Order Parameter Model Research Articles

A new order parameter model for the improper ferroelastic phase transitions in KMnF3 single crystal.

This paper proposes a new order parameter model which satisfactorily explains complicated symmetry changes, the temperature-pressure (T-P) phase diagram and elastic anomalies observed experimentally with the improper ferroelastic phase transitions in multiferroic KMnF3 single crystal. First, it is shown that the order parameter model is transformed according to the four-dimensional reducible representation of the wavevector star channel group. Second, based on the order parameter model and the singularity theory, the sixth-order structurally stable Landau potential model is constructed. Finally, the theoretical T-P phase diagram is plotted and the elastic anomalies possible for each of the phase transitions are discussed.

Design and experimental investigation of a herringbone grooved gas bearing supported turbocharger

The design of an oil free turbocharger supported on herringbone grooved gas bearing was formulated as a multi-objective problem, which was solved by coupling a reduced order parametric model for gas bearing supported rotors with an evolutionary algorithm. The resulting Pareto curve offers the best possible tradeoff between the two competing objectives of maximizing the rotordynamic stability and minimizing the power losses. After manufacturing, the turbocharger was successfully operated up to 170 krpm, beyond a hybrid mode composed of a rigid body cylindrical and a flexural mode. Supercritical operation above a flexural bending mode on rigid gas lubricated bearings was possible due to the smart selection of the location of two balancing planes, to avoid the excitation of the flexural mode. A coast down test suggests minimum friction torque and therefore lift-off at 3 krpm. Bearing power loss tests performed at 40 ℃ and 100 ℃ showed that the herringbone grooved gas bearing supported oil-free turbocharger yields only 50% to 70% of the traditional semi-floating oil bearing supported turbochargers, which is a distinct advantage in terms of efficiency and cut in emissions. The theoretical and experimental results presented in this paper clearly demonstrate the rotordynamic feasibility of oil-free turbochargers supported on herringbone grooved gas bearings.

Smectic layering: Landau theory for a complex-tensor order parameter

Composed of microscopic layers that stack along one direction while maintaining fluid-like positional disorder within layers, smectics are excellent systems for exploring topology, defects and geometric memory in complex confining geometries. However, the coexistence of crystalline-like characteristics in one direction and fluid-like disorder within layers makes lamellar liquid crystals notoriously difficult to model—especially in the presence of defects and large distortions. Nematic properties of smectics can be comprehensively described by the -tensor; however, lamellar order can exist independent of nematic alignment. To capture the features of the smectic layering alone, we develop a phenomenological Landau theory for a complex-tensor order parameter , which is capable of describing the local degree of lamellar ordering, layer displacement, and orientation of the layers. This theory accounts for both parallel and perpendicular elastic contributions. In addition to resolving the potential ambiguities inherent to complex scalar order parameter models, this model reduces to previously employed models of simple smectics, and opens new possibilities for numerical studies on smectics possessing many defects, within complex geometries and under extreme confinement.

Phase-field modeling of crack propagation in heterogeneous materials with multiple crack order parameters

The phase-field method is widely established for modeling crack propagation in material science. It shows good agreement with analytical solutions and is able to describe a complex fracture behavior. Nevertheless, the models are mostly introduced for homogeneous systems, and there are only a few approaches for heterogeneous systems. So models, that are able to describe the crack propagation in such systems, are highly desirable. Based on a classic crack propagation phase-field approach, existing models are discussed, and a new model is derived. The first model, which is based on an already existing approach, uses homogenized properties and a single-crack order parameter, while the second model, a new approach, introduces multiple crack order parameters, each of which only tracks the damage of a corresponding phase. Furthermore, the issues of the single-crack order parameter model are demonstrated, such as the ability to reproduce the quantitative surface energies for an interfacial crack and the non-physical behavior of a crack propagating along a sloped material interface. In contrast, the novel multi-crack order parameter model prevents distortions for an interfacial crack and propagates along the interface in a more physical manner. In comparison with an analytical solution, based on linear elastic fracture mechanics, the novel model shows a good agreement, even for strongly sloped interfaces, where the single-crack order parameter model fails to reproduce the analytical solution. In a subsequent application to fiber-reinforced polymers, the new model has proven to be able to predict fractures in complex systems, including crack nucleation, branching, and merging. Finally, the applicability to a 3D system is illustrated.

