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In this paper, we studied the nature of shockwave induced cavitation bubble collapse using molecular dynamics (MD) simulation. A major objective of this study is to determine how the variation of nanoscale bubble size and entrapped gas density affects the bubble dynamics. It is known that cavitation bubble collapse/implosion is a robust dynamic event that occurs when the potential energy of the acting pressure performs work in a rapid and violent manner. Usually, the energy converges into a significantly smaller region compared to the original cavitation bubble. While the mechanisms of cavitation have been studied for more than a century, recently, it has received renewed interests due to its connection with biomedical applications and traumatic brain injury (TBI). One of the common causes of TBI is blast-induced shock exposure. A shockwave, as a moving discontinuity of pressure, can lead to the formation and collapse of cavitation bubble and produce an impactful jet stream. The jet stream may cause a localized mechanical/thermal damage to the structures that come on its path. We have considered two different bubble sizes (10 and 20 nm). We found that different gas densities inside the cavitation bubble largely change the intensity of the aftermath. We also found the peak temperature during the collapse is linked to the bubble size but unrelated with the peak pressure.

In this paper, we study the exact solutions of Riemann problem for the compressible ideal fluid flow, where the external force is a continuous function of time. The exact expressions for contact discontinuity curve, shock wave curve and rarefaction wave curve are provided. Six types of exact solutions of the Riemann problem are also obtained. In particular, a vacuum arises at t > 0 although the initial data never involves the vacuum, and these solutions do not possess self-similarity in the ( t , x ) -plane.

This paper is concerned with the distributed control of vehicle platoons. The dynamics of each vehicle are nonlinear and heterogeneous. The control objective is to regulate vehicles to travel at a common speed while maintaining desired intervehicle gaps. The information flow topology dictates the pattern of communication between vehicles in the platoon. This information is essential to effective platoon control and, therefore, plays a central role in affecting the design and performance of platoon control strategies. Our key contribution is a unified distributed control framework that explicitly incorporates and supports a diversity of information flow topologies. Specifically, we propose a distributed sliding mode control (DSMC) framework for a class of generic topologies. The DSMC constructs the topological sliding surface and reaching law via a so-called “topologically structured function.” The control law obtained by matching the topological sliding surface and topological reaching law is naturally distributed. The Lyapunov stability analysis is carried out for the closed-loop system in the sense of Filippov to cope with the discontinuity originated from switching terms. Moreover, a tradeoff between tracking precision and chattering elimination is discussed with a continuous approximation of the switching control law. The effectiveness of the DSMC for platoons is verified under four different topologies through numerical simulation.

The comparisons of an AE source location performance of two widely used methods, time of arrival (TOA) and difference of arrival time (DOAT) have been analyzed in a complex planar multilayered surface. The complex surface has been prepared by covering a steel plate (SM400A) with a multilayered rubber material (Natural Rubber). The purpose of using this structure has been defined to get the comparable AE source location performance in a complicated signal propagation pathway. Both source location techniques have been conducted in a simulated AE wave propagating plane (300 mm * 200 mm in size) under Hsu-Nielsen method. Investigations reveal that the TOA technique gives several erroneous results along with good results. However, the DOAT method has produced all excellent results, even when using a complex surface. It was found since the TOA method is sensitive to constant velocity continuity, the present complex pathway leads to the velocity discontinuity, and thus, several incorrect results have been found. On the other hand, the DOAT method is dependent on the arrival time difference only, and therefore, it shows a higher performance in the source location, even in the presence of a complex structure.

Planar junctions between reactive surface impedances with dual character (capacitive/inductive) can sustain line waves localized both in-plane and out-of-plane around the discontinuity, which propa...

The presence of seismic absorption distorts seismic record and reduces seismogram resolution, which can be partially compensated by application of absorption compensation algorithms. Conventional absorption compensation techniques are based on 1D forward model with each seismic trace being compensated independently. Therefore, the 2D results combined by each compensation trace may be noisy and discontinuity. To eliminate this issue, we extend the 1D forward model to the 2D forward system and further add an additional lateral constraint to the compensation algorithm for enforcing the lateral continuity of the compensated section. Solving the proposed laterally constrained absorption compensation (LCAC) problem, we simultaneously obtain the multiple compensated traces with lateral smoother transition and higher signal-to-noise ratio (S/N). We testify the effectiveness of the proposed method by applying both synthetic and field data. Synthetic data examples demonstrate the superior performance of the LCAC algorithm in terms of improving algorithmic stability and protecting lateral continuity. The field data tests further indicate its ability to not only improve seismic resolution, but also inhibit the amplification of high-frequency noise.

