Three-mode Model Research Articles

Intermodal network design: a three-mode bi-objective model applied to the case of Belgium

Freight transport planning is nowadays encouraged to align with environmental objectives. Among those, climate change is of particular interest for many countries. In its White Paper on Transport, the European Commission considers intermodal transport as a potential solution for reducing environmental impacts. In order to make good strategic transport decisions, realistic decision support models for freight transport networks must be developed, so that insights can be derived for the different stakeholders of the transportation chain. This research proposes a bi-objective mathematical formulation which takes into account economic and environmental objectives, on a road and intermodal network with three modes of transport (road, intermodal rail, and intermodal inland waterways), and in which economies of scale of intermodal transport can be considered. With this model better fitting reality, an application to the Belgian case study provides practical information on how flows, terminal types and locations vary depending on the chosen policy, on the integration or not of economies of scale, on costs or emissions modifications and on the number of terminals to locate. Results show that the chosen policy influences the terminal type and the intermodal market share. The study also highlights the interest of intermodal transport on short distances, and the risk of flow exchanges inside the intermodal market share, rather than between road and intermodal transport.

Phase-field crystal modelling the nucleation processes of graphene structures on different substrates

Two-dimensional materials with unique and excellent physical and chemical properties have attracted much attention in recent years. Among the two-dimensional materials, graphene or grapheme-like materials with honeycomb structure can be mainly prepared by the chemical vapor deposition (CVD) method. The key of this method is to select the substrates and control the nucleation and growth process of honeycomb structures. Graphene prepared by CVD contains many structure defects and grain boundaries, which mainly arise from nucleation process. However, the nucleation mechanism of graphene prepared by CVD method is not very clear. In addition, more than ten kinds of metal substrates can be used as substrate materials in CVD methods, such as Cu and Ni, which have nearly always face-centered cubic (FCC) structures and similar functions in the preparation process. In order to better describe the nucleation of graphene and understand the influences of metal substrates, we introduce the structural order parameter into the three-mode phase-field crystal model to distinguish the low-density gas phase from condensed phases. Nucleation processes of graphene on substrates with different symmetries are studied at an atomic scale by using the three-mode phase-field crystal model, which can simulate transitions between highly correlated condensed phases and low-density vapor phases. Simulation results indicate that no matter whether there is a substrate in the nucleation process, firstly gaseous atoms gather to form amorphous transitional clusters, and then amorphous transitional clusters gradually transform into ordered graphene crystals, with continuous accumulation of new gaseous atoms and position adjustment of atoms. In the nucleation process, five membered ring structures act as a transitional function. When grown on the substrate with a good geometric match with the honeycomb lattice, such as (111) plane of FCC metals, the graphene island has small structural defects. However, when grown without a substrate or on the substrate with a bad geometric match, such as (100) plane of FCC metals, the graphene island contains many structural defects and grain boundaries, which are not conducive to the preparation of high quality graphene. Compared with the (100) crystal plane of the tetragonal cell, the (110) crystal plane of the rectangular cell is favorable for the preparation of graphene single crystals with less defects. Therefore, the appropriate metal substrate can promote the nucleation process of graphene and reduce the formation of distortions and defects during the nucleation and growth of graphene.

STUDYING PHOTOKINETICS OF THE IR LASER RADIATION EFFECT ON MIXTURE OF THE CO2-N2-H2O GASES FOR DIFFERENT ATMOSPHERIC MODELS

A kinetics of energy exchange in the mixture of the atmosphere CO2-N2-H2O gases under passing the powerful CO2 laser radiation pulses within the three-mode model of kinetical processes is studied. More accurate data for the absorption coefficient are presented.

Non-linear reduced-order model for parametric excitation analysis of an immersed vertical slender rod

A unidirectional three-mode reduced-order model (ROM) for the lateral motion of a slender and immersed rod subjected to harmonic and axial top motion was derived from the continuum equation of motion. Simple trigonometric functions were employed as approximations for the vibration modes and projection functions in Galerkin׳s method. The non-linear character of the ROM comes from the extensibility of the rod axis and the quadratic hydrodynamic damping. The focus of this investigation is the principal Mathieu׳s instability with respect to the first vibration mode, i.e., the condition in which the top-motion frequency is twice the structural first natural frequency. Time histories of modal amplitude, as well as maps of post-critical steady-state vibration amplitudes were obtained and discussed. It is seen that, within the principal parametric instability region of the first mode, the time history corresponding to the second classic (sinusoidal) mode oscillates with dominant frequency of the first classic (sinusoidal) mode. Another finding is that, besides the principal Mathieu׳s instability region, there are also other regions of instability, but with considerably smaller amplitudes. This aspect is due to the non-linear character of the coupled system of equations that defines the ROM.

