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This paper deals with a design method for boundary shapes using filtering techniques based on a partial differential equation (PDE). In shape optimization, it is known that oscillatory boundaries appear when design variables are directly assigned to the design boundaries. In addition, during the optimization process, discretized elements in a computational domain are distorted due to extremely large shape changes along the design boundaries. The distorted elements may cause accuracy deterioration or numerical instability in a forward problem. In this paper, we propose a shape optimization method by using the PDE as a low pass filter which prevents the oscillatory boundaries of the optimized design. For restricting the shape distortion of the discretized elements, the shear deformation of the elements is constrained in the optimization problem. Mathematical programming is used to find the boundary shapes under the KKT conditions. The effectiveness of the proposed method is demonstrated through numerical examples in solid and fluid mechanics.

Optical studies of the density wave (DW) salt of $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{KHg}(\mathrm{SCN})}_{4}$ revealed a pseudogap due to a charge fluctuation below ${T}^{*}\ensuremath{\simeq}$ 200 K. Moreover, $^{13}\mathrm{C}$-NMR studies of the DW salt of $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{RbHg}(\mathrm{SCN})}_{4}$ and of the superconductivity (SC) salt of $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{NH}}_{4}\mathrm{Hg}{(\mathrm{SCN})}_{4}$ suggested that the NMR line width of the A site increased and the charge disproportionation in the A column developed below ${T}^{*}$. These phenomena may be due to the development of a horizontal stripe modulation of the local charge density. However, whether the horizontal stripe modulation develops or not and the relationships among ${T}^{*}$ anomalies, the pseudogap, and line broadening, were unclear. In this study, $^{13}\mathrm{C}$-NMR measurements were obtained of the metallic salt of $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{TlHg}(\mathrm{SeCN})}_{4}$, and its electronic structure was compared with those of the DW and SC salts. The NMR line width of the A site and ${\ensuremath{\chi}}_{\mathrm{B}}/{\ensuremath{\chi}}_{\mathrm{C}}$ in Rb(SCN) and $\mathrm{NH}{}_{4}$(SCN) increased and deviated from that in Tl(SeCN) below ${T}^{*}$, suggesting the development of the instability of horizontal stripe modulation in Rb(SCN) and $\mathrm{NH}{}_{4}$(SCN) and that ${T}^{*}$ anomalies could be due to the instability.

The physical properties of the organic conductor $\ensuremath{\kappa}\text{\ensuremath{-}}(\mathrm{BEDT}\text{\ensuremath{-}}{\mathrm{TTF})}_{2}{\mathrm{Cu}[\mathrm{N}(\mathrm{CN})}_{2}]\mathrm{I}$ $(\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{I})$ are inconsistent with the universal phase diagram of isostructural $\ensuremath{\kappa}$-Br and $\ensuremath{\kappa}$-Cl. To systematically understand $\ensuremath{\kappa}$-type salts, we measured and compared $^{13}\mathrm{C}$ NMR spectra of $\ensuremath{\kappa}$-I, $\ensuremath{\kappa}$-Br, and $\ensuremath{\kappa}$-Cl. The $\ensuremath{\kappa}$-I spectra manifested abrupt line broadening below 40 K due to the development of electronic inhomogeneity and an increase in the spin-lattice relaxation rate divided by temperature $1/{T}_{1}T$ down to the lowest temperature, suggesting an enhanced antiferromagnetic (AF) fluctuation. These results imply that AF fluctuation without long-range order in $\ensuremath{\kappa}$-I is induced by electronic inhomogeneity, which disturbs the development of coherency. Consequently, $\ensuremath{\kappa}$-I is an insulator with AF fluctuation at low temperature similar to x-ray-irradiated $\ensuremath{\kappa}$-Cl. We suggest that not only pressure but also disorder is a key parameter in the physical properties of $\ensuremath{\kappa}$-type salts.

An electron paramagnetic resonance study for an organic superconductor ${\ensuremath{\beta}}^{\ensuremath{'}\ensuremath{'}}\text{\ensuremath{-}}{(\text{BEDT-TTF})}_{4}[({\mathrm{H}}_{3}\mathrm{O})\mathrm{Ga}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{3}]\phantom{\rule{0.16em}{0ex}}\ifmmode\cdot\else\textperiodcentered\fi{}\phantom{\rule{0.16em}{0ex}}{\mathrm{C}}_{6}{\mathrm{H}}_{5}{\mathrm{NO}}_{2}$ reveals that superconductivity coexists uniformly with the charge ordered state in one material. In the charge ordered state, the interplane spin exchange is gapped, while the in-plane conductivity is not significantly modified. This anisotropic behavior is explained by an exotic charge ordered state, in which molecular-site-selective carrier localization coexists with conducting carriers on other molecules. The relationship between superconductivity and this conductive charge ordered state is investigated.