Dynamic core capabilities of IoT firms in the product lifecycle: a resource-based view

ABSTRACT External resources are a crucial factor in the development of corporate dynamic core capabilities. Following a resource-based view, we study the impact of external technical coordination on the development of dynamic core capabilities for product innovation of IoT firms. Based on the survey of 184 IoT firms, we construct order parameter models at different stages of the product lifecycle to explore the comprehensive influence mechanism of external technical coordination on dynamic core capabilities (integration capability and modularity capability) and innovation performance. The results find that the influence of external technical coordination on dynamic core capabilities and innovation performance changes with the product lifecycle on the whole. It shows a trend of weakening. Meanwhile, we reveal the heterogeneous impact of external technical coordination at different stages of the product lifecycle. Its influence on integration and modularity capabilities is different. This study provides some insights for strategic management research and builds a theoretical basis for the development of dynamic core capabilities for product innovation of IoT firms at different stages of the product lifecycle.

Impedance Spectroscopy Sensing Material Properties for Self-Tuning Ratio Control in Pharmaceutical Industry

Following the paradigm shift in the pharmaceutical industry from batch to continuous production, additional instrumentation and revision of control strategies to optimize material flow throughout the downstream processes are required. Tableting manufacturing is one of the most productive in terms of turnover and investment into new sensor technologies is an important decision-making step. This paper proposes a continuous solution to detect changes in material properties, and a control algorithm to aid in minimizing risk at the end-product line. Some of the sub-processes involved in tableting manufacturing perform changes in powder and liquid mixtures, granulation, density, therefore changing flow conditions of the raw material. Using impedance spectroscopy in a continuous sensing and monitoring context, it is possible to perform online identification of generalized (fractional) order parametric models where the coefficients are correlated to changes in material properties. The model parameters are then included in a self-tuning control gain used in ratio control as part of the local process control loop. The solution proposed here is easy to implement and poses a significant added value to the current state of art in pharmaceutical manufacturing technologies.

Stochastic order parameter dynamics for phase coexistence in heat conduction.

We propose a stochastic order parameter model for describing phase coexistence in steady heat conduction near equilibrium. By analyzing the stochastic dynamics with a nonequilibrium adiabatic boundary condition, where total energy is conserved over time, we derive a variational principle that determines thermodynamic properties in nonequilibrium steady states. The resulting variational principle indicates that the temperature of the interface between the ordered region and the disordered region becomes greater (less) than the equilibrium transition temperature in the linear response regime when the thermal conductivity in the ordered region is less (greater) than that in the disordered region. This means that a superheated ordered (supercooled disordered) state appears near the interface, which was predicted by an extended framework of thermodynamics proposed in Nakagawa and Sasa [Liquid-Gas Transitions in Steady Heat Conduction, Phys.Rev. Lett. 119, 260602 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.260602.].

Quantitative phase field simulations of polycrystalline solidification using a vector order parameter.

A vector order parameter phase field model derived from a grand potential functional is presented as an alternative approach for modeling polycrystalline solidification of alloys. In this approach, the grand potential density is designed to contain a discrete set of finite wells, a feature that naturally allows for the growth and controlled interaction of multiple grains using a single vector field. We verify that dendritic solidification in binary alloys follows the well-established quantitative behavior in the thin interface limit. In addition, it is shown that grain boundary energy and solute back-diffusion are quantitatively consistent with earlier theoretical work, with grain boundary energy being controlled through a simple solid-solid interaction parameter. Moreover, when considering polycrystalline aggregates and their coarsening, we show that the kinetics follow the expected parabolic growth law. Finally, we demonstrate how this vector order parameter model can be used to describe nucleation in polycrystalline systems via thermal fluctuations of the vector order parameter, a process that cannot be treated consistently with multiphase or multi-order-parameter based phase field models. The presented vector order parameter model serves as a practical and efficient computational tool for simulating polycrystalline materials. We also discuss the extension of the order parameter to higher dimensions as a simple method for modeling multiple solid phases.

