Infinite Length Research Articles

Vacancy-Induced Thermal Transport and Tensile Mechanical Behavior of Monolayer Honeycomb BeO.

Because of the rapid shrinking trend of integrated circuits, the performances of nanodevices and nanomechanical systems are greatly affected by the joule heating and mechanical failure dilemma. In addition, structural defects are inevitable during experimental synthesis of nanomaterials, which may alter their physical properties significantly. Investigation of the thermal transport and mechanical behavior of nanostructured materials with structural defects is thus a crucial requirement. In this study, the thermal conductivity (TC) and tensile mechanical behavior of monolayer honeycomb BeO are systematically explored using molecular dynamics simulations. An infinite length bulk TC of ∼277.77 ± 8.93 W/mK was found for the pristine monolayer BeO. However, the insertion of 1% single vacancy (SV) and double vacancy (DV) defects reduces the TC by ∼36.98 and ∼33.52%, respectively. On the other hand, the uniaxial tensile loading produces asymmetrical fracture stress, elastic modulus, and fracture strain behaviors in the armchair and zigzag directions. The elastic modulus was reduced by ∼4.7 and ∼6.6% for 1% SV defects along the armchair and zigzag directions, respectively, whereas the reduction was ∼2.7 and ∼ 5.1% for 1% DV defects. Moreover, because of the strong symmetry-breaking effect, both the TC and mechanical strength were significantly lower for the SV defects than those for the DV defects. The highly softening and decreasing trends of the phonon modes with increasing vacancy concentration and temperature, respectively, were noticed for both types of defects, resulting in a reduction of the TC of the defected structures. These findings will be helpful for the understanding of the heat transport and mechanical characteristics of monolayer BeO as well as provide guidance for the design and control of BeO-based nanoelectronic and nanoelectromechanical devices.

BGG categories in prime characteristics

Let \({\mathfrak {g}}\) be a simple complex Lie algebra. In this paper we study the BGG category \({\mathcal {O}}_q\) for the quantum group \(U_q({\mathfrak {g}})\) with q being a root of unity in a field K of characteristic \(p >0\). We first consider the simple modules in \({\mathcal {O}}_q\) and prove a Steinberg tensor product theorem for them. This result reduces the problem of determining the corresponding irreducible characters to the same problem for a finite subset of finite dimensional simple modules. Then we investigate more closely the Verma modules in \({\mathcal {O}}_q\). Except for the special Verma module, which has highest weight \(-\rho \), they all have infinite length. Nevertheless, we show that each Verma module has a certain finite filtration with an associated strong linkage principle. The special Verma module turns out to be both simple and projective/injective. This leads to a family of projective modules in \({\mathcal {O}}_q\), which are also tilting modules. We prove a reciprocity law, which gives a precise relation between the corresponding family of characters for indecomposable tilting modules and the family of characters of simple modules with antidominant highest weights. All these results are of particular interest when \(q = 1\), and we have paid special attention to this case.

Thermomechanical analysis of snap-buckling phenomenon in long FG-CNTRC cylindrical panels resting on nonlinear elastic foundation

Snap-buckling phenomenon in an infinitely long nanocomposite cylindrical panel subjected to uniformly distributed transverse pressure loading is analyzed in this research. It is assumed that the functionally graded (FG) carbon nanotube reinforced composite (CNTRC) shell is resting on nonlinear elastic foundation. The uniform thermal field is also included into the formulation. Thermomechanical properties of the shell are assumed to be temperature dependent. The CNTs distribution pattern can be uniform or functionally graded through the shell thickness. The shell is formulated using a general high-order shear deformation theory. Governing equilibrium equations of the shell which undergoes thermal–mechanical coupling loading are established via the virtual displacement principle. To capture the large deflections, the von Kármán type of kinematic assumptions is utilized. Two types of edge conditions are considered for the shell with infinite length which are immovable simply supported and clamped–clamped. To obtain the limit buckling load of the shell, the two-step perturbation technique and Galerkin procedure are used. Results of this study reveal that the snap-buckling phenomenon can take place in a shallow cylindrical panel subjected to lateral pressure loading. This attractive behavior is observed due to the immovability of the flat edges of the shell. It is shown that the snap-buckling phenomenon in a long cylindrical panel is highly dependent upon the elastic foundations, thermal environments, geometrical parameters and material properties.

