter-propagating multiply transmitted (reflected/refracted) wave modes, representing an analytical solution to the problem. Since the wave motion statement of the forward problem enables analysis of separate wave modes of the total wavefield, it has an advantage over the particle motion statement. The suggested wavefield representation therefore solves both forward and inverse wave motion problems. Calculation of separate wave modes of TPDOT can be done by the software package of the tip-wave superposition method (TWSM) introduced in our earlier papers (in co-authorship). The proposed TPDOT provides the theoretical foundations for TWSM.

Optimal model of manufacturing control system

. It is noted that the manufacturing control optimization is an effective way both in the production processes automation and in the application of the mode of an operational transition to the new products release. Joint consideration of the options from the standpoint of system analysis made it possible to form a methodology of structural-algorithmic modeling, on the basis of which a homogeneous mathematical method is proposed. Interesting results for technical and economic procedures with an aggregate consideration of operational procedures are presented. Results for operational procedures (with detailed representation) together with the theory of description are obtained simultaneously. It is noted that a more complete use of optimization requires a joint description of the specified subject areas. The proposed solution is built on the basis of cyber-physical systems, methodology of structural-algorithmic modeling and a homogeneous method of description. The illustration on a two-block model of the system is given. The features of operational procedures from the standpoint of an integral description are formulated, and a joint description of subject areas is presented.

A faster generalized ADMM-based algorithm using a sequential updating scheme with relaxed step sizes for multiple-block linearly constrained separable convex programming

The multi-block linearly constrained separable convex optimization is frequently applied in numerous applications, including image/signal processing, statistical learning, and data mining, where the objective function is the sum of multiple individual convex functions, and the key constraints are linear. A classical approach to solving such optimization problem could be the alternating direction method of multipliers (ADMM). It decomposes the subproblem into a series of small-scale ones such that its per-iteration cost may be meager. ADMM, however, is designed initially for the two-block model, and its convergence cannot be guaranteed for a general multi-block model without additional assumptions. Dai et al. (2017) proposed the algorithm SUSLM (for Sequential Updating Scheme of the Lagrange Multiplier) for separable convex programming problems. The Lagrange multipliers are updated several times at each iteration, and a correction step is imposed at the end of each iteration. In order to derive its convergence property, a correction step is imposed at the end of each iteration. In this paper, we improve the SUSLM algorithm by introducing two controlled parameters in the updating expressions for decision variables and Lagrange multipliers. The condition of step sizes is then relaxed. We show experimentally that our SUSLM algorithm converges faster than SUSLM. Moreover, result comparisons on robust principal component analysis (RPCA) show better performances than other ADMM-based algorithms.

Two-Block Model of a Digital Corrector for Radio Tract Linearization with an Analog Square Modulator

A two-block model of a digital corrector is proposed for linearization of an analog radio path with a nonlinear characteristic and frequency-dependent mismatch of the modulator quadrature channels. Using the stochastic gradient method and the recursive least squares method, the problem of identifying each block of a given model on the basis of once measured data is solved. A comparative analysis of systems with digital correction, implemented using two-block and one-block structures, is carried out.

Two-block model of a digital corrector for linearization of an analog radio channel

A two-block model of an analog radio channel of a digital communication system is proposed. Problems of identification of the model of the data transmission channel and synthesis of a digital precorrector for adaptive linearization of nonlinear dynamic distortions are solved using the stochastic gradient method. The results of comparative analysis of two-block and one-block structures are presented.

Study on the Damping of the Discontinuous Deformation Analysis Based on Two-Block Model

The deformation and failure of rock mass is a process of energy dissipation; the damping of DDA is a very important and basic problem. The correctness and effectiveness of DDA rely on the appropriate values of the numeric controlling parameters like time interval, spring stiffness, and assumed maximum displacement ratio g2, and the contact using the penalty method is the core content of DDA. A mechanical model of two contact blocks loaded with the normal force acting along one side of block boundary is established to study the DDA damping problem, which involves the contact and eliminates the influence of some numeric control parameters (e.g., g2). Based on the Newmark method and the theory of DDA, the motion equations of two-block system can be established, and then the relationship of some numeric control parameters and the influence of damping can be obtained. The algorithmic damping increases with the increasing of time interval. Given a very small time interval, the spring stiffness may have no obvious effect on the algorithmic damping. The numerical results reveal that the essence of time interval influencing the open-close iteration is the fact that the algorithmic damping is mainly controlled by time interval.