The G01 tool path, which consisted of linear segments, is commonly used in NC machining. There is the tangential and curvature discontinuity at the junctions of adjacent linear segments, which can ...

In this paper, studied are periodic motions in a discontinuous system with three vector fields switching through two branches of a hyperbola. The switchability conditions of flows at the discontinuous boundaries are presented through G-functions. Such conditions are presented for passable motions and grazing motions at the boundary with sliding motions on the boundary. With such analytical conditions, periodic motions with specific mapping structures are analytically predicted, and the corresponding stability and bifurcations are presented through eigenvalue analysis. Numerical illustrations of periodic motions are carried out, and the corresponding G-functions are presented for illustration of motion switchability at the hyperbolic boundaries. The discontinuity of periodic motions is shown in phase trajectories. This study tells the complex motions can be obtained through a few individual systems with arbitrary switching boundaries, and the corresponding discontinuous dynamics can be discussed for dynamical system design and control.

This paper presents an automated method for discontinuity trace mapping using three-dimensional point clouds of rock mass surfaces. Specifically, the method consists of five steps: (1) detection of trace feature points by normal tensor voting theory, (2) contraction of trace feature points, (3) connection of trace feature points, (4) linearization of trace segments, and (5) connection of trace segments. A sensitivity analysis was then conducted to identify the optimal parameters of the proposed method. Three field cases, a natural rock mass outcrop and two excavated rock tunnel surfaces, were analyzed using the proposed method to evaluate its validity and efficiency. The results show that the proposed method is more efficient and accurate than the traditional trace mapping method, and the efficiency enhancement is more robust as the number of feature points increases.

In this paper, we first consider a combined boundary element method for numerical simulation of effect of temperature change on deformation due to time-varying heat conditions. The numerical simulation uses combination of an indirect boundary element method (IBEM) for temperature field and displacement discontinuity method (DDM) for displacement and stress fields. Time-varying fictitious heat source is employed in the IBEM and is approximated with a series of fictious heat sources with constant strengths that are applied incrementally at different times. Mathematically, the smooth-varying strength function of fictitious heat source is approximated with a stepwise function. The solution schemes previously developed for fictitious heat sources with constant strength are used for each increment. The combined scheme is used to compare the thermal effects caused by constant temperature and time-varying temperature on surface of a spherical cavity in an infinite body. The approximation scheme is verified with analytical solution when the temperature on the spherical cavity surface varies linearly with time. Then thermal fields around a conceptual thermal energy storage tank is simulated. Finally, the effects of temperature change in cracks connected to a vertical borehole on the propagation pattern of the cracks are investigated with the numerical scheme. It is found that cold temperature on the crack surfaces could help to reduce curvature of crack surfaces when multiple cracks are used, compared with fluid flow driven growth.

A low-dissipation numerical method based on a combination of Godunov’s method and a piecewise parabolic method on a local stencil is presented. The construction of the method is described in detail. The method is tested using a one-dimensional problem of breakdown of a discontinuity. The results of a numerical simulation of collision of two relativistic gas spheres are given.

In the current research, formulations of the displacement discontinuity method (DDM) for crack problems based on boundary element method (BEM) are proposed in finite domain. Four different boundary element methods, i.e., the conventional direct displacement boundary element method (CBEM), the hyper-singular traction direct boundary element (HBEM), the displacement discontinue indirect boundary element method (DD-IBEM), and the fictitious stress indirect boundary element method (FS-IBEM), are considered. The original two indirect boundary element methods, DD-IBEM and FS-IBEM, are unstable and may obtain inaccurate results, and a new modified method is applied to improve the accuracy. Numerical examples have been proposed to demonstrate the accuracy of the proposed methods.

In the study, energy flow analysis is performed to predict the performance of silencers. To date, deterministic approaches such as finite element method have been widely used for silencer analysis. However, they have limitations in analyzing large structures and mid-high frequency ranges due to unreasonable computational costs and errors. However, silencers used for ships and off-shore plants are much larger than those used in other engineering fields. Hence, energy governing equation, which is significantly efficient for systems with high modal density, is solved for silencers in ships and off-shore plants. The silencer is divided into two different acoustic media, air and absorption materials. The discontinuity of energy density at interfaces is solved via hypersingular integrals for the 3-D modified Helmholtz equation to analyze multi-domain problems with the energy flow boundary element method. The method is verified by comparing the measurements and analysis results for ship silencers over mid–high frequency ranges. The comparisons confirm good agreement between the measurement and analysis results. We confirm that the applied analysis method is useful for large silencers in mid-high frequency ranges. With the proven procedures, energy flow analysis can be performed for various types of silencer used in ships and off-shore plants in the first stage of the design.