Defect-Induced Long-Range Order and the Imry–Ma State in 2-D O(n) Models

The anisotropic distribution of the defect-induced random local field directions in 2-D systems with continuous symmetry of the order parameter (O(n) models) can induce a global anisotropy of the “easy axis” type which transfers the system to the universality class of Ising models and the long-range order arises in it at finite temperature. At the same time, statistical fluctuations of random defect fields cause the appearance of the disordered Imry-Ma phase in which the order parameter follows fluctuations of the random field. The confrontation of these two opposite trends in 2-D O(n) models with defects of the “random local field” type was investigated, and their phase diagrams were constructed.

Polymeric Ionic Liquids Derived from L-Valine for the Preparation of Highly Selective Silica-Supported Stationary Phases in Gas Chromatography.

A series of silica-supported polymeric ionic liquid (PIL)-based stationary phases derived from a vinylic L-valine ionic liquid monomer and divinylbenzene (DVB) as the crosslinking agent have been prepared and studied as gas chromatographic stationary phases. These coated gas chromatographic columns exhibited good thermal stabilities (230–300 °C) and high efficiencies (1700–2700 plates/m), and were characterized using a linear solvation parameter model in order to understand the effects of the amount of DVB on the features of the resulting composite systems. Their retention behavior and separation efficiencies were demonstrated using the Grob test. By tuning the crosslinking degree for the IL-derived stationary phase, the separation selectivity and resolution of different compounds were improved. The different retention behaviors observed for many analytes indicate that these stationary phases may be applicable as new types of GC stationary phases.

Two-band superconductivity with unconventional pairing symmetry in HfV2Ga4

In this letter, we have examined the superconducting ground state of the HfV$_2$Ga$_4$ compound using resistivity, magnetization, zero-field (ZF) and transverse-field (TF) muon-spin relaxation and rotation ($\mu$SR) measurements. Resistivity and magnetization unveil the onset of bulk superconductivity with $T_{\bf c}\sim$ 3.9~K, while TF-$\mu$SR measurements show that the temperature dependence of the superfluid density is well described by a nodal two-gap $s$+$d$-wave order parameter model. In addition, ZF muon relaxation rate increases with decreasing temperature below 4.6 K, indicating the presence of weak spin fluctuations. These observations suggest an unconventional multiband nature of the superconductivity possibly arising from the distinct $d$-bands of V and Hf ions with spin fluctuations playing an important role. To better understand these findings, we carry out first-principles electronic-structure calculations, further highlighting that the Fermi surface consists of multiple disconnected sheets with very different orbital weights and spin-orbit coupling, bridging the way for a nodal multiband superconductivity scenario. In this vein, therefore, HfV$_2$Ga$_4$-family stands out as an open avenue to novel unexplored unconventional superconducting compounds, such as ScV$_2$Ga$_4$ and ZrV$_2$Ga$_4$, and other many rare earths based materials.

Dynamic coupling of substructures with sliding friction interfaces

The study of complex systems composed by substructures connected together by frictional interfaces can benefit of the framework developed for dynamic substructuring. These systems are generally composed by time-invariant substructures in relative motion, implying time variant contact interfaces. Although the classical formulations of dynamic substructuring deal with time-invariant systems, they can be extended to include time-invariant component subsystems subjected to time-variant coupling conditions. The problem can be tackled in time domain using both primal and dual assembly, and in time-frequency domain using dual assembly to obtain the Time Dependent Frequency Response Functions (TD-FRFs). The equilibrium and the compatibility conditions are time-dependent and have to be defined under the assumption that the relative sliding motion at the contact interfaces is known a priori, at least approximately. The proposed method is applied to a lumped parameter model in order to evaluate its feasibility, and to a finite element model to verify its effectiveness.