Stability estimates in inverse problems for the Schrödinger and wave equations with trapping

For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish Hölder type stability estimates in the geometric inverse problem of determining the electric potential or the conformal factor from the Dirichlet-to-Neumann map associated with the Schrödinger equation and the wave equation. The novelty in this result lies in the fact that we allow some geodesics to be trapped inside the manifold and have infinite length.

The Nonzero External Magnetic Field of Long Solenoids

A widespread assertion has existed for a long time, believing the external field of an infinitely long solenoid should be zero, but it is proofed to be wrong in this work. The components of magnetic flux density of current-carrying, closely wound cylindrical solenoids are calculated. At a distant field point, the external field definitely has a nonzero component, being equal to that of a straight wire of equal length. Since this equivalence is length-independent, it still holds true for ideal solenoids having infinite length. Hence the incorrect and still spreading inference about long solenoids should be rectified. Furthermore, theoretical and experimental discussions involving solenoids should be reviewed again carefully.

Mixed traffic flow of human-driven vehicles and connected autonomous vehicles: String stability and fundamental diagram.

The introduction of connected autonomous vehicles (CAVs) gives rise to mixed traffic flow on the roadway, and the coexistence of human-driven vehicles (HVs) and CAVs may last for several decades. CAVs are expected to improve the efficiency of mixed traffic flow. In this paper, the car-following behavior of HVs is modeled by the intelligent driver model (IDM) based on actual trajectory data. The cooperative adaptive cruise control (CACC) model from the PATH laboratory is adopted for the car-following model of CAVs. The string stability of mixed traffic flow is analyzed for different market penetration rates of CAVs, showing that CAVs can effectively prevent stop-and-go waves from forming and propagating. In addition, the fundamental diagram is obtained from the equilibrium state, and the flow-density chart indicates that CAVs can improve the capacity of mixed traffic flow. Furthermore, the periodic boundary condition is designed for numerical simulation according to the infinite length platoon assumption in the analytical approach. The simulation results are consistent with the analytical solutions, suggesting the validity of the string stability and fundamental diagram analysis of mixed traffic flow.

Dreamworlds, Storyworlds: Narrative Proliferation and the Case of Stjörnu-Odda draumr

Dreamworlds, Storyworlds: Narrative Proliferation and the Case of <i>Stjörnu-Odda draumr</i>

Optimization of the 3p keys kernel parameters by minimizing the ripple of the spectral characteristic

The ideal interpolation kernel is described by the sinc function, and its spectral characteristic is the box function. Due to the infinite length of the ideal kernel, it is not achievable. Therefore, convolutional interpolation kernels of finite length, which should better approximate the ideal kernel in a specified interval, are formed. The approximation function should have a small numerical complexity, so as to reduce the interpolation execution time. In the scientific literature, great attention is paid to the polynomial kernel of the third order. However, the time and spectral characteristic of the third-order polynomial kernels differs significantly from the shape of the ideal kernel. Therefore, the accuracy of cubic interpolation is lower. By optimizing the kernel parameters, it is possible to better approximate the ideal kernel. This will increase the accuracy of the interpolation. The first part of the paper describes a three-parameter (3P) Keys interpolation kernel, r. After that, the algorithm for optimizing the parameters of the 3P Keys kernel, is shown. First, the kernel is disassembled into components, and then, over each kernel component, Fourier transform is applied. In this way the spectral characteristic of the 3P Keys kernel, H, was determined. Then the spectral characteristic was developed in the Taylor series, HT. With the condition for the elimination of the members of the Taylor series, which greatly affect the ripple of the spectral characteristic, the optimal kernel parameters (?opt, ?opt, gopt) were determined. The second part of the paper describes an experiment, in which the interpolation accuracy of the 3P Keys kernel, was tested. Parametric cubic convolution (PCC) interpolation, with the 3P kernel, was performed over the images from the Test database. The Test database is created with standard Test images, which are intensively used in Digital Image Processing. By analyzing the interpolation error, which is represented by the Mean Square Error, MSE, the accuracy of the interpolation was determined. The results (?opt, ?opt, gopt, MSEmin) are presented on tables and graphs. Detailed comparative analysis showed higher interpolation accuracy with the proposed 3P Keys interpolation kernel, compared to the interpolation accuracy with, 1P Keys and 2P Keys interpolation kernels. Finally, the numerical values of the optimal kernel parameters, which are determined by the optimization algorithm proposed in this paper, were experimentally verified.