This study explores continuous and discontinuous word order patterns of multi-word nominal expressions in flexible word order languages (traditionally referred to as “free word order” or “non-configurational” languages). Besides describing syntagmatic patterns, this paper seeks to identify any functional or other correlates that can be associated with different word orders. The languages under investigation are a number of Australian languages as well as Vedic Sanskrit, all of which have long been known for their syntagmatic flexibility. With respect to continuous order, evidence from several of these languages suggests that default ordering is primarily governed by functional templates. Deviations from default order, while maintaining continuity, can be attributed to different types of “focus” interpretations or heaviness effects. With respect to discontinuous order, I identify three sub-types. The most widespread one, “Left-Edge Discontinuity”, involves one element placed in or near utterance-initial position. It shows a clear, if not an absolute, correlation with different kinds of focus interpretations, similarly to deviations from the default order in continuity. The other two types of discontinuity are linked to the behaviour of specific function words. Besides teasing out cross-linguistic similarities, this paper also sheds light on language-specific characteristics that affect the forms and functions of complex (i.e. multi-word) nominal expressions in flexible word order languages, such as the nature of 2nd position (“Wackernagel”) elements.

The present work is concerned with a novel generalized thermoelasticity theory introduced by Yu et al. [A modified Green-Lindsay thermoelasticity with strain rate to eliminate the discontinuity. Me...

The contribution of a spherical cap crack having an “island” of contact between its faces into elastic compliance of a material is analyzed. Vector of the displacement discontinuity at the crack faces in response to remotely applied stress is calculated using the mesh free technique based on the solution approximation by Gaussian functions. The result is used to construct the compliance contribution tensor of this crack as a function of the island position and extent of non-flatness of the crack. This tensor is orthotropic and the two mentioned factors produce complex combined effect. To study these effects, simple analytical approximation for the obtained numerical result is proposed. The effect of position of the contact is substantial even for planar cracks and it becomes much stronger for non-planar ones; the effect of the size of the contact is generally similar to that for planar cracks. Moderately non-planar cracks may be approximated by planar ones with acceptable accuracy.

Flows of two immisible fluids are considered taking into account the capillary and gravity forces. The flow is described using a viscous incompressible fluid model within a two-dimensional formulation. The Navier–Stokes equations are solved numerically by an extended finite-element method, which allows for the presence of a strong discontinuity on the interface. The interface location is tracked using the level set method. This approach makes it possible to study flows with a varying topology of the interface. The calculation results are presented for the problems of a rising 2D bubble, development of the Rayleigh–Taylor instability, and a film flowing down a vertical wall in an extended region.

The displacement discontinuity method is extended to study the fracture behavior of interface cracks in one-dimensional hexagonal quasicrystal coating subjected to anti-plane loading. The Fredholm integral equation of the first kind is established in terms of displacement discontinuities. The fundamental solution for anti-plane displacement discontinuity is derived by the Fourier transform method. The singularity of stress near the crack front is analyzed, and Chebyshev polynomials of the second kind are numerically adopted to solve the integral equations. The displacement discontinuities across crack faces, the stress intensity factors, and the energy release rate are calculated from the coefficients of Chebyshev polynomials. In combination with numerical simulations, a comprehensive study of influencing factors on the fracture behavior is conducted.

In layered media, the solution of Maxwell’s equations suffers a strong or weak discontinuity at the layer boundaries. Finite-difference schemes providing convergence on strong discontinuities have been proposed for the first time. These are conservative bicompact two-point schemes with mesh nodes lying on the layer boundaries. A fundamentally new technique for taking into account the medium dispersion is proposed. All these features ensure the second order of accuracy of the schemes on discontinuous solutions. Numerical examples illustrating these results are given.

O objetivo do presente artigo é examinar, com base na Gramática Discursivo-Funcional (HENGEVELD; MACKENZIE, 2008), o comportamento de sintagmas nominais com ordenações não canônicas de suas partes constituintes, denominados descontínuos por Keizer (2007), bem como investigar as motivações que ativam a descontinuidade. Para tanto, elegem-se dois princípios de ordenação: o de complexidade estrutural e o de peso comunicativo. Ambos podem favorecer uma mesma ordem, mas, quando eles entrarem em competição e favorecerem ordens diferentes, o falante irá selecionar a ordenação que melhor cumpre seu propósito comunicativo. A partir de dados extraídos do córpus IBORUNA, foram analisadas 77 ocorrências de sintagmas nominais descontínuos. O resultado da análise aponta para a prevalência do princípio de peso comunicativo na determinação da ordem dos constituintes do SN.

Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm for solving the inverse problems. The key role in our method is played by the Riesz-basis property of a special vector-functional system in a Hilbert space. In addition, we obtain a new uniqueness theorem for recovering the potential on a part of the interval, by using a fractional part of the spectrum.

We consider a nonlinear, frame indifferent Griffith model for nonsimple brittle materials where the elastic energy also depends on the second gradient of the deformations. In the framework of free discontinuity and gradient discontinuity problems, we prove existence of minimizers for boundary value problems. We then pass to a small strain limit in terms of suitably rescaled displacement fields and show that the nonlinear energies can be identified with a linear Griffith model in the sense of $\Gamma$-convergence. This complements the study in [Arch. Ration. Mech. Anal. 225 (2017), 425-467] by providing a linearization result in arbitrary space dimensions.

When employing end milling for the thin-walled elements, in particular aircraft gas-turbine engines, it is possible to observe their forced vibrations due to the machining discontinuity. The authors present the calculation method for determining the best performance of discontinuous milling of the given elements, which minimizes the forced vibrations’ level and provides the required quality of the machined surface. The proposed method is based on the modeling of machining, considering the differences between the end milling and standard milling. The main difference lies in the discontinuity in the process of machining. The authors developed a model for determining the milling force with the considered type of machining of thin-walled elements. A dissipative system with one degree of freedom is chosen as the calculation model to investigate the forced vibrations. The experimental investigations are performed on the specially designed facilities to study the vibrations in the thin-walled structural elements in their end milling. The paper provides the calculation results, which are compared with the experimental data in the wide range of rotational spindle frequency. A satisfactory coincidence between the rotational spindle frequencies with the largest and smallest vibration amplitudes is demonstrated. The reduced analysis of roughness of the machined surface shows an evident dependence of the given parameter on the vibration amplitude. Therefore, the smallest vibration amplitude denotes the highest quality of machining. The spectrum analysis of the deviation element signal implies the presence of beats when the natural element frequency is close to the excitation frequency of its vibrations, which is the main source of their amplitude increase and degradation of the machined surface. Here the smallest vibration amplitudes are observed with the frequencies of their excitation between the resonance peaks. Thus, the analysis of the motion law of the thin-walled element during milling confirms the accuracy of modeling of the considered process and determination of its vibration stability modes.

The stability of grazing bifurcation is lost in three ways through the local analysis of the near-grazing dynamics using the classical concept of discontinuity mappings in the two-degree-of-freedom vibroimpact system with symmetrical constraints. For this instability problem, a control strategy for the stability of grazing bifurcation is presented by controlling the persistence of local attractors near the grazing trajectory in this vibroimpact system with symmetrical constraints. Discrete-in-time feedback controllers designed on two Poincare sections are employed to retain the existence of an attractor near the grazing trajectory. The implementation relies on the stability criterion under which a local attractor persists near a grazing trajectory. Based on the stability criterion, the control region of the two parameters is obtained and the control strategy for the persistence of near-grazing attractors is designed accordingly. Especially, the chaos near codimension-two grazing bifurcation points was controlled by the control strategy. In the end, the results of numerical simulation are used to verify the feasibility of the control method.

i»?When the first commercial electromagnetic (EM) simulators appeared in the late 1980s and early 1990s, we were thrilled to be able to accurately simulate a single microstrip discontinuity, even if the simulation ran overnight. Today, computer hardware is cheaper and much faster, and EM simulation software is more efficient and sophisticated. Even so, putting an EM simulator inside an optimization loop is still not practical in most cases. Even our simple N = 5 hairpin filter example does not lend itself to directly driven EM optimization. The desire to efficiently optimize microwave filters using accurate EM simulation data led us to the port-tuning concept [1].

A new machine-learning approach based on a Dynamic Time Warping (DTW) algorithm is introduced to detect faults and fractures in 3D seismic data from an unconventional resource play in Eastern Cis- Caucasia (Russia). This novel approach allows for better edge detection in seismic amplitude volumes because it employs a detailed comparison of two neighbouring traces to detect discontinuity via a minimal horizontal distance. For benchmarking purposes the proposed DTW method is compared to a widely used multi-trace attribute (Variance). Subsequently, both calculated attribute cubes serve as an input for ANT-Tracking to delineate fault strike and fracture corridor trends. A comparison of results shows that better resolution and more complete fault images are obtained when the DTW method is applied.