Online Estimation Method for Permanent Magnet Temperature of High‐Density Permanent Magnet Synchronous Motor

Since it can be difficult to directly estimate the temperature of permanent magnets (PM) in high‐density permanent magnet motor rotors, this paper proposes a method based on lumped parameter thermal networks (LPTN) for online estimation of PM temperature. Firstly, a parameter model is established that contains a four‐node thermal network model and a loss model. For the online estimation, an extended Kalman filter algorithm with fading factor is used to dynamically update the thermal network parameter model in order to estimate the PM temperature. The simulation and experimental results show that the parameter model can quickly converge to a value that is close to the true value. Therefore, this online estimation method for PM temperature can accurately monitor the PM temperature online without increasing the required motor hardware; thus not affecting the motor operation. © 2020 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Enhanced Orientational Ordering Induced by an Active yet Isotropic Bath.

Can a bath of isotropic but active particles promote ordering of anisotropic but passive particles? In this Letter, we uncover a fluctuation-driven mechanism by which this is possible. Somewhat counterintuitively, we show that the passive particles tend to be more ordered upon increasing the noise strength of the active isotropic bath. We first demonstrate this in a general dynamical model for a nonconserved order parameter (model A) coupled to an active isotropic field and then concentrate on two examples: (i)a collection of polar rods on a substrate in an active isotropic bath and (ii)a passive apolar suspension in a momentum conserved, actively forced but isotropic fluid, which are relevant for current research in active systems. Our theory, which is relevant for understanding ordering transitions in out-of-equilibrium systems can be tested in experiments, for instance, by introducing a low concentration of passive rodlike objects in active isotropic fluids and, since it is applicable to any nonconserved dynamical field, may have applications far beyond active matter.

Grid and Polytopic LPV Modeling of Aeroelastic Aircraft for Co-design

Future aircraft tend to have increased flexibility that leads to increased aeroservoe-lastic (ASE) effects. Therefore, future aircraft control systems need active control to suppress ASE effects. Active flutter suppression can be effectively done in the linear parameter varying (LPV) framework. Control surface sizing for aircraft is traditionally done by iterations. In this approach engineering rules are used to determine the size of the control surfaces and the control laws are designed afterwards. Such method, besides being time consuming, might have further challenges in the future due to the coupling between the flexible and rigid body dynamics. Instead, ”co-design” was recently proposed. In the co-design approach parametric aircraft models are developed based on which the control surface sizing and the control design are optimized in a single step. The purpose of this paper is to create a control oriented, parametric control surface model of the mini MUTT aircraft that can be applied for co-design. The resulting control oriented LPV model needs to have sufficiently low dynamic order, which is achieved by the ”bottom-up” modeling approach. A grid based LPV model is obtained from the nonlinear model by Jacobian linearization and the Tensor Product (TP) type polytopic model is obtained from the grid based LPV model via TP model transformation. The resulting low order parametric control surface LPV models are assessed with the v-gap metric. These models can serve as the basis of simultaneous baseline/flutter suppression control synthesis and control surface sizing optimization.

Exponential Decay of Correlations in the 2D Random Field Ising Model

An extension of the Ising spin configurations to continuous functions is used for an exact representation of the Random Field Ising Model's order parameter in terms of disagreement percolation. This facilitates an extension of the recent analyses of the decay of correlations to positive temperatures, at homogeneous but arbitrarily weak disorder.

Shared parameter model for competing risks and different data summaries in meta-analysis: Implications for common and rare outcomes.

