Conventional Linear Theory Research Articles

Refined linearly anisotropic couple-stress elasticity

A recently developed, refined version of the conventional linear couple-stress theory of isotropic elasticity is extended to include the influence of anisotropic material effects. With this development, the implied refined theory (1) retains ability to determine the spherical part of the couple-stress and (2) is further furnished with constitutive ability to embrace modelling of linearly elastic solids that exhibit inherent polar material anisotropy of advanced levels that reach the class of locally monoclinic materials. This type of anisotropy embraces most of the structural material subclasses met in practice, such as those of general and special orthotropy, as well as the subclass of transverse isotropy. The thus obtained, enhanced version of the refined theory is furnished with ability to also handle structural analysis problems of polar fibrous composites reinforced by families of perfectly flexible fibres or, more generally, polar anisotropic solids possessing one or more material preference directions that do not possess bending resistance. A relevant example application considers and studies in detail the subclass of polar transverse isotropy caused by the presence of a single family of perfectly flexible fibres. By developing the relevant constitutive equation, and explicitly presenting it in a suitable matrix rather than indicial notation form, that application also exemplifies the way that the spherical part of the couple-stress is determined when the fibres are straight. It further enables this communication to initiate a discussion of further important issues stemming from (1) the positive definiteness of the full, polar form of the relevant strain energy function and (2) the lack of ellipticity of the final form attained by the governing differential equations.

Molecular investigation on CO₂-CH₄ displacement and kerogen deformation in enhanced shale gas recovery

CO₂-enhanced gas recovery (EGR) is a promising method that can not only improve the production of adsorbed shale gas but also achieve the geological storage of CO₂. During the injection of CO₂, shale is expected to deform due to both CH₄ desorption-induced shrinkage and CO₂ adsorption-induced swelling. Regardless of the potential effects on gas permeability and transport, the sorption-induced deformation remains poorly understood and is generally overlooked in large-scale simulations of CO₂-EGR. In this paper, Monte Carlo and molecular dynamics simulations are performed to study the CO₂-CH₄ displacement in the type II-D overmature kerogen (i.e., the primary organic matter in shale). Our results indicate that the CO₂-CH₄ displacement efficiency increases with the increase of the CO₂ injection pressure but decreases linearly with the increase of the reservoir depletion pressure. Moreover, the sorption-induced deformation is measured as volumetric strain and analyzed after initial CH₄ saturation, pressure drawdown, and CO₂ injection. It is observed that CO₂ injection can induce a volume expansion of the original CH₄-saturated kerogen up to 5%. In addition, a novel non-linear adsorption-strain model is derived to provide a theoretical basis for kerogen deformation by taking the gas adsorption and deformation coupling into consideration. Different from the conventional linear theory, the increment of volumetric strain induced by gas adsorption becomes much faster when close to adsorption saturation. The derived model can accurately capture the observed non-linearity and predict deformation caused by single-component gas and gas mixtures. Since swelling can further reduce shale permeability, these results imply that CO₂ injectivity and CH₄ production rate may both decline faster than expected in CO₂-EGR.

On the nature of instabilities in externally perturbed liquid sheets

The evolution of the interfacial instabilities on a smooth and laminar liquid sheet formed by the oblique impingement of two liquid jets is investigated in the presence of external acoustic forcing. The forced liquid sheet exhibits different instability patterns, such as flapping flag, sinuous breakup and vibrating membrane structure, depending on the forcing frequency. The transition frequencies, where the instability pattern changes, are obtained using the linear theory of sheet instability and are shown to be increasing functions of the jet Weber number. These different instability patterns show distinct growth rate behaviours, which cannot be predicted using a unique theory such as the conventional linear theory of sheet breakup. The dynamics of liquid sheet breakup in the presence of forcing is further assessed with the help of established instability theories. Our measurements show that the sheet thickness distribution plays a major role in dictating the relative influence of different mechanisms on the instability characteristics. All the results are finally consolidated to arrive at the instability regime map on the Weber number versus frequency ( $We$ – $\tilde {\omega }$ ) space to serve as a guideline for adopting a suitable modelling approach.