Thermodynamic picture induced by π-d interaction in a molecular magnetic superconductor κ-(BETS)2FeX4 (X = Cl, Br), where BETS is bis(ethylenedithio)tetraselenafulvalene, studied by single crystal calorimetry is reviewed. Although the S = 5/2 spins of Fe3+ in the anion layers form a three-dimensional long-range ordering with nearly full entropy of Rln6, a broad hump structure appears in the temperature dependence of the magnetic heat capacity only when the magnetic field is applied parallel to the a axis, which is considered as the magnetic easy axis. The scaling of the temperature dependence of the magnetic heat capacity of the two salts is possible using the parameter of |Jdd|/kB and therefore the origin of the hump structure is related to the direct magnetic interaction, Jdd, that is dominant in the system. Quite unusual crossover from a three-dimensional ordering to a one-dimensional magnet occurs when magnetic fields are applied parallel to the a axis. A notable anisotropic field-direction dependence against the in-plane magnetic field was also observed in the transition temperature of the bulk superconductivity by the angle-resolved heat capacity measurements. We discuss the origin of this in-plane anisotropy in terms of the 3d electron spin configuration change induced by magnetic fields.

Elucidation of the mechanism by which the shape of bones is formed is essential for understanding vertebrate development. Bones support the body of vertebrates by withstanding external loads, such as those imposed by gravity and muscle tension. Many studies have reported that bone formation varies in response to external loads. An increased external load induces bone synthesis, whereas a decreased external load induces bone resorption. This relationship led to the hypothesis that bone shape adapts to external load. In fact, by simulating this relationship through topology optimization, the internal trabecular structure of bones can be successfully reproduced, thereby facilitating the study of bone diseases. In contrast, there have been few attempts to simulate the external structure of bones, which determines vertebrate morphology. However, the external shape of bones may be reproduced through topology optimization because cells of the same type form both the internal and external structures of bones. Here, we constructed a three-dimensional topology optimization model to attempt the reproduction of the external shape of teleost vertebrae. In teleosts, the internal structure of the vertebral bodies is invariable, exhibiting an hourglass shape, whereas the lateral structure supporting the internal structure differs among species. Based on the anatomical observations, we applied different external loads to the hourglass-shaped part. The simulations produced a variety of three-dimensional structures, some of which exhibited several structural features similar to those of actual teleost vertebrae. In addition, by adjusting the geometric parameters, such as the width of the hourglass shape, we reproduced the variation in the teleost vertebrae shapes. These results suggest that a simulation using topology optimization can successfully reproduce the external shapes of teleost vertebrae. By applying our topology optimization model to various bones of vertebrates, we can understand how the external shape of bones adapts to external loads., Author summary In this paper, we developed a computational method to investigate the relationship between three-dimensional bone shape and external loads imposed on bones. Many studies report that bone formation varies in response to external loads. An increased external load induces bone synthesis, whereas a decreased external load induces bone resorption. This relationship led to the hypothesis that the shape of bones adapts to external load. However, it remains unclear whether this hypothesis can explain the shape of bones. Here, we constructed a three-dimensional mathematical model that imitates the cellular activities of bone formation to attempt the reproduction of the shape of teleost vertebrae. In teleosts, the shape of the vertebrae differs among the species. We set the multiple types of external load conditions in the simulations and compared the simulation results with different teleost vertebrae. The produced structures that can resist the deformation of the surrounding tissues exhibited multiple structural features similar to the vertebrae of several teleost species. This result shows that the formation of bone shape can be explained by the adaptation to external load.

λ-type molecular π–d systems are coupled systems consisting of π electron systems with strong magnetic interactions and 3d electron systems with weak magnetic interactions. They exhibit an unconven...

In this paper, we propose grayscale-free topology optimization for a reactor design problem where the electromagnetic performance needs to be optimized. A reactor is an electric device to boost electric voltage, and is used as a part of a DC-DC converter in electric and hybrid vehicles. When designing reactors, we need to consider many performance indicators such as inductance and fringing loss. In general, high-performance reactor design that satisfies all requirements is not obvious, and topology optimization is promising for such non-trivial design problems. In this paper, we therefore establish a framework for the electromagnetic design of an in-vehicle reactor on the basis of boundary tracking type level-set topology optimization, which realizes grayscale-free topology optimization. Because of its grayscale-free characteristic, the established framework can completely resolve the numerical problems caused by the so-called grayscale elements. We present several numerical examples to demonstrate the usefulness of the established framework, and we discuss the possibilities for the expansion of the established framework to more difficult and valuable design problems.

Orthotropic elastic moduli of composite structures can be identified by nonlinear least squares fit between measured and computed natural frequencies. However, due to measurement errors contained in the measured natural frequencies and mode shapes, the process of elastic moduli identification is error-prone. This paper proposes an efficient method to estimate the errors in the elastic moduli caused by the measurement errors in the natural frequencies. The method utilizes an efficient semi-analytic expression of the sensitivities of the eigenvalues with respect to the orthotropic elastic moduli. First, the first-order approximation of the analytic sensitivity of orthotropic elastic moduli with respect to the measurement errors is introduced. The approximation is then used to estimate the variability of the identified elastic moduli due to the measurement errors. It is shown that the aspect ratio of the test specimen greatly affects the standard deviation of the identified elastic moduli. Second, using the first-order approximation, the effects of aspect ratio of the test specimen as well as the values of the elastic moduli are further investigated. Based on the results of numerical experiments, guidelines for the dimension of the test specimen for the elastic moduli identification are proposed.

