Equilibrium Mode Research Articles

New method for the investigation of mode coupling in graded-index polymer photonic crystal fibers using the Langevin stochastic differential equation

The mode coupling in a graded-index polymer photonic crystal fiber (GI PPCF) with a solid core has been investigated using the Langevin equation. Based on the computer-simulated Langevin force, the Langevin equation is numerically integrated. The numerical solutions of the Langevin equation align with those of the time-independent power flow equation (TI PFE). We showed that by solving the Langevin equation, which is a stochastic differential equation, one can successfully treat a mode coupling in GI PPCFs, which is an intrinsically stochastic process. We demonstrated that, in terms of effectiveness, the Langevin equation is preferable compared to the TI PFE. The GI PPCF achieves the equilibrium mode distribution (EMD) at a coupling length that is even shorter than the conventional GI plastic optical fiber (POF). The application of multimode GI PCFs in communications and optical fiber sensor systems will benefit from these findings.

A magnetic diagnostic suite for the Pegasus-III experiment.

Pegasus-III is an ultralow aspect ratio spherical tokamak providing a dedicated US experiment for comparative solenoid-free startup studies. A new magnetic diagnostic suite for equilibrium and low frequency (<200kHz) magnetohydrodynamic mode analysis has been installed. These new diagnostics address the significant challenges of measuring magnetic field in a high noise environment with the majority constrained to fit in an 8mm diagnostic gap on the high field side. Electrostatic switching noise generated by the 16 independent current feedback-controlled power supplies produces dVcm/dt ∼ 1kV/μs and volt level common mode noise on the magnetics. Immunity to this switching noise is accomplished through differential signal runs and signal processing, along with end-to-end electromagnetic interference shielding. The magnetic measurements are simultaneously digitized at 1MHz and conditioned by precision 8 pole Butterworth filters with a corner frequency of 200kHz to prevent aliasing down to the 16-bit level over the full passband. Ex-vessel calibrations of the Bp coils were completed with a typical uncertainty of <0.5%. Stray toroidal field pickup from coil misalignment or positioning errors is corrected using a physics-based model. Comparisons of the corrected measurements to modeling agree to within 1.3% on average. This is within the 1.5% measurement uncertainty that a sensitivity analysis determined is needed for accurate fast boundary and equilibrium reconstruction.

A spectroscopic investigation of thermal instability for cylindrical equilibria with background flow

Context. Flows are omnipresent and govern the dynamics of plasma. Solar tornadoes are a class of apparently rotating prominences that might be formed by thermal instability. In spectroscopic studies on thermal instability, background flow is commonly neglected. Aims. We here determine the effect of background flow on thermal instability in cylindrical magnetic field configurations. How various parameters affect the distribution of eigenmodes in the magnetohydrodynamic (MHD) spectrum is also explored. We investigate whether discrete thermal modes exist. Methods. In an analytical study, we extended upon the literature by including a generic background flow in a cylindrical coordinate system. The non-adiabatic MHD equations are linearised, Fourier-analysed, and examined to understand how a background flow changes the continua. An approximate expression for discrete thermal modes is derived using a Wentzel-Kramers-Brillouin (WKB) analysis. The analytical results are then verified for a benchmark equilibrium using the eigenvalue code Legolas. The eigenfunctions of discrete thermal modes are visualised in 2D and 3D. Results. The thermal continuum is Doppler-shifted due to the background flow, just like the slow and Alfvén continua. Discrete modes are altered because the governing equations contain flow-related terms. An approximate expression to predict the appearance of discrete thermal modes based on the equilibrium parameters is derived. All analytical expressions match the numerical results. The distribution of the density perturbations of the discrete thermal modes is not a uniform or singular condensation, due to the shape of the eigenfunctions and the dependence of the assumed waveform on the coordinates and wavenumbers. A 3D visualisation of the total velocity field shows that the helical field is heavily influenced by the radial velocity perturbation. Conclusions. We derived analytic expressions for non-adiabatic MHD modes of a cylindrical equilibrium with background flow and verified them using a coronal equilibrium. However, the equations are valid for and can be applied in other astrophysical environments.