Analysis of Impedance and Noise Data of an X-Ray Transition-Edge Sensor Using Complex Thermal Models

The so-called excess noise limits the energy resolution of transition-edge sensor (TES) detectors, and its physical origin has been unclear, with many competing models proposed. Here we present the noise and impedance data analysis of a rectangular X-ray Ti/Au TES fabricated at SRON. To account for all the major features in the impedance and noise data simultaneously, we have used a thermal model consisting of three blocks of heat capacities, whereas a two-block model is clearly insufficient. The implication is that, for these detectors, the excess noise is simply thermal fluctuation noise of the internal parts of the device. Equations for the impedance and noise for a three-block model are also given.

A Sequential Monte Carlo Method for Motif Discovery

We propose a sequential Monte Carlo (SMC)-based motif discovery algorithm that can efficiently detect motifs in datasets containing a large number of sequences. The statistical distribution of the motifs is modeled by an underlying position weight matrix (PWM), and both the PWM and the positions of the motifs within the sequences are estimated by the SMC algorithm. The proposed SMC motif discovery technique can locate motifs under a number of scenarios, including the single-block model, two-block model with unknown gap length, motifs of unknown lengths, motifs with unknown abundance, and sequences with multiple unique motifs. The accuracy of the SMC motif discovery algorithm is shown to be superior to that of the existing methods based on MCMC or EM algorithms. Furthermore, it is shown that the proposed method can be used to improve the results of existing motif discovery algorithms by using their results as the priors for the SMC algorithm.

Increased Concentration of Polyvalent Phospholipids in the Adsorption Domain of a Charged Protein

We studied the adsorption of a charged protein onto an oppositely charged membrane, composed of mobile phospholipids of differing valence, using a statistical-thermodynamical approach. A two-block model was employed, one block corresponding to the protein-affected region on the membrane, referred to as the adsorption domain, and the other to the unaffected remainder of the membrane. We calculated the protein-induced lipid rearrangement in the adsorption domain as arising from the interplay between the electrostatic interactions in the system and the mixing entropy of the lipids. Equating the electrochemical potentials of the lipids in the two blocks yields an expression for the relations among the various lipid fractions in the adsorption domain, indicating a sensitive dependence of lipid fraction on valence. This expression is a result of the two-block picture but does not depend on further details of the protein-membrane interaction. We subsequently calculated the lipid fractions themselves using the Poisson-Boltzmann theory. We examined the dependence of lipid enrichment, i.e., the ratio between the lipid fractions inside and outside the adsorption domain, on various parameters such as ionic strength and lipid valence. Maximum enrichment was found for lipid valence in the range between −3 and −4 in physiological conditions. Our results are in qualitative agreement with recent experimental studies on the interactions between peptides having a domain of basic residues and membranes containing a small fraction of the polyvalent phosphatidylinositol 4,5-bisphosphate (PIP 2). This study provides theoretical support for the suggestion that proteins adsorbed onto membranes through a cluster of basic residues may sequester PIP 2 and other polyvalent lipids.

Sensitivity kernels for shear wave splitting in transverse isotropic media

SUMMARY Shear wave splitting observations are often used to constrain upper-mantle anisotropy. However, their interpretation, which is still controversial, always implicitly relies on geometric ray theory. This high-frequency approximation does not take the finite frequency of the shear wavefield into account. In this paper, the effects of transverse isotropic perturbations of the elastic parameters on shear wave splitting are investigated. The theory, based on the first-order Born approximation, allows the derivation of 2-D and 3-D Frechet or sensitivity kernels for a new seismic observable called the splitting intensity. It is shown that the splitting intensity measured at the surface can be written to first order as a weighted average of two anisotropic perturbation parameters γc and γs related to the anisotropic parameter γ introduced by Mensch & Rasolofosaon. We also demonstrate, using a stationary-phase approximation, that the volume integral of the sensitivity kernels for a homogeneous transverse isotropic medium leads to the ray theoretical prediction for the splitting intensity. A numerical experiment on a two-block model demonstrates that lateral variations of anisotropy in the upper mantle introduce complicated and counterintuitive effects on shear wave splitting observed at the surface.