WITHDRAWN: Understanding complexity and dynamics in the career development of eSports athletes

ABSTRACT With the accelerated growth of the esports industry over the last few years, there has been a corresponding increase in the number of esports athletes. Yet there is limited research examining these athletes’ professional career journeys. This study provides a novel investigation into their career development process. This qualitative study uses a sample of 35 esports athletes from 16 professional esports clubs in China. Findings from semi-structured interviews confirmed our proposition that traditional career theories may be inadequate to capture the complex and dynamic nature of the newly emerged careers within esports. The authors propose that Chaos Theory in Careers (CTC) provides principles that may more effectively describe and explain the nature and main characteristics of esports careers, compared to the more conventional linear or stage-based sports career theories. This study makes a significant theoretical contribution through developing esports career theory which is applicable to a contemporary setting and has practical implications to practitioners for esports talent identification, recruitment and development.

Mathieu instability of Arctic Spar by nonlinear time-domain simulations

Arctic Spar typically has a sloped hull surface near the waterline to break ice through bending. However, the rapid variation of its waterplane area by the heave motion may cause unexpected nonlinear behaviors, which can result in instability. In the current study, the heave-to-pitch/roll and heave-to-heave Mathieu instability (MI) of Arctic Spar are investigated by using a nonlinear time-domain simulation program. The time-dependent nonlinear hydrostatic-restoring coefficient (HC) and nonlinear Froude-Krylov (FK) force are considered for the instantaneous wetted body underneath the instantaneous wave elevation. The effects of the two nonlinear terms for the generation of heave-to-pitch and heave-to-heave MI are systematically compared and discussed by employing four different approaches including conventional linear theory. Analytical equations of heave and pitch are also used with Hill's infinite determinants method to determine the boundaries of Mathieu's equation parameters where instability occurs. Through a series of numerical simulations, the occurrences of both heave-to-pitch and heave-to-heave MI have been clearly demonstrated both in regular and irregular waves. The simulated results agree well with the theoretical instability diagram. The importance of the combined effects of nonlinear FK forces and nonlinear HC in triggering pronounced heave-to-heave MI is underscored especially in the case of 100-year storm condition.

Atomistic-to-continuum description of edge dislocation core: Unification of the Peierls-Nabarro model with linear elasticity

Conventional linear elasticity theory predicts the strain fields of a dislocation core to diverge, whereas it is known from atomistic simulations that core strains should remain finite. We present an analytical solution to a generalized, variational Peierls-Nabarro model of edge dislocation displacement fields that features a finite core width and correct isotropic elastic behavior at large distances away from the core. We derive an analytical expression for the dislocation core radius, representing the convergence radius of the linear elasticity far-field expansion. The strain fields are in qualitative agreement with atomistic simulations of $\frac{1}{2}[111](10\overline{1})$ edge dislocations in bcc tungsten and iron. The treatment is based on the multistring Frenkel-Kontorova model that we reformulate as a generalized Peierls-Nabarro model using the principle of least action.

Nonlinear kinematics analysis and internal resonance of wind turbine blade with coupled flapwise and edgewise vibration modes

Environmental issues and energy crisis have caused the world attention to the renewable energies; especially the wind power, since they have low cost and high reliability. To achieve higher capacity, wind turbines have increased in their size over the years. However, the large size of the modern turbines has exacerbated the problem of vibrations, which results in lower efficiency and power generation. Because of the large deformations, the conventional linear theories cannot model the blades accurately, due to the importance of nonlinear effects in large scale wind turbines. In this research, a nonlinear kinematic model of the wind turbine blade is developed using the Hamilton's principle. This model is then simplified to three modal equations, two in flapwise direction and one in edgewise direction. These equations are then solved analytically using the multiple scales perturbation method, under the free vibration conditions including the non-resonance and internal resonance cases. In the non-resonance case, the accuracy of the perturbation method is compared with the numerical solutions. In the internal resonance case, the phenomenon of energy transfer between the modes is shown in three different conditions.