Snap-through dynamics of buckled flexible filaments in a side-by-side configuration

The flow-induced snap-through dynamics of side-by-side buckled flexible filaments in a uniform flow were investigated using the penalty immersed boundary method. We systematically examined the effects of gap distance and bending rigidity on the filament's motion and energy harvesting performance. Four distinct modes were observed as we varied the aforementioned parameters: the dual equilibrium mode, the dual streamwise oscillation mode, the single snap-through oscillation (STO) mode, and the dual STO mode. We analyzed the corresponding wake patterns associated with each of these modes. A phase transition from out-of-phase to in-phase motion was observed at low gap distances and bending rigidities. At lower gap distances, the interaction between two filaments was pronounced, leading to a co-motion of the filaments and enhanced elastic energy. This interaction decreased as the gap distance increased. Filaments in the 2STO mode exhibited significantly higher strain energy compared to the other modes. The elastic energy was concentrated at the rear part of the filaments and increased with higher gap distances and bending rigidities. Considering both energy harvesting efficiency and space utilization rate, a gap distance equal to 1 exhibited the best performance.

Wavelength dependent transmission in multimode graded-index microstructured polymer optical fibers

Up to now, there have been no commercial simulation tools accessible for researching the transmission properties of multimode microstructured optical fibers (MOFs). In order to avoid this problem, this study uses the time-independent power flow equation (TI PFE) numerical solution to examine the wavelength dependency of the equilibrium mode distribution (EMD) and steady state distribution (SSD) in multimode graded-index microstructured polymer optical fibers (GI mPOF) with a solid core. We showed that the lengths zs at which an SSD is obtained in GI mPOF and the coupling length Lc necessary to create an EMD are shorter at λ = 568 nm than they are found to be at λ = 633 nm. The lengths Lc and zs stay constant when the wavelength decreases further from λ = 568 to 522 and then to 476 nm. As a result, it is anticipated that a faster bandwidth enhancement in the tested GI mPOF will take place at wavelengths around λ = 568 nm as opposed to λ = 633 nm. Such a bandwidth improvement is not brought about by additional wavelength reduction. The study’s findings can be used in communication and sensory systems that use multimode GI mPOFs at different wavelengths.

Exclusion or Subsidization? A Competitive Analysis of Quality Regulation Strategy for Two-Sided Platforms

With two-sided platforms becoming an increasingly ubiquitous business model, quality is a vital factor for the success of high-technology platforms that face fierce competition. To maintain competency, high-technology platforms commonly use two quality regulation strategies: the exclusion strategy (E strategy), in which the platform denies access to low-quality complementors, and the subsidization strategy (S strategy), in which the platform provides a fixed subsidy to high-quality complementors. This paper investigates the optimal quality regulation strategy for platforms in a duopoly setting. We examine and compare three scenarios: (i) both platforms adopt the exclusion strategy, i.e. mode EE, (ii) both platforms adopt the subsidization strategy, i.e. mode SS, and (ii) one platform adopts the subsidization strategy while the other adopts the exclusion strategy, i.e. mode SE. First, we find that although the developer network size is larger and the platforms charge developers higher access fees under SS, the average quality and the consumer access fees are lower under SS than under EE, leading to lower profits for platforms. Second, under SE, in comparison with the platform that adopts the exclusion strategy, the platform that uses the subsidization strategy achieves lower average quality and larger network sizes on both sides but may set higher or lower access fees on both sides. Moreover, the platform under the subsidization strategy profits more (less) when the operation cost on the developer side is high (low). Third, asymmetric mode SE does not necessarily induce moderate outcomes for market participants compared to modes EE and SS. We also examine the equilibrium mode by considering platforms’ optimal strategies for quality regulation. Our analyses reveal that as the operation cost on the developer side increases, the equilibrium mode evolves from EE to SE/ES and then to SS. These results and insights are robust to several alternative assumptions.