Period doubling as a result of slip complexities in sliding surfaces with strength heterogeneity

Period doubling bifurcation of stress drop is one of the non-linear dynamic phenomena in the transition from stable sliding to stick-slip of rock friction, and the onset of period doubling has been suggested to be related with stiffness and constitutive parameters as well as load point velocity. However, we find in the experiment that period doubling bifurcation of stick-slip can occur due to macroscopic heterogeneity of the sliding surface under conditions favorable for the occurrence of stick-slip. The strain measurement shows that the period doubling bifurcation of stress drop results from the alternate occurrence of strain release along whole fault and that along parts of fault, i.e. strong patches of fault. We conduct numerical analysis using a two-block model based on the rate and state friction law, and it confirms the experimental result. The numerical results show the interaction between the two blocks in detail during single and double stress drops. The strong block is active and moves spontaneously in the early stage of inertial motion, and the weak block is either to be loaded aseismically or triggered to produce stress drops by the velocity pulse in the strong block. Numerical results also show that the stress drops in both strong and weak segments are comparable despite the big contrast in strength and rate dependence.

Stress on the seismogenic and deep creep plate interface during the earthquake cycle in subduction zones

The deep creep plate interface extends from the down-dip edge of the seismogenic zone down to the base of the overlying lithosphere in subduction zones. Seismogenic/deep creep zone interaction during the earthquake cycle produces spatial and temporal variations in strains within the surrounding elastic material. Strain observations in the Nankai subduction zone show distinct deformation styles in the co-seismic, post-seismic, and inter-seismic phases associated with the 1946 great earthquake. The most widely used kinematic model to match geodetic observations has been a 2-D Savage-type model where a plate interface is placed in an elastic half-space and co-seismic slip occurs in the upper seismogenic portion of the interface, while inter-seismic deformation is modeled by a locked seismogenic zone and a constant slip velocity across the deep creep interface. Here, I use the simplest possible 2-D mechanical model with just two blocks to study the stress interaction between the seismogenic and deep creep zones. The seismogenic zone behaves as a stick-slip interface where co-seismic slip or stress drop constrain the model. A linear constitutive law for the deep creep zone connects the shear stress (σ) to the slip velocity across the plate interface (s′) with the material property of interface viscosity (ζ ) as: σ = ζ s′. The analytic solution for the steady-state two-block model produces simple formulas that connect some spatially-averaged geodetic observations to model quantities. Aside from the basic subduction zone geometry, the key observed parameter is τ, the characteristic time of the rapid post-seismic slip in the deep creep interface. Observations of τ range from about 5 years (Nankai and Alaska) to 15 years (Chile). The simple model uses these values for τ to produce estimates for ζ that range from 8.4 × 1013 Pa/m/s (in Nankai) to 6.5 × 1014 Pa/m/s (in Chile). Then, the model predicts that the shear stress acting on deep creep interface averaged over the earthquake cycle ranges from 0.1 MPa (Nankai) to 1.7 MPa (Chile). These absolute stress values for the deep creep zone are slightly smaller than the great earthquake stress drops. Since the great earthquake recurrence time ( T recur) is much larger than τ for Nankai, Alaska, and Chile, the model predicts that rapid post-seismic creep should re-load the seismogenic zone to about (1/3) of the co-seismic change; geodetically observed values range from about (1/10) to more than (1/2). Also, for the case of (Trecur/τ) ≫1, the model predicts that the slip velocity across the deep creep interface during the inter-seismic phase should be about (2/3) the plate tectonic velocity (R). Thus the deep creep velocity used in Savage-type models should be less than R. Even complex 3-D models with non-linear creep laws should make a similar prediction for inter-seismic deep creep rates. At present, it seems that geodetic observations at Nankai and other subduction zones are more consistent with a deep creep rate of R rather than (2/3) R. This discrepancy is quite puzzling and is difficult to explain in the context of a 2-D steady-state earthquake cycle model. Future observational and modeling studies should examine this apparent discrepancy to gain more understanding of the earthquake cycle in subduction zones.