Predicting long-term depression outcome using a three-mode principal component model for depression heterogeneity

BackgroundDepression heterogeneity has hampered development of adequate prognostic models. Therefore, more homogeneous clinical entities (e.g. dimensions, subtypes) have been developed, but their differentiating potential is limited because neither captures all relevant variation across persons, symptoms and time. To address this, three-mode Principal Component Analysis (3MPCA) was previously applied to capture person-, symptom- and time-level variation in a single model (Monden et al., 2015). This study evaluated the added prognostic value of such an integrated model for longer-term depression outcomes. MethodsThe Beck Depression Inventory (BDI) was administered quarterly for two years to major depressive disorder outpatients participating in a randomized controlled trial. A previously developed 3MPCA model decomposed the data into 2 symptom-components (‘somatic-affective’, ‘cognitive’), 2 time-components (‘recovering’, ‘persisting’) and 3 person-components (‘severe non-persisting depression’, ‘somatic depression’ and ‘cognitive depression’). The predictive value of the 3MPCA model for BDI scores at 3-year (n=136) and 11-year follow-up (n=145) was compared with traditional latent variable models and traditional prognostic factors (e.g. baseline BDI component scores, personality). Results3MPCA components predicted 41% and 36% of the BDI variance at 3- and 11-year follow-up, respectively. A latent class model, growth mixture model and other known prognostic variables predicted 4–32% and 3–24% of the BDI variance at 3- and 11-year follow-up, respectively. LimitationsOnly primary care patients were included. There was no independent validation sample. ConclusionAccounting for depression heterogeneity at the person-, symptom- and time-level improves longer-term predictions of depression severity, underlining the potential of this approach for developing better prognostic models.

Evaluations of tropospheric aerosol properties simulated by the community earth system model with a sectional aerosol microphysics scheme.

A sectional aerosol model (CARMA) has been developed and coupled with the Community Earth System Model (CESM1). Aerosol microphysics, radiative properties, and interactions with clouds are simulated in the size‐resolving model. The model described here uses 20 particle size bins for each aerosol component including freshly nucleated sulfate particles, as well as mixed particles containing sulfate, primary organics, black carbon, dust, and sea salt. The model also includes five types of bulk secondary organic aerosols with four volatility bins. The overall cost of CESM1‐CARMA is approximately ∼2.6 times as much computer time as the standard three‐mode aerosol model in CESM1 (CESM1‐MAM3) and twice as much computer time as the seven‐mode aerosol model in CESM1 (CESM1‐MAM7) using similar gas phase chemistry codes. Aerosol spatial‐temporal distributions are simulated and compared with a large set of observations from satellites, ground‐based measurements, and airborne field campaigns. Simulated annual average aerosol optical depths are lower than MODIS/MISR satellite observations and AERONET observations by ∼32%. This difference is within the uncertainty of the satellite observations. CESM1/CARMA reproduces sulfate aerosol mass within 8%, organic aerosol mass within 20%, and black carbon aerosol mass within 50% compared with a multiyear average of the IMPROVE/EPA data over United States, but differences vary considerably at individual locations. Other data sets show similar levels of comparison with model simulations. The model suggests that in addition to sulfate, organic aerosols also significantly contribute to aerosol mass in the tropical UTLS, which is consistent with limited data.

Phonon focusing and temperature dependences of thermal conductivity of silicon nanofilms

The effect of phonon focusing on the anisotropy and temperature dependences of the thermal conductivities of silicon nanofilms is analyzed using the three-mode Callaway model. The orientations of the film planes and the directions of the heat flux for maximal or minimal heat removal from silicon chip elements at low temperatures, as well as at room temperature, are determined. It is shown that in the case of diffuse reflection of phonons from the boundaries, the plane with the {100} orientation exhibits the lowest scattering ability (and the highest thermal conductivity), while the plane with the {111} orientation is characterized by the highest scattering ability (and the lowest thermal conductivity). The thermal conductivity of wide films is determined to a considerable extent by the orientation of the film plane, while for nanowires with a square cross section, the thermal conductivity is mainly determined by the direction of the heat flux. The effect of elastic energy anisotropy on the dependences of the thermal conductivity on the geometrical parameters of films is analyzed. The temperatures of transition from boundary scattering to bulk relaxation mechanisms are determined.