Research on Exhibition Marketing Strategies in the Context of Network Era

Abstract In the network era, consumers’ behavior of shopping through the Internet can be seen everywhere in daily life. In this paper, starting from consumers’ online shopping behavior preference, the equilibrium mode of conventional advertising is studied, based on which the mass and targeted advertising strategies under decentralized and centralized decision-making modes are proposed, respectively. After comparing and studying the marketing channel structure in various modes, the corresponding advertising optimization model was established to derive four theorems. According to the deduced theorems, the enterprise revenue model is constructed and solved to maximize the benefits. Compare the mixed and separated equilibrium models of the two-stage model in the sales process, and at the same time, construct the XGBoost algorithm model to classify the characteristics of consumers’ shopping behaviors and collect the enterprise’s product marketing strategies. The results of the empirical experiments show that the reasons why consumers do not buy the exhibits of Company W are mainly due to “the price is too high”, “the sense of participation is insufficient” and “the attraction is too low”, with the values of 2.5, 2.5, 2.5, 2.5 and 2.5 respectively. The number of consumers who are satisfied and very satisfied with W brand exhibitions is the largest, and the number of people in all four aspects is around 50, so the marketing strategy of W company exhibitions adjusted according to consumer behavioral preferences is effective.

Gravity-coupled flutter and contact of a flag near a wall

The stability and postcritical behaviour of a horizontal flag undergoing gravity-induced deformation and periodic contact with a nearby horizontal rigid wall are experimentally investigated. The results elucidate the combined effects of gravity and contact on flutter, and reveal design principles for application to triboelectric energy harvesting. By varying the free-stream velocity, flag thickness and distance between the flagpole and the wall, the dynamics of the flag are classified into quasistatic equilibrium, flutter, partial contact and saturated contact modes. Considering the significance of gravitational effects, a new dimensionless flow velocity is proposed to identify the distribution of the dynamic modes, and its definition varies according to whether the wall is placed above or below the flag. The critical conditions for transitions between the dynamic modes are determined from the balance of fluid dynamic and gravitational effects. The distance from the flagpole to the wall is found to be more critical for transitions in the lower-wall configuration than in the upper-wall configuration. The peak contact force as well as the oscillation amplitude and frequency at postequilibrium exhibits remarkably different trends depending on the location of the wall. The peak contact force imposed on the wall by the fluttering flag weakens as the distance to the wall increases in the case of an upper wall, whereas it becomes stronger in the case of a lower wall.

Analysis of Excitement Caused by Colored Noise in a Thermokinetic Model

In this paper, a thermokinetic model forced by colored noise is studied. We analyze the mechanisms of stochastic excitement of equilibrium modes under variation of correlation time and noise intensity. It is shown that the phenomenon of colored-noise-induced excitement is accompanied by stochastic P-bifurcations. The region of the correlation parameter in which resonance occurs is localized. To study the phenomenon of colored-noise-induced excitement, we develop the probabilistic analysis based on the confidence domains method.

Snap-through dynamics of a buckled flexible filament with different edge conditions

The flow-induced snap-through dynamics of a buckled flexible filament under different edge conditions were explored using the penalty immersed boundary method. Three filament edge conditions were simulated: a simply supported leading edge and a clamped trailing edge (SC), a clamped leading edge and a simply supported trailing edge, and both edges clamped. The effects of the bending rigidity and density ratio on the energy harvesting performance were systematically examined. Two different modes were observed: an equilibrium mode and a snap-through oscillation mode. The parameter range under which the modes were observed changed depending on the edge conditions. Mode transitions, induced by an increase in transverse fluid force, occurred when the bending rigidity was low. A clamped leading edge enhanced filament stability, whereas a simply supported leading edge reduced stability. Among the three configurations, the SC case showed the highest critical bending rigidity and oscillation frequency, resulting in superior energy harvesting performance. The greater energy harvesting ability of the SC case derives from the larger deflection and the higher strain energy in this system. The strain energy in the filament with SC edges tended to concentrate in two regions of the filament: the rear part and the section near the clamped end. The SC case, coupled with low density and high rigidity, offers favorable conditions for energy harvesting purposes.