Calculation of hole distribution in YBa 2Cu 3O 7−δ and its correlation with superconductivity

The combinative energy in the YBa 2Cu 3O 7−δ with the different δ value, from 0.07 to 0.62, was calculated based on two-block model. In order to compensate for the deficiency of the ionic model for the YBa 2Cu 3O 7−δ, some holes were directly put on the different planes in the YBa 2Cu 3O 7−δ. When the holes are on the Cu(2)O plane, the calculated result is perfectly consistent with the fact that the carriers mainly concentrate on the Cu(2)O plane. When the holes are on the Cu(1)O plane, The combinative energy shows the same trend as that on the Cu(2)O plane, but the plateau in the range of δ ∼ 0.35 – 0.55 is different. When the holes are on the BaO plane, the relationship between the combinative energy and the oxygen deficiency is ambiguous. The calculation of the holes on different planes supplies abundant information about the charge distribution in the YBa 2Cu 3O 7−δ.

The strength profile for bimineralic shear zones: an insight from high-temperature shearing experiments on calcite–halite mixtures

Shearing experiments on mixed halite–calcite layers (0.7 mm thick) have been performed to understand the behavior of bimineralic fault zones, using a high-temperature biaxial testing machine at a slip rate of 0.3 μm/s and shear strains to about 30. Temperature was increased to 700°C in linear proportion to the normal stress, with the experimental geotherm of about 22°C/MPa, simulating the natural geothermal gradient. The experimental data clearly demonstrate that the effect of mineral composition on the ultimate frictional strength is distinctly different from that on the residual frictional strength. Tharp's framework model (1983) quantitatively accounts for the ultimate frictional strength, whereas the residual frictional strength at large shear strains can be predicted by Jordan's two-block model (1988). Thus, the frictional behavior of a bimineralic shear zone changes from the framework model to the two-block model with increasing displacement. Inclusion of halite, the weaker member, in quantities as small as 5% by volume, reduces the friction almost to the level of pure halite and suppresses stick-slip at large shear strains, because halite grains are extremely sheared at the zone of strain concentration. The strength profile and the slip mode, including the lower limit of seismic behavior, of bimineralic shear zones at large shear strains are controlled primarily by the weaker member. The present results disprove Strehlau's fault model (1986). The role of individual constituent mineral is not clarified in Scholz's fault model (1988), and his model disagrees with existing experimental data.

On the numerical stability of block structured algorithms with applications to 1-D advection-diffusion problems

In this work an analysis of the stability of multiblock structured algorithms for the solution of initial-boundary value problems is carried out. The influence of artificial interfaces on the time integration is investigated with application to a multistage time stepping algorithm; the multiblock structured approach (MSA) is applied to 1-D linear model problems (diffusion and advection-diffusion equations). Stepwise stability is investigated by means of the classical eigenvalues analysis, giving results in perfect agreement with the numerical experiments. Finally a simple procedure to avoid stability restrictions is proposed and analyzed for a two-block model problem.

A four-parameter, two degree-of-freedom block-spring model: Effect of the driver velocity

We analyze the effect of tectonic plate velocities in the earthquake pattern using a simple mass-spring model of the Burridge and Knopoff type with two blocks and a velocity-weakening friction law. Previous versions of the two-block model assume a steady driver during slip events (limit of zero driver velocity), which, in some cases makes necessary the introduction of artificial parameters to start the numerical integration of the equations of motion at impending slip of any block. Still maintaining the condition of zero driver velocity during slip, we shall introduce a procedure to start the numerical integration without introducing artificial parameters and this will be done by using a linearized version of the equations of motion valid for small velocities and considering nonzero driver velocity. We also introduce a four parameter model in which the driver velocity enters the equations during the whole simulation, and analyze the effect of the new parameter, the driver velocity, in the displacement and time patterns of blocks motion, directly related to earthquake statistics such as coseismic slips and average repeat times.