The system-optimal dynamic traffic assignment (SO-DTA) problem aims at solving for the time-dependent link and path flow of a network that yields the minimal total system cost, provided with the Origin-Destination (O-D) demand. The key to solving the path-based formulation of SO-DTA is to efficiently compute the path marginal cost (PMC). Existing studies implicitly assume that the total system cost (TC) is always differentiable with respect to the path flow when computing PMC. We show that the TC could be non-differentiable with respect to the link/path flow in some cases, especially when the flow is close or under the SO conditions. Overlooking this fact can lead to convergence failure or incorrect solutions while numerically solving the SO-DTA problem. In this paper we demonstrate when the TC would be indifferentiable and how to compute the subgradients, namely the lower and upper limit of path marginal costs. We examine the relations between the discontinuity of PMC and the SO conditions, develop PMC-based necessary conditions for SO solutions, and finally design heuristic solution algorithms for solving SO in general networks with multi-origin-multi-destination OD demands. Those algorithms are tested and compared to existing algorithms in four numerical experiments, two toy networks where we compare analytical solutions with numerical solutions, one small network and one sizable real-world network. We show that the proposed heuristic algorithms outperform existing ones, in terms of both the total TC, convergence, and the resultant path/link flow.

The stability of one-dimensional steady flows of an ideal (inviscid and non-heat-conducting) gas in channels of variable cross section with combustion in a structurally stable detonation wave is studied. The detonation wave represents a discontinuity surface propagating normally to the axis of the channel. It was previously established that, in this formulation, steady flows with combustion in a Chapman–Jouguet detonation wave are always unstable, in contrast to combustion flows in an overcompressed detonation wave. The stability analysis of such flows is reduced to the numerical solution of an initial-boundary value problem describing the evolution of finite flow perturbations between the moving detonation wave and the minimal nozzle cross section (in the case of a sudden contraction) or the exit nozzle cross section. The problem is solved by applying a modified Godunov scheme of higher order accuracy. More specifically, a Riemann solver with switching (between the overcompressed and Chapman–Jouguet detonation waves) with an explicitly represented detonation wave is created. Examples of stable flows and flows collapsing due to large initial perturbations are given, and their dynamics with transitions to a Chapman–Jouguet detonation wave and back are computed.

A linear problem of small perturbations of the flow of immiscible polymer fluids in a flat channel is formulated. For this problem, the existence of solutions unlimitedly increasing with time, the presence of which means linear instability of the state of rest of a polymer fluid with a strong discontinuity, is studied.

Water infiltration into layered soils is studied, considering a two dimensional spatial domain. The focus is on the treatment of discontinuity at the intersection of non-overlapping soils. The novelty of this paper is based on a mixed MoL–TMoL, which merges desirable features of both Method of Lines (MoL) and Transversal Method of Lines (TMoL); such a numerical approach allows us the numerical treatment of the solution at the discontinuous interfaces by means of Filippov theory for dynamical systems. Numerical simulations, based on implicit and semi-implicit schemes of low accuracy, are provided for validating this approach.

The continuity of the position-vector gradients at the nodal points of a finite element mesh does not always ensure the continuity of the gradients at the element interfaces. Discontinuity of the gradients at the interface not only adversely affects the quality of the simulation results, but can also lead to computer models that do not properly represent realistic physical system behaviors, particularly in the case of soft and fluid material applications. In this study, the absolute nodal coordinate formulation (ANCF) finite elements are used to define general curvature-continuity conditions that allow for eliminating or minimizing the discontinuity of the position gradients at the element interface. For the ANCF solid element, with four-node surfaces, it is shown that continuity of the gradients tangent to an arbitrary point on a surface is ensured as the result of the continuity of the gradients at the nodal points. The general ANCF continuity conditions are applicable to both reference-configuration straight and curved geometries. These conditions are formulated without the need for using the computer-aided-design knot vector and knot multiplicity, which do not account properly for the concept of system degrees of freedom. The ANCF curvature-continuity conditions are written in terms of constant geometric coefficients obtained using the matrix of position-vector gradients that defines the reference-configuration geometry. The formulation of these conditions is demonstrated using the ANCF fully parameterized three-dimensional solid and tetrahedral elements, which employ a complete set of position gradients as nodal coordinates. Numerical results are presented in order to examine the effect of applying the curvature-continuity conditions on achieving a higher degree of smoothness at the element interfaces in the case of soft and fluid materials.