Weight-Balanced Timed Event Graphs to Model Periodic Phenomena in Manufacturing Systems

Timed event graphs (TEGs) are suitable to model manufacturing systems in which synchronization and delay phenomena appear. Since 1980s, TEGs are studied as a class of linear discrete event systems in idempotent semirings such as the (min,+) algebra. In this paper, we consider the class of weighted TEGs (WTEGs) that corresponds to TEGs where the edges have integer weights. By introducing nonunitary weights, WTEGs widen the class of manufacturing systems that can be modeled, especially systems with batches and duplications. Moreover, a subclass of WTEGs called weight-balanced TEGs (WB-TEGs) can be studied with the algebraic tools that stem from the theory of (min,+) linear systems. In this paper, the focus lies on some modeling issues for manufacturing systems. Besides cutting and palletization operations, it is shown that WB-TEGs are also well adapted to describe periodic routing policies and, in a symmetrical way, how to merge flows similar to a multiplexer. In order to simplify the modeling step, a class of cycloweighted TEGs (CW-TEGs) is introduced. It is an extension of WTEGs where the weights of the edges can change according to a periodic sequence. Finally, we propose some elements of modeling that can be described by CW-TEGs or equivalently with an input–output transfer relation in an appropriate idempotent semiring of operators. Note to Practitioners — The (min,+) linear system theory used in this paper aims at obtaining linear models for a subclass of man-designed systems, such as automated manufacturing systems or traffic networks. This theory has many analogies with the conventional linear system theory (for continuous systems) and it provides the basis to develop a specific control theory for man-made systems. More precisely, the theory of (min,+) linear systems is well suited to systems where the prevailing phenomena are synchronizations, delays, duplications, and batches. These phenomena arise, for example, in operations such as assembly/matching, cutting/lot splitting, and palletization/lot making. Among the possible representations, we can describe these systems by transfer functions obtained by the combination of a finite number of basic operators. This is analogous to block diagram in the conventional system theory, i.e., a transfer function describes the complete input-output behavior of a system. In the context of manufacturing systems, a transfer function describes the way a system maps an input flow of materials (raw part inputs) into an output flow (finished parts), without the necessity of simulation tools to predict this. Moreover, the transfer function thus obtained can be used to compute controllers in order to regulate the internal flows of a system, for instance to decrease internal stocks. In the case of an automated system, the obtained controllers can be implemented on a programmable logic controller as supplementary code. This paper focuses on the use of these algebraic tools in the model process of manufacturing systems and, in particular, on their ability to describe splitting and merging flows of materials.

Assessment of interfacial charge accumulation in oil-paper interface in transformer insulation from polarization-depolarization current measurements

Accumulation of interfacial space charge in oil-paper interface is a critical issue in insulation diagnostics of transformers. This interfacial charge mainly accumulates due to the conductivity difference of oil and paper. Accumulation of interfacial charge leads to localized field enhancement, which further leads to partial discharges and acceleration in the aging of insulation. Therefore, from the point of view of transformer insulation diagnostics, assessment of interfacial charge is very important. However, it is not easy to estimate interfacial space charge behavior from the transformer diagnostics methods currently in use. In case of Polarization-Depolarization Current (PDC) measurement, a well known method for transformer condition monitoring, the effect of interfacial charge is reflected in the non-linearity of current response during polarization and de-polarization. During de-polarization process, a part of the interfacial charge accumulated during polarization period is absorbed by the electrodes producing a current, which is difficult to separate using conventional linear dielectric theory. In this paper, an attempt has been made to separate this current component from de-polarization current through considering charge de-trapping mechanism. Terming this current component as de-trapping current, its relationship with other parameters of transformer insulation is discussed. The developed methodology has been applied on several practical transformers. It was observed that the time constant of de-trapping current is related to the paper conductivity, oil conductivity, dissipation factor and age of the insulation.