A Real-Time Capable PDE Model for an Industrial Heating Process

This paper presents a modeling approach of an industrial heating process where a stripe-shaped workpiece is heated up to a specific temperature by applying hot air through a nozzle. The workpiece is moving through the heating zone and is considered to be of infinite length. The speed of the substrate is varying over time. The derived model is supposed to be computationally cheap to enable its use in a model-based control setting. We start by formulating the governing PDE and the corresponding boundary conditions. The PDE is then discretized on a spatial grid using finite differences and two different integration schemes, explicit and implicit, are derived. The two models are evaluated in terms of computational effort and accuracy. It turns out that the implicit approach is favorable for the regarded process. We optimize the grid of the model to achieve a low number of grid nodes while maintaining a sufficient amount of accuracy. Finally, the thermodynamical parameters are optimized in order to fit the model's output to real-world data that was obtained by experiments.

Current channel in plasma of inverse exploding planar foils

In the research of &lt;i&gt;Z&lt;/i&gt;-pinch, the initial establishment of current in load, current density distribution mode and current evolution characteristics in different stages are of great significance in studying the development of plasma dynamics, analyzing plasma instability mode, and carrying out the MHD numerical simulation. Thin planar foil is an ideal configuration with continuous two-dimensional structure to study the problem. Based on an ideal model that consists of foil-backpost configuration under the assumption of infinite length in reverse exploding condition, the establishment, distribution and evolution of the current channel, magnetic field distribution characteristics and the force state of foil plasma by the inductive mode are calculated and analyzed theoretically. Relevant experiments are carried out on the QG-1 facility with about 1.4 MA peak current and 100 ns rise time to verify the calculated results. The self-emission graphs of exploding foils are recorded by visible-light frame cameras from side-on view and end-on view. Different load configurations are utilized including symmetric and asymmetric condition both assembled with two 20-μm-thick aluminum foils. The results show that the establishment of the initial current in foil (0–70 ns) accord with the expectation of the inductance model. The inductance feature determines the distribution of the current in this stage, which causes the current to aggregate in foil edges and then the edges will suffer much higher magnetic field and &lt;i&gt; &lt;b&gt;J&lt;/b&gt; &lt;/i&gt; × &lt;i&gt; &lt;b&gt;B&lt;/b&gt; &lt;/i&gt; force than the center. This results in the formation of a clamp plasma morphology. The later images (70–120 ns) show that the intense emission region will transfer from the foil edges to the center, which proves a transfer of current channel. So the magnetic field and &lt;i&gt; &lt;b&gt;J&lt;/b&gt; &lt;/i&gt; × &lt;i&gt; &lt;b&gt;B&lt;/b&gt; &lt;/i&gt; force in the foil center increase and a peak convex plasma morphology forms then. It shows that the current distribution will be affected by the plasma evolution process. The convergence process of ablated plasma with current finally leads to rapidly switch the current channel (in 60–80 ns).

Torsional Wave in a Dissipative Cylindrical Shell Under Initial Stresses

The dispersion relation of torsional wave in a dissipative, incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated. The governing equation and closed form solutions are derived with the aid of Biot's principle. Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details. We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form. Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs. The analytical and numerical solutions reveal that, the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell. The numerical results reveal that, the initial stresses and dissipation, considerably, effect the phase velocity of the torsional wave. It has been observed that, any change in dissipation parameter (δ) produces a substantial change in damping velocity of torsional wave. In addition, it can be seen that, the phase velocity increases as the initial stress parameter increases. Finally, the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation. The conclusion made shown the consistency with the Biot's incremental deformation theory, and the effective on model such as engineering mechanics and displacement of particles.