In this paper, we present a two-grid partially penalized immersed finite element (IFE) scheme for the approximation of semi-linear elliptic interface problems. Extra stabilization terms are introduced at interface edges for penalizing the discontinuity in IFE functions. Optimal error estimates in both H 1 and L p norms are obtained for IFE discretizations. To linearize the IFE equations, two-grid algorithm based on some Newton iteration approach is applied. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O ( h 1 ∕ 4 ) . As a result, solving such a large class of non-linear equation will not be much more difficult than solving one single linearized equation.

Recently, in [Linear Algebra Appl. 578 (2019), 153–158], Chmielinski and Goldberg studied the continuity and discontinuity of seminorms on infinite-dimensional spaces. Motivated by their paper, we present results concerning seminorms. More precisely, the aim of this work is to investigate geometric consequences of decomposition of seminorm. Moreover, we complement and extend the results from both the paper mentioned above and [Linear Algebra Appl. 515 (2017) 175–179].

In this paper, we prove that any $W^{2,1}$ strong solution to second-order non-divergence form elliptic equations is locally $W^{2,\infty}$ and piecewise $C^{2}$ when the leading coefficients and data are of piecewise Dini mean oscillation and the lower-order terms are bounded. Somewhat surprisingly here the interfacial boundaries are only required to be $C^{1,\text{Dini}}$. We also derive global weak-type $(1,1)$ estimates with respect to $A_{1}$ Muckenhoupt weights. The corresponding results for the adjoint operator are established. Our estimates are independent of the distance between these surfaces of discontinuity of the coefficients., 41 pages; submitted

This article reviews, from a very personal point of view, the origins and the early work on the superfluid to normal transition in very thin films of 4He driven by vortex topological defects using a very crude description of the system which contains only the important physics. I cover the early papers with David Thouless and describe the important insights but also the errors and oversights since corrected by other workers. I then describe some of the all important experimental verifications of the smoking gun prediction of the universal discontinuity of the superfluid density at $$T=T_{{{\mathrm{c}}}}$$ and the necessary extensions to describe the dynamics necessary to compare with experiment.

In this paper, an improved version of the analog equation method (AEM) is proposed, ideally suitable for non-linear dynamic analysis of time-fractional beams with discontinuities. Various sources of non-linearity will be considered as well as different discontinuities, such as those associated with external point supports (shear force discontinuity) and local flexural flexibility (rotation discontinuity). The main idea of the proposed approach is to reformulate the classical AEM by considering an analog equation with an unknown space-time dependent fictitious load and a spatial generalised operator, which includes the classical 4th-order differential operator and generalised functions modelling the discontinuities along the beam. Consistently, the solution to the analog equation is represented by an integral form involving appropriate Green’s functions of the generalised operator. As in the classical AEM formulation, the integral representation of the solution is then approximated dividing the beam in finite elements and considering a constant value of the fictitious load within every beam element. Substituting the so-built approximate solution in the original equation of motion yields a system of fractional differential equations governing the discrete values of the fictitious load, solved by employing a Newmark integration scheme in conjunction with a G-1 algorithm to account for the fractional-derivative memory effects. Computational efficiency and accuracy will be demonstrated against the classical AEM formulation.

Contact force optimization problems exist extensively in engineering. However, there are few simple and universal methods to solve contact force optimization due to the high nonlinearity and discontinuity. This paper proposes an equivalent static displacements (ESD) method to solve the contact force optimization, which is a dual method of the existed equivalent static loads method. The ESD is defined as a set of enforced displacements, whose reaction forces in linear static analysis are equal to the contact forces in nonlinear analysis. Therefore, the contact force optimization problem can be solved by performing static optimization considering reaction forces response. Two engineering examples verify that the ESD method can effectively solve the contact force optimization problem.

In this paper, two three-node triangular thin plate/shell elements are proposed based on the absolute nodal coordinate formulation. As the gradient deficient element, the thin plate/shell element does not possess a full Jacobian matrix for the mapping between different configurations. Thus, the formulation cannot be derived in the conventional method directly based on the continuum mechanics. The independent area coordinate gradients with obvious geometrical interpretation are introduced to simplify the derivation of the shape function. To account for the initially curved reference configuration, the curvilinear coordinate system is used as the global structure coordinate system to calculate the Green-Lagrange strain and formulate the elastic force. The tangent plane is built node-wise to transform the global curvilinear structural gradients to the local area gradients. In this way, the problem of the slope discontinuity associated with the area gradient is circumvented and the continuity of the structural gradient is guaranteed by the standard element assembly procedure. The generalized transformation between the vectors of the Bezier triangle control points and the nodal vectors of the triangular element is presented. Thus, the elements can be used for the integration of computer-aided design and analysis. Finally, the accuracy and convergence property of the new ANCF triangular plate/shell elements are verified by both static and dynamic numerical examples.