Linear equivalent models at the maximum power point based on variable weather parameters for photovoltaic cell

In order to sweep completely the obstacle to the whole linearization of photovoltaic (PV) system with non-linear PV cell, in this paper, the voltage-current characteristic of PV cell at the maximum power point (MPP) is linearized and two linear equivalent models including Thevenin equivalent model and Norton equivalent model are proposed. On the basis of this work, the whole linearization of PV system is workable and reasonable, and then the conventional linear theories or laws can be used to study PV system conveniently. Meanwhile, in this work, the direct relationships between three linear model parameters and variable weather parameters (VWP) were found, which ensures the strong adaptation of these proposed models to the varying weather conditions. Finally, some simulation experiments verify that these proposed models are feasible and available in practical application, illustrate that the characteristics of three linear model parameters are influenced by varying weather conditions and unaffected by varying load, and show that PV system using the proposed Thevenin equivalent model has the same maximum power point tacking (MPPT) stead-state performance and similar MPPT transient-state performance with the conventional four-parameter model under fast varying weather conditions.

Numerical investigation of heated gas flow in a thermoacoustic device

Self-sustained oscillation in a standing wave thermoacoustic device is reproduced via computational fluid dynamics simulations, and heated flow behavior in the device is explored using the results obtained. The straight-type thermoacoustic device is composed of two resonance tubes, two heat exchangers and a stack. In these simulations, both the acoustic characteristics and the temperature field during self-sustained oscillation are considered. Therefore, to reproduce the self-sustained oscillatory flow, an acoustic signal is injected into the computational domain as a trigger pulse. From the results, oscillatory fluid motion around the engine is investigated, and characteristics, including the acoustic field or work flow, the energy dissipation, the work source and other associated aspects, are estimated. The results agree well with those of linear theory, although high energy dissipation caused by vortex generation is observed near the engine. This result verifies the computational fluid dynamics simulation results. The temperature field around the engine is also investigated. The results show occurrence of asymmetrical temperature oscillations within the heat exchangers. This behavior cannot be predicted using linear theory because the non-uniform temperature gradient in the engine unit is transferred in stream-wise by convection. Finally, a modification to conventional linear theory is suggested to reproduce this behavior.

Resilient controller design availing recursive technique rooted Lyapunov function for a dynamic system

Traditional control of nonlinear processes is based on conventional linear control theories, due to existence of wealthy tools for the linear design and analysis. Nonlinear control theories are always deal the concept of nonlinear control design. Recursive (backstepping) technique is a novel framework for nonlinear control design. Backstepping is recently developed design tool for constructing globally stabilized control laws for a certain class of nonlinear dynamic systems. Backstepping technique is designed by breaking down a complex nonlinear system into smaller subsystems and design control Lyapunov function and virtual controls for each and every subsystem individually. Finally, combined the individual controllers designed for the subsystem and make a single one. Lower triangular form can only handle with this technique. A trademark of backstepping is that allows us to benefit from useful nonlinearities. This can be done by choosing virtual control laws properly. Effectiveness of the controller is demonstrated through simulations for large perturbations in plant parameters. The main advantage of backstepping technique is that it can use everywhere irrespective of the operating points.

Coulomb Crystals with Isotopic Impurities

AbstractVibration modes and thermodynamic properties of a body‐centered cubic (bcc) Coulomb crystal with a small admixture of substitutional isotopic impurities are studied analytically applying the perturbation theory of disordered crystal spectra and the Lifshitz‐Krein trace formula. We calculate the density of phonon states of the perfect bcc Coulomb crystal and use it to compute the heat capacity of the crystal with impurities in a wide range of temperatures. It is shown that the ratio of an impurity contribution to the crystal heat capacity over the perfect crystal specific heat tends to a constant in the low‐temperature quantum regime and decays as T–2 in the classic regime of high temperatures. It is also shown that even a small concentration of heavy impurities amplifies significantly the total crystal heat capacity. The results are compared with those obtained using the more conventional linear mixing theory. It is demonstrated that both methods give similar results at all tempera‐tures when the impurity mass is not too different from that of the base ions but a strong discrepancy is observed at low and intermediate temperatures when impurities are noticeably lighter or heavier. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonlinear thermokinetic phenomena due to the Seebeck effect.