This paper considers the problem in aggregate data meta‐analysis of studies reporting multiple competing binary outcomes and of studies using different summary formats for those outcomes. For example, some may report numbers of patients with at least one of each outcome while others may report the total number of such outcomes. We develop a shared parameter model on hazard ratio scale accounting for different data summaries and competing risks. We adapt theoretical arguments from the literature to demonstrate that the models are equivalent if events are rare. We use constructed data examples and a simulation study to find an event rate threshold of approximately 0.2 above which competing risks and different data summaries may bias results if no adjustments are made. Below this threshold, simpler models may be sufficient. We recommend analysts to consider the absolute event rates and only use a simple model ignoring data types and competing risks if all of underlying events are rare (below our threshold of approximately 0.2). If one or more of the absolute event rates approaches or exceeds our informal threshold, it may be necessary to account for data types and competing risks through a shared parameter model in order to avoid biased estimates.

Building a free-energy functional from atomically resolved imaging: Atomic-scale phenomena in La-doped BiFeO3

Scanning Transmission Electron Microscopy (STEM) has enabled mapping of atomic structures of solids with sub-pm precision, providing insight to the physics of ferroic phenomena and chemical expansion. However, only a subset of information is available, due to projective nature of imaging in the beam direction. Correspondingly, the analysis often relies on the postulated known form of macroscopic Landau-Ginzburg energy, and some predefined relationship between experimentally determined atomic coordinates and the order parameter field. Here, we propose an approach for exploring the structure of ferroics using reduced order parameter models constructed based on experimental data only. We develop a four sublattices model (FSM) for the analytical description of A-cation displacement in (anti)ferroelectric-antiferrodistortive perovskites of ABO3-type. The model describes the displacements of cation A in four neighboring unit cells and determines the conditions of different structural phases appearance and stability in ABO3. We show that FSM explains the coexistence of rhombohedral (R), orthorhombic (O) and spatially modulated (SM) phases, observed by atomic-resolution STEM in La-doped BiFeO3. Using this approach, we atomically resolve and theoretically model the sublattice asymmetry inherent to the case of the A-site La/Bi cation sublattice in LaxBi1-xFeO3 polymorphs. This approach allows exploring the ferroics behaviors from experimental data only, without additional assumptions on the nature of the order parameter.

A parametric study on the effect of rotational ground motions on building structural responses

The characteristics of the rotational components of strong earthquake ground motion and their effects on structural response are rarely considered. A reduced order parametric model is used to investigate the effects of the rotational ground motions upon buildings, which includes the influence of Soil-Structure Interaction. An indirect method of extracting rotational ground components using a multi-station procedure is employed. Ground accelerogram data recorded from the SMART-1 array in Taiwan for three different events are used. Over 3 million system/ground motion cases are analysed in this extensive parametric study. The results show that the rotational ground motion can significantly affect the displacement and acceleration responses of certain structures. The impact of the rotational ground motion depends principally on the amplitude ratio of the rotational to horizontal ground motion and the phase difference content at the structural system’s frequencies.

Cubic anisotropy created by defects of “random local anisotropy” type, and phase diagram of the O(n) Model

The expression for the cubic-type-anisotropy constant created by defects of "random local anisotropy" type is derived. It is shown that the Imry-Ma theorem stating that in space dimensions d<4 the introduction of an arbitrarily small concentration of defects of the "random local anisotropy" type in a system with continuous symmetry of the n-component vector order parameter (O(n) model) leads to the long-range order collapse and to occurrence of a disordered state, is not true if an anisotropic distribution of the defect-induced random easy axes directions in the order parameter space creates a global effective anisotropy of the "easy axis" type. For a weakly anisotropic distribution of the easy axes, in space dimensions 2<d<4 there exists some critical defect concentration, when exceeded, the inhomogeneous Imry-Ma state can exist as an equilibrium one. At lower defect concentration the long-range order takes place in the system. For a strongly anisotropic distribution of the easy axes, the Imry-Ma state is suppressed completely and the long-range order state takes place at any defect concentration.