The classical problem of the construction of C 1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method. In order to achieve the C 1 conformity on the interfaces of quadrilateral elements, complete second-order derivatives are used at the element vertices, and the information of geometrical mapping is also considered into the construction of shape functions. It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes. However, the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes. Therefore, very fast convergence can be achieved. A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements. Since the present elements are over conforming on element vertices, an approach for handling problems of material discontinuity is also proposed. Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.

Low-cost air quality sensors are promising supplements to regulatory monitors for PM2.5 exposure assessment. However, little has been done to incorporate the low-cost sensor measurements in large-scale PM2.5 exposure modeling. We conducted spatially varying calibration and developed a downweighting strategy to optimize the use of low-cost sensor data in PM2.5 estimation. In California, PurpleAir low-cost sensors were paired with air quality system (AQS) regulatory stations, and calibration of the sensors was performed by geographically weighted regression. The calibrated PurpleAir measurements were then given lower weights according to their residual errors and fused with AQS measurements into a random forest model to generate 1 km daily PM2.5 estimates. The calibration reduced PurpleAir's systematic bias to ∼0 μg/m3 and residual errors by 36%. Increased sensor bias was found to be associated with higher temperature and humidity, as well as longer operating time. The weighted prediction model outperformed the AQS-based prediction model with an improved random cross-validation (CV) R2 of 0.86, an improved spatial CV R2 of 0.81, and a lower prediction error. The temporal CV R2 did not improve due to the temporal discontinuity of PurpleAir. The inclusion of PurpleAir data allowed the predictions to better reflect PM2.5 spatial details and hotspots.

We propose a parameter estimation method for non-stationary Poisson time series with the abnormal fluctuation scaling, known as Taylor&rsquo, s law. By introducing the effect of Taylor&rsquo, s fluctuation scaling into the State Space Model with the Particle Filter, the underlying Poisson parameter&rsquo, s time evolution is estimated correctly from given non-stationary time series data with abnormally large fluctuations. We also developed a discontinuity detection method which enables tracking the Poisson parameter even for time series including sudden discontinuous jumps. As an example of application of this new general method, we analyzed Point-of-Sales data in convenience stores to estimate change of probability of purchase of commodities under fluctuating number of potential customers. The effectiveness of our method for Poisson time series with non-stationarity, large discontinuities and Taylor&rsquo, s fluctuation scaling is verified by artificial and actual time series.

A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization; 2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix; 3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.

This paper deals with an interesting open problem of B.E. Rhoades (Contemporary Math. (Amer. Math. Soc.) 72(1988), 233-245) on the existence of general contractive conditions which have fixed points, but are not necessarily continuous at the fixed points. We propose some more solutions to this problem by introducing two new types of contractive mappings, that is, A-contractive and A`-contractive, which are, in some sense, more appropriate than those of the important previous attempts. We establish some new fixed point results involving these two contractive mappings in compact metric spaces and also in complete metric spaces and show that these contractive mappings are not necessarily continuous at their fixed points. Finally, we suggest an applicable area, where our main results may be employed.

Neuro-transfer function (neuro-TF) approaches have become more and more popular in parametric modeling for electromagnetic (EM) behavior of microwave components. Existing pole-residue-based neuro-TF approach has better capability of dealing with high-order problem than the rational-based neuro-TF approach, but has the discontinuity issue and the associated non-smoothness issue of the poles/residues when the geometrical variations become large while the rational-based neuro-TF approach does not have. This paper addresses this situation and presents a novel hybrid-based neuro-TF technique which systematically combines both pole-residue and rational formats of the transfer functions. Starting with the pole-residue-based transfer functions, we propose a novel technique to automatically identify the poles/residues that are smooth-continuous and the poles/residues that have the discontinuity and non-smoothness issues. The proposed technique converts the poles/residues that have those issues into the coefficients of the rational-based transfer function to solve the discontinuity and non-smoothness issues in the existing pole-residue-based neuro-TF approach. The proposed technique remains the smooth-continuous poles/residues in the pole-residue format of the transfer function to maintain the capability of handling high-order problem. Compared with the existing neuro-TF modeling methods, the proposed technique can obtain better accuracy in challenging applications of large geometrical variations and high order. The proposed technique is illustrated by two examples of parametric modeling of microwave components.