We propose a novel mechanism to produce nonlinear thermokinetic vortex flows around a circular cylinder with ideally high thermal conductivity in an electrolyte. That is, the nonlinear thermokinetic slip velocity, which is proportional to the square of the temperature gradient [∇(T)0(2)], is derived based on the electrolyte Seebeck effect, heat conduction equation, and Helmholtz–Smoluchowski formula. Different from conventional linear thermokinetic theory, our theory predicts that the inversion of the temperature gradient does not change the direction of the thermokinetic flows and thus a Janus particle using this phenomenon can move to the both hotter and colder regions in a temperature gradient field by changing the direction of its dielectric end. Our findings bridge the gap between the electro- and thermo-kinetic phenomena and provide an integrated physical viewpoint for the interface science.

Periodic projectile linear theory for aerodynamically asymmetric projectiles

A new analytical tool is proposed to aid in the design and performance evaluation of advanced guided projectile concepts. A projectile linear theory applicable to aerodynamically asymmetric configurations is created, leading to a linear, periodic dynamic system. Utilizing concepts in Floquet theory, stability of asymmetric projectile configurations is explored. While stability of many asymmetric projectile configurations can be accurately predicted using averaged linear, constant coefficient system dynamics, there are some configurations where the use of linear periodic systems theory is required for accurate stability prediction. This fact is shown by comparing stability boundaries of an example projectile configuration using the conventional projectile linear theory model and the new periodic projectile linear theory model.

Hubbard-model description of the high-energy spin-weight distribution in La2CuO4

The spectral-weight distribution in recent neutron scattering experiments on the parent compound La$_2$CuO$_4$ (LCO), which are limited in energy range to about 450\,meV, is studied in the framework of the Hubbard model on the square lattice with effective nearest-neighbor transfer integral $t$ and on-site repulsion $U$. Our study combines a number of numerical and theoretical approaches, including, in addition to standard treatments, density matrix renormalization group calculations for Hubbard cylinders and a suitable spinon approach for the spin excitations. Our results confirm that the $U/8t$ magnitude suitable to LCO corresponds to intermediate $U$ values smaller than the bandwidth $8t$, which we estimate to be $8t \approx 2.36$ eV for $U/8t\approx 0.76$. This confirms the unsuitability of the conventional linear spin-wave theory. Our theoretical studies provide evidence for the occurrence of ground-state d-wave spinon pairing in the half-filled Hubbard model on the square lattice. This pairing applies only to the rotated-electron spin degrees of freedom, but it could play a role in a possible electron d-wave pairing formation upon hole doping. We find that the higher-energy spin spectral weight extends to about 566 meV and is located at and near the momentum $[\pi,\pi]$. The continuum weight energy-integrated intensity vanishes or is extremely small at momentum $[\pi,0]$. This behavior of this intensity is consistent with that of the spin waves observed in recent high-energy neutron scattering experiments, which are damped at the momentum $[\pi,0]$. We suggest that future LCO neutron scattering experiments scan the energies between 450 meV and 566 meV and momenta around $[\pi,\pi]$.