Adsorption of bisphenol A by granular activated carbon prepared with different silicates as binders

Nowadays, the emerging pollutants, such as bisphenol A, are object of increased attention by the citizens and the sectors of industry and academia, as a result of the problems they cause, particularly at the health level. In this study, a set of granulated samples was prepared from a commercial powdered activated carbon, aiming its application in the removal of bisphenol A via the adsorption process. The granulation allowed to obtain granulated adsorbents with higher adsorption capacity (37.0–54.8 mg/g) than the original activated carbon (32.2 mg/g). The samples were structurally and chemically characterised using scanning electron microscopy, X-ray diffraction, nitrogen adsorption at 77 K, Fourier-transformed infrared spectroscopy, point of zero charge and energy-dispersive X-ray spectroscopy techniques. The bisphenol A adsorption tests are carried out in kinetic and equilibrium modes, involving variables such as mass, pH and temperature. The results show that, using different commercial silica binders, it was possible to prepare mechanical, dimensional, chemical and structurally stable granulated adsorbents with a good capacity for bisphenol A adsorption, widening the potential and range of application for these materials.

Modification of grain boundary microstructure by controlling dissolution behavior of θ particles in Cr-containing hypereutectoid steel

To overcome the brittleness of high‑carbon steels, it is necessary to develop the strategy to remove the carbides on the grain boundaries and strengthen grain boundaries. In this paper, we achieved them by simply controlling the heat treatment conditions and the microstructure before heat treatment. It was found the dissolution behavior of the θ-cementite particles is changed greatly with and without Cr in the high‑carbon steels. In the Cr-free hypereutectoid steel, dissolution of θ particles at high temperatures is remarkably fast, but the dissolution behavior is greatly affected by the microstructure in the Cr-containing hypereutectoid steel. In the Cr-containing hypereutectoid steel, the dissolution of θ particles into the γ-austenite phase was rapid in steel with smaller θ particles in fine α grains, but slow in steel with larger θ particles in coarse α grains. The θ particles on the grain boundaries preferentially dissolved and rapidly disappeared in the initial stage of the dissolution treatment owing to the contribution of grain boundary diffusion, since the grain boundary diffusion of Cr is fast as comparable to C. However, the θ particles inside the grains slowly dissolved and then remained until the later stage, owing to slow dissolution via the partition local equilibrium (PLE) mode controlled by the lattice diffusion of Cr. Owing to the preferential dissolution of θ particles on the grain boundaries in the initial stage, large amounts of Cr atoms dissociated from the θ particles diffused along the grain boundaries with grain boundary diffusion, forming Cr-enriched grain boundaries. Such grain boundary microstructure control is expected to lead to the suppression of intergranular fracture, resulting in the improvement of fracture toughness.

Investigation of mode coupling in strained and unstrained multimode step-index POFs using the Langevin equation

The Langevin equation (LE) is used to evaluate mode coupling in multimode step-index polymer optical fiber (SI POF) that is both unstrained and strained. The numerical solution of the LE matches the numerical solution of the power flow equation (PFE). Strain-induced mode coupling is noticeably stronger in strained fiber than in unstrained fiber of the same types. Therefore, compared to similar lengths for unstrained fibers, the coupling length of the equilibrium mode distribution (EMD) is attained and the length of fiber required to produce a steady-state distribution (SSD) are both much shorter for strained fibers. We have demonstrated that the mode coupling in strained and unstrained multimode SI POFs that comes from the random perturbations (RPs) of the fiber can be successfully treated by the LE. The study's findings can be used to improve communication and sensory systems that use multimode SI POFs under different bending circumstances. Additionally, it is crucial to be able to compute the modal distribution of the SI POFs used in the optical fiber sensory system at a specific length and under various bending scenarios.