A novel finite difference time domain (FDTD) method based on space transformations is developed that overcomes the inherent obstacles of the conventional FDTD algorithm in a spatially complex domain. Our method leads to an adaptive mesh for the investigated structure based on its geometrical shape without adding additional numerical problems such as late-time instability. In this method, mesh boundaries can follow arbitrary geometrical shapes precisely meaning that discretization errors are minimized. Such errors can be considerable when dealing with large material differences or boundary conditions within the simulation domain. Different meshing and transformation techniques for a variety of different scenarios are presented. We show how boundaries discontinuity can be handled using our method without resulting artificial singularities or zeros. Unlike previous works no dispersive medium has been used so the simulation speed is similar to the standard FDTD method. The usability and superiority of this method in terms of simulation run time and accuracy are shown through a couple of scattering and plasmonic problems. Also, the result of any simulations are validated using finite element method.

We present a systematic method of removing endpoint-discontinuity artifacts in the Fourier analysis of spectral segments, enabling the more accurate extraction of information. This principal-component-removal approach differs from a previous version by using extrapolated (or extended) data outside rather than inside the spectral range. This not only allows coefficients to be accessed to the white-noise limit with no distortion of the segment, but also generates interpolated coefficients for improved analytic insight. Examples are provided.

We consider the random process at − v+(pt) + v−(−qt), t ∈ (−∞, −), where v− and v+ are independent standard Poisson processes if t ≥ 0 and v−(t) = v+(t) = 0 if t < 0. Under certain conditions on the parameters a, p, and q, we study the distribution function G = G(x) of the time of attaining the maximum for a trajectory of this process. In the present article, we find an exact asymptotics for the tails of G. We also find a connection between this problem and the statistical problem of estimation of an unknown discontinuity point of a density function.

This paper presents a methodology to predict the fatigue lifetime in notched geometries subjected to multiaxial loading based on the effective strain energy density concept. The modus operandi consists of defining a fatigue master curve that relates the strain energy density with the number of cycles to failure from standard cylindrical specimens tested under low-cycle fatigue conditions. After that, the multiaxial loading history at the geometric discontinuity is reduced to an equivalent uniaxial loading scenario via the calculation of an averaged value of the strain energy, which is done by combining the equivalent strain energy density concept along with the theory of critical distances. Then, this energy is inserted into the fatigue master curve to estimate the fatigue lifetime. The method is tested in solid round bars with lateral notches subjected to in-phase bending-torsion loading. Overall, the comparison between the experimental and predicted fatigue lives shows a very good agreement. Additionally, the proposed approach enables the determination of the most likely initiation sites as well as the crack angles at the early stage of crack growth. This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.

In minimally invasive surgery, one of the main objectives is to ensure safety and target reaching accuracy during needle steering inside the target organ. In this research work, the needle steering approach is determined using a robust control algorithm namely the Integral sliding mode control &#x0028 ISMC &#x0029 strategy to eliminate the chattering problem associated with the general clinical scenario. In general, the discontinuity component of feedback control input is not appropriate for the needle steering methodology due to the practical limitations of the driving actuators. Thus in ISMC, we have incorporated the replacement of the discontinuous component using a super twisting control &#x0028 STC &#x0029 input due to its unique features of chattering elimination and disturbance observation characteristics. In our study, the kinematic model of an asymmetric flexible bevel-tip needle in a soft-tissue phantom is used to evaluate stability analysis. A comparative study based on the analysis of chattering elimination is executed to determine the performance of the proposed control strategy in real-time needle steering with conventional sliding mode control using vision feedback through simulation and experimental results. This validates the efficacy of the proposed control strategy for clinical needle steering.

In problems involving strong shock waves (the problem of a strong explosion, the motion of bodies with large supersonic speeds, and the problem of supersonic piston expansion), a significant increase in temperature occurs in the disturbed flow region. It is therefore necessary to take the real properties of the gas into account when determining the parameters of the gas flow behind the front of a strong shock wave. This significantly complicates the construction of approximate analytical solutions. However, studies show that the effect of the real properties of the gas on the gas-dynamic parameters of the flow can be taken into account by changing the adiabatic index, i.e., by introducing an effective adiabatic index. If the gas behind the shock wave is in a state of thermodynamic equilibrium, then the effective adiabatic index changes insignificantly in the entire flow zone. This allows us to simulate the flow behind the shock wave front using some perfect gas, whose adiabatic index is determined by the shock wave front depending on the Mach number and the thermodynamic state of the gas. To obtain more accurate solutions for problems with strong shock waves, the model must allow a discontinuity in the adiabatic index at the shock wave. An explicit expression for gas parameters behind the front of an intense shock wave is obtained in this study under the assumption that the adiabatic index undergoes discontinuity during the transition of gas particles through the shock wave surface. Plane and axisymmetric cases are considered.