Existence criterion of homoclinic trajectories in the Glukhovsky–Dolzhansky system

Abstract Existence criterion of homoclinic trajectories in the Glukhovsky–Dolzhansky system, describing three-mode model of rotating fluid convection, is obtained. New applications of the Fishing principle are developed.

Vibration Dynamics of an Inclined Cable Excited Near Its Second Natural Frequency

Inclined cables are essential structural elements that are used most prominently in cable-stayed bridges. When the bridge deck oscillates due to an external force, such as passing traffic, cable vibrations can arise not only in the plane of excitation, but also in the perpendicular plane. This undesirable phenomenon can be modeled as an auto-parametric resonance between the in-plane and out-of-plane modes of vibration of the cable. In this paper, we consider a three-mode model, capturing the second in-plane, and first and second out-of-plane modes, and use it to study the response of an inclined cable that is vertically excited at its lower (deck) support at a frequency close to the second natural frequency of the cable. Averaging is applied to the model and then the solutions and bifurcations of the resulting averaged differential equations are investigated and mapped out with numerical continuation. In this way, we present a detailed bifurcation study of the different possible responses of the cable. We first consider the equilibria of the averaged model, of which there are four types that are distinguished by whether each of the two out-of-plane modes is present or not in the cable response. Each type of equilibrium is computed and represented as a surface over the plane of amplitude and frequency of the forcing. The stability of the equilibria changes and different surfaces meet along curves of bifurcations, which are continued directly. Overall, we present a comprehensive geometric picture of the two-parameter bifurcation diagram of the constant-amplitude coupled-mode response of the cable. We then focused on bifurcating periodic orbits, which correspond to cable dynamics with varying amplitudes of the participating second in-plane and second out-of-plane modes. The range of excitation amplitude and frequency is determined where such whirling cable motion can occur. Further bifurcations — period-doubling cascades and a Shilnikov homoclinic bifurcation — are found that lead to a chaotic cable response. Whirling and chaotic cable dynamics are confirmed by time-step simulations of the full three-mode model. The different cable responses are characterized, and can be distinguished clearly, by their motion at the quarter-span and by their frequency spectra.

Anisotropy and temperature dependences of thermal conductivity for silicon nanowires

The anisotropy and temperature dependences of thermal conductivity for silicon nanowires with diameters higher than 50 nm is investigated using the Callaway three-mode model. Contributions to the thermal conductivity from the boundary and bulk mechanisms of phonon scattering are calculated at room temperature. The relationship between the thermal conductivity and nanowire diameter is analyzed in symmetrical directions and at room temperature.

Reduced Fokker-Planck models for fast particle distribution across a transition layer of disparate plasma temperatures

Across a transition layer of disparate plasma temperatures, the high energy tail of the plasma distribution can have appreciable deviations from the local Maxwellian distribution due to the Knudson layer effect. The Fokker-Planck equation for the tail particle population can be simplified in a series of practically useful limiting cases. The first is the approximation of background Maxwellian distribution for linearizing the collision operator. The second is the supra-thermal particle speed ordering of vTi ≪ v ≪ vTe for the tail ions and vTi ≪ vTe ≪ v for the tail electrons. Keeping both the collisional drag and energy scattering is essential for the collision operator to produce a Maxwellian tail distribution. The Fokker-Planck model for following the tail ion distribution for a given background plasma profile is explicitly worked out for systems of one spatial dimension, in both slab and spherical geometry. A third simplification is an expansion of the tail particle distribution using the spherical harmonics, which are eigenfunctions of the pitch angle scattering operator. This produces a set of coupled Fokker-Planck equations that contain energy-dependent spatial diffusion terms in two coordinates (position and energy), which originate from pitch angle scattering in the original Fokker-Planck equation. It is shown that the well-known diffusive Fokker-Planck model is a poor approximation of the two-mode truncation model, which itself has fundamental deficiency compared with the three-mode truncation model. The cause is the lack of even-symmetry representation in pitch dependence in the two-mode truncation model.

Static and Dynamic Response of Beams on Nonlinear Viscoelastic Unilateral Foundations: A Multimode Approach

Nonlinear viscoelastic behavior is a characteristic of many engineering materials including flexible polyurethane foam, yet it is difficult to develop dynamic models of systems that include these materials and are able to predict system behavior over a wide range of excitations. This research is focused on a specific example system in the form of a pinned-pinned beam interacting with a viscoelastic foundation. Two cases are considered: (1) the beam and the foundation are glued so that they are always in contact and the foundation can undergo both tension and compression, and (2) the beam is not glued to the foundation and the foundation reacts only in compression so that the contact region changes with beam motion. Static as well as dynamic transverse and axial forces act on the beam, and the Galerkin method is used to derive modal amplitude equations for the beam-foundation system. In the second case of the beam on tensionless foundation, loss of contact between the beam and the foundation can arise and determination of the loss-of-contact points is integrated into the solution procedure through a constraint equation. The static responses for both cases are examined as a function of the foundation nonlinearity and loading conditions. The steady-state response of the system subject to static and harmonic loads is studied by using numerical direct time-integration. Numerical challenges and the accuracy of this approach are discussed, and predictions of solutions by the three-mode and five-mode approximate models are compared to establish convergence of solutions. Frequency responses are studied for a range of foam nonlinearities and loading conditions.