An economic analysis of a multi-modal transportation system with ride-sourcing services and multi-class users

This paper proposes a tractable bi-level model to explore the mode choice of travelers and optimal operation decisions of a public transit operator and a ride-sourcing operator under a multi-modal transportation system. In such a multi-modal system, users may travel by bus, metro, and/or ride-sourcing service. The lower-level network model is utilized to capture the equilibrium mode choices with the consideration of travelers’ heterogeneity in terms of the value of time (VOT), where deterministic user equilibrium (DUE) and stochastic user equilibrium (SUE) are formulated and compared. In the upper-level model, subject to the DUE/SUE, the two operators optimize their operation decisions in the notion that the profit is maximized or the total system cost is minimized. The existence and uniqueness/non-uniqueness of the multi-modal mode choice equilibrium are analyzed. The optimal operation decisions are also compared under different operation regimes. Our results show that SUE model provides a more conservative estimate of the ride-sourcing operator’s profit and total system travel cost compared to DUE. Besides, the total system cost can be reduced while the profit of the ride-sourcing company can be increased under appropriate operation decisions of the public transit operator and the ride-sourcing operator. Sensitivity analysis further indicates that travelers with longer total travel distance tend to use short-distance ride-sourcing services, which suggests that the ride-sourcing operator should dispatch more vehicles to suburbs located in remote areas to enhance service quality.

Bifurcations and Stability Analysis of Elastic Slender Structures Using Static Discrete Elastic Rods Method

Abstract Discrete elastic rods (DER) method provides a computationally efficient means of simulating the nonlinear dynamics of one-dimensional slender structures. However, this dynamic-based framework can only provide first-order stable equilibrium configuration when combined with the dynamic relaxation method, while the unstable equilibria and potential critical points (i.e., bifurcation and fold point) cannot be obtained, which are important for understanding the bifurcation and stability landscape of slender bodies. Our approach modifies the existing DER technique from dynamic simulation to a static framework and computes eigenvalues and eigenvectors of the tangential stiffness matrix after each load incremental step for bifurcation and stability analysis. This treatment can capture both stable and unstable equilibrium modes, critical points, and trace solution curves. Three representative types of structures—beams, strips, and gridshells—are used as demonstrations to show the effectiveness of the modified numerical framework, which provides a robust tool for unveiling the bifurcation and multistable behaviors of slender structures.

High bandwidth performance of multimode graded-index microstructured polymer optical fibers

The investigation of the bandwidth in multimode graded-index microstructured polymer optical fiber (GI mPOF) with a solid core is proposed using a modal diffusion approach. For a variety of launch radial offsets of multimode GI mPOF, bandwidth is reported by numerically solving the time-dependent power flow equation (TD PFE) using the explicit finite difference method (EFDM) and physics-informed neural networks (PINN). The decline in bandwidth with fiber length becomes slower at fiber lengths close to the coupling length Lc at which an equilibrium mode distribution (EMD) is attained, showing that mode coupling enhances bandwidth at longer fiber lengths. As fiber length is increased, bandwidth approaches complete independence from radial offset, suggesting the steady-state distribution (SSD) has been reached. We compare multimode GI mPOF performance in terms of bandwidth with that of traditional multimode GI POFs made of the same material. Higher bandwidth performance and quicker bandwidth improvement are displayed by the GI mPOF. To enhance fiber performance in GI mPOF links, such a fiber characterization can be used.

Public policies and conservation plans of historic urban landscapes under the sustainable heritage tourism milieu: discussions on the equilibrium model on Kulangsu Island, UNESCO World Heritage site

PurposeThe tensions and threats in historic urban landscapes brought about by heritage tourism are still regional, global, general, and dynamic issues. For Kulangsu, there is an obvious problem in the connection between the current conservation plan and public policy. To a large extent, public policy cannot effectively, specifically, and flexibly respond to the dynamic problems in the implementation of the conservation plan, which seems insufficient concerning the effect of these conservation plans and public policies on promoting the adaptive reuse and sustainable tourism of the historic urban in Kulangsu heritage sites. Thus, giving more consideration to the combination of public policies and conservation plans of historic urban landscapes under the heritage tourism milieu, ensuring a balanced, sustainable, and integrated development pattern still calls for new discussions in achieving good performance of sustainable heritage tourism. This study conceptually discusses the equilibrium model of historic urban landscapes with a range of strategies under a sustainable heritage tourism background and responds to the synthetic contradiction of the imbalances among public policy, conservation plans, and development practices.Design/methodology/approachThe study is based on a range of prepared desktop studies (public policy studies, conservation plans), field surveys, participant observations, and randomised interviews to respond to the insufficiency of the current heritage practices.FindingsThis study discusses the equilibrium model of sustainable heritage tourism at heritage sites. It takes Kulangsu Island, a UNESCO World Heritage site in Southeast China, as an example to discuss the equilibrium model, which encompasses a convergent parallel framework and three dimensions concerning heritage management and policymaking. The equilibrium model of historic urban landscapes is a dynamic framework that integrates social, economic, environmental, and cultural concerns into a holistic collaborative framework under a sustainable heritage tourism background.Originality/valueIn line with the requirements of the Historic Urban Landscape (HUL) approach and general principles in support of sustainable urban heritage management promoted by UNESCO and ICOMOS, the study points out the peculiarities and potential of the equilibrium mode in solving the current challenges of historic urban landscapes for sustainable heritage tourism. Finding ways of linking policymaking, conservation, development, heritage tourism, and different interest groups to a holistic framework can stimulate effective means and management mechanisms for the complicated and changeable issues of sustainable heritage tourism.