Image properties of embedded lenses

We give analytic expressions for image properties of objects seen around point mass lenses embedded in a flat $\ensuremath{\Lambda}\mathrm{CDM}$ universe. An embedded lens in an otherwise homogeneous universe offers a more realistic representation of the lense's gravity field and its associated deflection properties than does the conventional linear superposition theory. Embedding reduces the range of the gravitational force acting on passing light beams thus altering all quantities such as deflection angles, amplifications, shears and Einstein ring sizes. Embedding also exhibits the explicit effect of the cosmological constant on these same lensing quantities. In this paper, we present these new results and demonstrate how they can be used. The effects of embedding on image properties, although small, i.e., usually less than a fraction of a percent, have a more pronounced effect on image distortions in weak lensing where the effects can be larger than 10%. Embedding also introduces a negative surface mass density for both weak and strong lensing, a quantity altogether absent in conventional Schwarzschild lensing. In strong lensing, we find only one additional quantity, the potential part of the time delay, which differs from conventional lensing by as much as 4%, in agreement with our previous numerical estimates.

Development of negative skin friction on single piles: uncoupled analysis based on nonlinear consolidation theory with finite strain and the load-transfer method

The development of negative skin friction (NSF) on single piles is investigated based on an uncoupled method of analysis with the Mikasa (1963) generalized nonlinear consolidation theory in terms of finite strain and the nonlinear load-transfer method. Predicted results are compared with results based on the conventional linear consolidation theory with infinitesimal strains. It is found that predicted development of dragload using the conventional consolidation theory is slightly greater and conservative compared to that using the nonlinear consolidation theory based on effective stress (β method). Effective stress predictions using the conventional theory are larger due to the faster dissipation of excess pore pressures, with the assumption of constant coefficient of consolidation and permeability. However, since the relative displacements required to mobilize the ultimate skin friction are small, and piles are usually installed near the final stages of soil consolidation, the differences in the predictions for the development of dragload on piles between the two consolidation theories are overshadowed. Using the uncoupled model for pile NSF, it is therefore found that the most significant factor for the estimation of dragload and downdrag is the proper selection of the β value rather than the consolidation theory used.

Time delay in Swiss cheese gravitational lensing

We compute time delays for gravitational lensing in a flat $\ensuremath{\Lambda}$ dominated cold dark matter Swiss cheese universe. We assume a primary and secondary pair of light rays are deflected by a single point mass condensation described by a Kottler metric (Schwarzschild with $\ensuremath{\Lambda}$) embedded in an otherwise homogeneous cosmology. We find that the cosmological constant's effect on the difference in arrival times is nonlinear and at most around 0.002% for a large cluster lens; however, we find differences from time delays predicted by conventional linear lensing theory that can reach $\ensuremath{\sim}4%$ for these large lenses. The differences in predicted delay times are due to the failure of conventional lensing to incorporate the lensing mass into the mean mass density of the universe.

The simplest problem in the collective dynamics of neural networks: is synchrony stable?

For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem—local stability of synchrony—is non-trivial to solve and requires novel methods for its solution. In particular, the discrete mode of pulsed communication together with the complicated connectivity of neural interaction networks requires a non-standard approach. The dynamics in the vicinity of the synchronous state is determined by a multitude of linear operators, in contrast to a single stability matrix in conventional linear stability theory. This unusual property qualitatively depends on network topology and may be neglected for globally coupled homogeneous networks. For generic networks, however, the number of operators increases exponentially with the size of the network.We present methods to treat this multi-operator problem exactly. First, based on the Gershgorin and Perron–Frobenius theorems, we derive bounds on the eigenvalues that provide important information about the synchronization process but are not sufficient to establish the asymptotic stability or instability of the synchronous state. We then present a complete analysis of asymptotic stability for topologically strongly connected networks using simple graph-theoretical considerations.For inhibitory interactions between dissipative (leaky) oscillatory neurons the synchronous state is stable, independent of the parameters and the network connectivity. These results indicate that pulse-like interactions play a profound role in network dynamical systems, and in particular in the dynamics of biological synchronization, unless the coupling is homogeneous and all-to-all. The concepts introduced here are expected to also facilitate the exact analysis of more complicated dynamical network states, for instance the irregular balanced activity in cortical neural networks.