A classical trajectory study of the intramolecular dynamics, isomerization, and unimolecular dissociation of HO2

The classical dynamics and rates of isomerization and dissociation of HO2 have been studied using two potential energy surfaces (PESs) based on interpolative fittings of ab initio data: An interpolative moving least-squares (IMLS) surface [A. Li, D. Xie, R. Dawes, A. W. Jasper, J. Ma, and H. Guo, J. Chem. Phys. 133, 144306 (2010)] and the cubic-spline-fitted PES reported by Xu, Xie, Zhang, Lin, and Guo (XXZLG) [J. Chem. Phys. 127, 024304 (2007)]. Both PESs are based on similar, though not identical, internally contracted multi-reference configuration interaction with Davidson correction (icMRCI+Q) electronic structure calculations; the IMLS PES includes complete basis set (CBS) extrapolation. The coordinate range of the IMLS PES is limited to non-reactive processes. Surfaces-of-section show similar generally regular phase space structures for the IMLS and XXZLG PESs with increasing energy. The intramolecular vibrational energy redistribution (IVR) at energies above and below the threshold of isomerization is slow, especially for O-O stretch excitations, consistent with the regularity in the surfaces-of-section. The slow IVR rates lead to mode-specific effects that are prominent for isomerization (on both the IMLS and XXZLG) and modest for unimolecular dissociation to H + O2 (accessible only on the XXZLG PES). Even with statistical distributions of initial energy, slow IVR rates result in double exponential decay for isomerization, with the slower rate correlated with slow IVR rates for O-O vibrational excitation. The IVR and isomerization rates computed for the IMLS and XXZLG PESs are quantitatively, but not qualitatively, different from one another with the largest differences ascribed to the ~2 kcal/mol difference in the isomerization barrier heights. The IMLS and XXZLG results are compared with those obtained using the global, semi-empirical double-many-body expansion DMBE-IV PES [M. R. Pastrana, L. A. M. Quintales, J. Brandão, and A. J. C. Varandas, J. Chem. Phys. 94, 8073 (1990)], for which the surfaces-of-section display more irregular phase space structure, much faster IVR rates, and significantly less mode-specific effects in isomerization and unimolecular dissociation. The calculated IVR results for all three PESs are reasonably well represented by an analytic, coupled three-mode energy transfer model.

Indentation response of human patella with elastic modulus correlation to localized fractal dimension and bone mineral density

The goal of this study was to determine material properties for the anterior cortex and subcortical regions of human patellae and relate those properties to mineral density and fractal dimension of the bone. Ten human patellae were obtained from eight fresh frozen human cadavers and subjected to anteriorly-directed spherical indentation–relaxation experiments using two different sized indenters to two different indentation depths. Response data were fit to a three-mode viscoelastic model obtained through elastic–viscoelastic correspondence of the Hertzian contact relation for spherical indentation. A location-specific effective bone density measurement that more heavily weighted bone material close to the indentation site (by von Mises stress distribution) was determined from micro-computed tomography (38µm resolution) data captured for each specimen. The same imagery data were used to compute location specific fractal dimension estimates for each indentation site. Individual and averaged patella material models verified the hypothesis that when the larger indenter and greater indentation depth is used to engage the surface and deeper (trabecular) bone, the bone exhibits a more compliant response than when only the surface (cortical) bone was engaged (instantaneous elastic modulus was 325MPa vs. 207MPa, p<0.05). Effective bone mineral density was shown to be a significant predictor of the elastic modulus for both small and large indentation types (p<0.05) despite relatively low correlations. Exponential regressions of fractal dimension on elastic modulus showed significant relationships with high correlation for both the small (R2=0.93) and large (R2=0.97) indentations.