Analytical Solution for Vibrations of a Modified Timoshenko Beam on Visco-Pasternak Foundation Under Arbitrary Excitations

An analytical solution is derived for dynamic response of a modified Timoshenko beam with an infinite length resting on visco-Pasternak foundation subjected to arbitrary excitations. The modified Timoshenko beam model is employed to further consider the rotary inertia caused by the shear deformation of a beam, which is usually neglected by the traditional Timoshenko beam model. By using Fourier and Laplace transforms, the governing equations of motion are transformed from partial differential forms into algebraic forms in the Laplace domain. The analytical solution is then converted into the time domain by applying inverse transforms and convolution theorem. Some widely used loading cases, including moving line loads for nondestructive testing, travelling loads for seismic wave passage, and impulsive load for impact vibration, are also discussed in this paper. The proposed generic solutions are verified by comparing their degraded results to the known solutions in other literature. Several examples are performed to further investigate the differences of the beam responses obtained from the modified and the traditional Timoshenko beam models. Results show that the modified Timoshenko beam simulates the beam responses more accurately than the traditional model, especially under the dynamic loads with a high frequency. The analytical solutions proposed in this paper can be conveniently used for design and applied as an effective tool for practitioners.

Linear-Time Temporal Answer Set Programming

AbstractIn this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.

A highly secure stream cipher based on analog-digital hybrid chaotic system

In recent decades, an avalanche of chaos-based cryptosystems have been proposed for information security. Most of these systems are not immune to the dynamical degradation of digital chaos and many have been shown to suffer from a lack of security. In this paper, a stream cipher system based on an analog–digital hybrid chaotic system is presented. The hybrid model can construct digital chaotic maps without degeneration and guarantee synchronization of analog chaotic systems for successful decryption. Moreover, focusing on the characteristics of low-dimensional chaotic maps, a modified three-dimensional Logistic map is proposed to improve the weaknesses of uneven distribution, low complexity and limited parameter space. Combining the three-dimensional Logistic map and the hybrid model, the proposed stream cipher has advantages of huge key space, virtually infinite cycle length and tight security. In particular, it is not affected by the dynamical degradation. Performance and security analyses indicate that the proposed stream cipher is highly resistant to various chaos-based attacks and cryptanalytic attacks.

Contradictions in the Plane Contact Problem of the Theory of Elasticity on the Compression of Cylinders in Contact with Parallel Generators

The inapplicability of the reference formula for determining the convergence of two statically compressed parallel cylinders made of a homogeneous, isotropic and physically linear material has been proved due to a well-known logarithmic feature in the plane classical problem of mechanics of elastic solids. In the special case of the elastic interaction of a cylinder with a half-plane, when one of the radii has an infinite length, it has been found that the convergence also becomes equal to infinity. This paradoxical result contradicts not only the physical and mechanical meaning of the process under study, but also confirms the inadequacy of Flamant model of a simple radial stress state in determining displacements. The authors have proposed an algorithm for eliminating the contradictions based on the solution of Fredholm integral equation of the first kind. In the future, it can be considered as a new fundamental and applied problem of the theory of elasticity, which is of a great importance for a refined assessment of the contact strength and stiffness of the cylindrical parts of load-bearing structures taking into account the general and local deformations (cylindrical rollers, gears, road surfaces, when they are compacted with steel rollers, etc.) on the basis of a flat Flamant calculation scheme considering three stress components and the width of the cylinder contact area previously developed and mathematically approximated by the authors.