Study of Reaction Mechanisms in α + 69Ga reaction at ≈10 – 50 MeV

The excitation functions of 69Ga(α, n)72As, 69Ga(α, 2n)71As, 69Ga(α, 3n)70As, 69Ga(α, x)69Ge, 69Ga(α, x)68Ga and 69Ga(α, x)67Ga reactions produced in the interaction of α-projectile with 69Ga-target were studied at ≈ 10-50 MeV. The produced nuclei were different isotopes of As, Ge, and Ga, some of which have important medical applications. The theoretical model predictions were based on the statistical code COMPLETE, and the predicted results were compared and discussed with existing experimental data. Good agreement between the theoretical predictions and experimental results were obtained. Pearson's relational statistics showed moderate to strong positive correlations between the theoretically predicted and experimentally measured reaction cross-sections. Furthermore, the present investigation revealed significant pre-compound contributions in the studied energy range. Therefore, it is important to consider the admixture of pre-equilibrium and equilibrium modes of reactions when predicting the reaction cross-sections.

Power Flow in Multimode Graded-Index Microstructured Polymer Optical Fibers.

We investigate mode coupling in a multimode graded-index microstructured polymer optical fiber (GI mPOF) with a solid core by solving the time-independent power flow equation (TI PFE). Using launch beams with various radial offsets, it is possible to calculate for such an optical fiber the transients of the modal power distribution, the length Lc at which an equilibrium mode distribution (EMD) is reached, and the length zs for establishing a steady-state distribution (SSD). In contrast to the conventional GI POF, the GI mPOF explored in this study achieves the EMD at a shorter length Lc. The earlier shift to the phase of slower bandwidth decrease would result from the shorter Lc. These results are helpful for the implementation of multimode GI mPOFs as a part of communications and optical fiber sensory systems.

Nonlinear Complementarity Model for Mixed-User Equilibrium Traffic Assignment and Mode Choice of Electric and Gasoline Vehicles

In the early years of 21st century, the ever-increasing volume of greenhouse gases from fossil fuel consumption have made humans seek alternative, non-polluting fuels as an effective strategy to reduce pollution and prevent related environmental issues. Electric vehicles (EVs) are today known as one of the most effective solutions for this purpose. To inform transportation planning and policies pertinent to EVs, models are needed to capture travelers’ behavior for vehicle type and route choice and the impacts on traffic congestion. The present study proposes a mixed complementarity traffic assignment model for the networks involving both EVs and gasoline vehicles so that the demand for each vehicle class depends on the characteristics of the paths and availability of electric charging stations on the paths. To determine the demand of each class, this study applies a logit choice model, which incorporates the effect of ownership and operating costs on demand of each class under different subsidy policies. This paper further investigates the charging behavior of EVs by considering private and public charging facilities in urban areas. To this end, the complementary traffic assignment algorithm has been used to solve the mentioned assignment problem. Besides, we used a label-setting algorithm for solving the constraint shortest path problem. The results of applying the mixed-user equilibrium to Sioux Falls and Chicago sketch networks demonstrate that our proposed algorithm outperforms existing algorithms for both solution time and accuracy across multiple networks.