Microcantilever dynamics in tapping mode atomic force microscopy via higher eigenmodes analysis

Microcantilever dynamics in tapping mode atomic force microscopy (AFM) is addressed via a multimode approximation, which allows to consider external excitation at primary or secondary resonance and to highlight the effect of higher order eigenmodes. Upon presenting the AFM model and its multimode discretization, the dynamic response is investigated via numerical simulation of single- and three-mode models by considering different bifurcation parameters. Typical features of tapping mode AFM response as nonlinear hysteresis, bistability, higher harmonics contribution, impact velocity, and contact force are addressed. The analysis is conducted by evaluating damping of higher modes according to the Rayleigh criterion, which basically accounts for structural damping representative of the behavior of AFMs in air. Nominal damping situations more typical of AFMs in liquids are also investigated, by considering sets of modal Q-factors with different patterns and ranges of values. Variable attractive-repulsive effects are highlighted, along with the possible presence of a coexisting multi-periodic orbit when the system is excited at second resonance.

Individual Difference Analysis in Impression Evaluation of the Appearance Colors of Cellular Phones

Individual differences in impressions created by the color of cellular phones were investigated. In the study, participants were asked to evaluate the appearance of cellular phones of 16 different body colors by using the Semantic Differential (SD) method. Three-mode individual difference analysis model TUCKER 2 was used for the analysis. The results indicated that there were three types of impressions: masculine-feminine, gorgeous-staid, and evaluation. We used hierarchical cluster analysis for examining individual differences in impressions and separated the participants into three groups. Results of comparing individual evaluation structures in each group identified differences in color impression structures of cellular phones between the groups. In addition, it revealed that the color preference differences among the groups were related to some of Value-Intention Scale subscores that assess value-intending mental acts based on Spranger's classification of values.

Study on Data Management of Fundamental Model in Control Center for Smart Grid Operation

The control center in smart grids requires the collaboration among different specialized groups to ensure the safety, reliability, greenness and efficiency of power system. However, each specialized group is interested in different aspects of the network model. In order to improve the teamwork and timeliness, the fundamental models should be managed in a unified way. This paper summarizes the requirements for data management of fundamental models, presents a concept of three-mode models, and designs the architecture of generic model access services. With the generic model access services, the differences of real-world model databases will be shielded, and the future virtual model can be managed as versions. The upper applications can obtain the fundamental model information through the data broker component and business model data through the business data organizing component.

Free vibrations control of a cantilever beam using combined time delay feedback

A new multi-input single-output delay feedback controller is presented to reduce free vibrations of a cantilever beam. A linear model using the first mode is derived and used to analyze and characterize the damping produced by different delay-feedback controllers as a function of the controller's gains and delay. The stability regions and amount of damping produced by three different single delay feedback and the new combined delayed feedback are investigated. A three-dimensional figure for the new controller showing the stability regions as a function of the controller gains and delay is presented. The characteristic damping of the controller as predicted by the linear model is compared with that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controllers gains and delay are obtained, simulated, and compared. To validate the single mode approximation, numerical simulations are performed using three-mode full nonlinear model. The results obtained using multi-input delay-feedback controllers demonstrate an excellent improvement in mitigating the first-mode vibration.

Band structure and dynamic behaviors of Bose–Einstein condensates in Fourier-Synthesized optical lattices

By employing a nonlinear three-mode model, we study the band structure of Bose–Einstein condensates in Fourier-Synthesized optical lattices, where the nonlinearity comes from the mean field treatment of interaction between atoms. In linear case, we present the band structure of the system. It is demonstrated that the energy band structure is strongly dependent on the value of relative phase of the two lattice harmonics. In the nonlinear case, we show that the eigenenergies as the functions of the quasi-momentum have a novel bowl structure in the middle energy level. It is found that there exist four critical values of interaction strength at which the band structure will undergo interesting changes. Furthermore, the stability of the eigenstate is also investigated.

Band structure and tunnelling dynamics of Bose–Einstein condensates in Fourier-synthesized optical lattices

By employing a nonlinear three-mode model, we study the band structure of Bose–Einstein condensates in Fourier-synthesized optical lattices, where the nonlinearity comes from the mean field treatment of interaction between atoms. In the linear case, we present the band structure of the system. It is observed that the energy band structure is strongly dependent on the relative phase between the two lattice harmonics. In the nonlinear case, we show that the eigenenergy as a function of energy bias has a striking bowl structure in the middle energy level. It is found that there exist four critical values of interaction strength where the band structure undergoes interesting changes. Because of these topological distortions on the energy levels, we expect that the tunnelling dynamics make a dramatic change. The tunnelling probability is nonzero when the nonlinear term is very small and the energy levels keep the same topological structure as that in the linear case. Especially, the tunnelling probability as a function of the sweeping rate shows an irregular oscillation for the state on the middle level.