Stability of an infinite beam on visco-elastic foundation under a uniformly moving distributed mass

The stability of a distributed mass of finite length travelling uniformly on an infinite beam resting on a visco-elastic foundation is considered in this paper. The focus is placed on the effects of the length of the distributed mass on the stability of the mass-beam-foundation system. It is argued that on the stability boundary, the mass-beam-foundation system is in the form of a steady state periodic motion. To seek the periodic solution, the infinite beam is divided into three segments, in each of which the differential equation is solved analytically. By comparing the stability boundary curves of the distributed mass of finite length with the one of infinite length, it is found that the stability boundary curves of finite length do not converge to the one of infinite length. It is believed that the course of the failure to converge towards the infinite length model is the differences in the boundary conditions at infinity. On the other hand, the stability boundary curves of finite length do converge to the point mass model when the mass length approaches zero. Compared to the point mass model, the distributed mass model is less stable. More precisely, for a specified system damping and total mass, the critical speed is in general much smaller if distributed model is adopted. The longer the mass length, the smaller the critical speed is. In short, the conventional point mass model overestimates the stability of the mass-beam-foundation system.

Mathematical model of the influence of the rheology of lubricating compositions on the safety of rolling stock movement

The article deals with the search for rational and balanced solutions to ensure maximum safety of rolling stock movement, taking into account the minimization of costs and technical measures. The paper presents a mathematical model for calculating the effect of rheological characteristics of lubricants on the service life of heavy-loaded friction units of rolling stock. The scheme of interaction of a wheel with a rail at a single-point contact is presented in the form of contacts of two cylinders of infinite length. The results of numerical analysis of the found analytical dependences of the influence of the plasticity parameter on the coefficient of friction, the influence of the plasticity parameter on the supporting force created by the lubricant layer during the movement of surfaces are presented. The influence of the coefficient of friction on the safety of rolling stock movement in the curved sections of the track is established.

An analytical solution of temperature near nuclear waste canister under three-dimensional heat transfer condition

The temperature distribution is an important issue for the design and safety assessment of the repository for disposing high-level radioactive nuclear waste (HLW). In order to analyze the heat conduction property near the HLW canister under three-dimensional heat transfer condition, a solution to the temperature distribution is obtained by combining the following two parts: (1) The ratio of temperature between the finite length heat source (FLHS) and infinite length heat source (ILHS), which are obtained by integrating the solution of the point source heat transfer model. (2) An analytical solution to the temperature distribution near HLW canister with two-dimensional heat transfer for double-layered media in the lateral direction. Then, the solution of temperature near the HLW canister under three-dimensional heat transfer condition is verified by checking against the existing ones for a special case in the literature. Finally, a parametric study is performed to investigate the temperature performance in the buffer layer and surrounding rock with different parameters.

Spatiotemporal characteristics of spin transport in compensated metals with electron–hole exchange interaction

We develop a theory describing spatiotemporal behavior of spin transport in two-band metals by postulating a spin–exchange interaction between electrons and holes. Starting with the semiclassical Boltzmann equation, we derive a system of coupled diffusion equations and solve them analytically under steady-state conditions. The solutions reveal two types of electron–hole coupled-spin transport modes: a dissipative mode and a nondissipative mode with an infinite spin diffusion length. The two modes are the manifestations of two types of spin coupling channels. Besides the exchange interaction, we incorporate into our derivation the relaxation caused by the spin–orbit interaction to show how it affects the spin transport characteristics of the two modes.

Shock-induced interfacial instabilities of granular media

This paper investigates the shock-induced instability of the interfaces between gases and dense granular media with finite length via the coarse-grained compressible computational fluid dynamics–discrete parcel method. Despite generating a typical spike-bubble structure reminiscent of the Richtmyer–Meshkov instability (RMI), the shock-driven granular instability (SDGI) is governed by fundamentally different mechanisms. Unlike the RMI arising from baroclinic vorticity deposition on the interface, the SDGI is closely associated with the interfacial and bulk granular dynamics, which evolve with the transient coupling between particles and gases. Consequently, the SDGI follows a growth law distinctly different from that of the RMI, namely a semilinear slow regime followed by an exponentially expedited regime and a quadratic asymptotic regime. We further establish the instability criteria of the SDGI for granular media with infinite and finite lengths, which do not exist in the RMI. A scaling growth law of the SDGI for dense granular media with finite length is derived by normalizing the time with the rarefaction propagation time, which successfully collapses the data from cases with varying shock strength, particle column length and particle volume fraction and ought to hold for granular media with varying particle parameters. The effect of the initial perturbation magnitude can be properly considered in the scaling growth law by incorporating it into the length normalization.