In this paper, a combined numerical–experimental methodology for the identification of elastic moduli of orthotropic media is presented. Special attention is given to the laminated electrical steel sheets, which are modeled as orthotropic media with nine independent engineering elastic moduli. The elastic moduli are determined specifically for use with finite element vibration analyses. We propose a three-step methodology based on a conventional nonlinear least squares fit between measured and computed natural frequencies. The methodology consists of: (1) successive augmentations of the objective function by increasing the number of modes, (2) initial condition updates, and (3) appropriate selection of the natural frequencies based on their sensitivities on the elastic moduli. Using the results of numerical experiments, it is shown that the proposed method achieves more accurate converged solution than a conventional approach. Finally, the proposed method is applied to measured natural frequencies and mode shapes of the laminated electrical steel sheets. It is shown that the method can successfully identify the orthotropic elastic moduli that can reproduce the measured natural frequencies and frequency response functions by using finite element analyses with a reasonable accuracy.

We performed heat capacity measurements on the molecular π–d system λ-(BEDT-STF)2FeCl4 to discuss the unconventional paramagnetic-like behavior. We observed a Schottky-type anomaly below TN of 16 K...

To verify the effect of geometrical frustration, we artificially distort the triangular lattice of the quasi-two-dimensional organic conductor $\ensuremath{\kappa}\ensuremath{-}{(\mathrm{BEDT}\ensuremath{-}\mathrm{TTF})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}$ [BEDT-TTF: bis(ethylenedithio)tetrathiafulvalene] by analogous-molecular substitution and apply $^{13}\mathrm{C}$ NMR of bulk and substituted sites, electric conductivity, and static magnetic susceptibility measurements. The results indicate that the magnetic characteristics of the substituted sample are quantitatively similar to those of the pure sample. Moreover, the magnetic characteristics at the substituted sites are also the same as in the bulk. These results suggest that the observed magnetic properties may not be due to the geometrical frustration but the importance of disorder.

We consider inverse problems for the first and half order time fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates., 27pages

We have performed $^{1}\mathrm{H}$ NMR and $^{13}\mathrm{C}$ NMR measurements to investigate the coupling between molecular dynamics and the electronic state of ${\ensuremath{\beta}}^{\ensuremath{'}}$-(BEDT-TTF)${}_{2}{\mathrm{ICl}}_{2}$. From the $^{1}\mathrm{H}$ NMR measurements, we observed a frequency-dependent anomaly in the nuclear spin-lattice relaxation rate $^{1}\mathrm{T}_{1}^{\ensuremath{-}1}$ that originates from the slowing down of the ethylene motion. In the $^{13}\mathrm{C}$ NMR measurements, we found an anomaly in the linewidth of the NMR spectra at around 150 K, which is attributed to a nuclear spin-spin relaxation rate $(^{13}\mathrm{T}_{2})$ anomaly. The magnitudes of the anomalies in the linewidth and in $^{13}\mathrm{T}_{2}^{\ensuremath{-}1}$ are related to the hyperfine coupling constant. These results suggest that the ethylene motion modulates the molecular orbital of the BEDT-TTF molecules and gives rise to a difference in the orbital energy between the ``staggered'' and ``eclipsed'' conformations. We propose that significant coupling exists between the ethylene motion and the electronic state of the molecular dimer and that the ethylene dynamics can trigger the emergence of charge degrees of freedom inside the dimers and cause the dielectric anomaly in ${\ensuremath{\beta}}^{\ensuremath{'}}$-(BEDT-TTF)${}_{2}{\mathrm{ICl}}_{2}$.

The electronic state of (TMTTF) 2 SbF 6 was investigated by the 1 H and 13 C NMR measurements. The temperature dependence of T 1 −1 in 1 H NMR shows a sharp peak associated with the antiferromagnetic transition at T AF =6 K. The temperature dependence of T 1 −1 is described by the power law T 2.4 below T AF . This suggests the nodal gapless spin wave excitation in antiferromagnetic phase. In 13 C NMR, two sharp peaks at high temperature region, associated with the inner and the outer carbon sites in TMTTF dimer, split into four peaks below 150 K. It indicates that the charge disproportionation occurs. The degree of charge disproportionation Δ ρ is estimated as (0.25±0.09) e from the chemical shift difference. This value of Δ ρ is consistent with that obtained from the infrared spectroscopy. In the antiferromagnetic state (AFI), the observed line shape is well fitted by eight Lorentzian peaks. This suggests that the charge order with the same degree still remains in the AF state. From the line assignment, the AF staggered spin amplitude is obtained as 0.70 μ B and 0.24 μ B at the charge rich and the poor sites, respectively. These values corresponding to almost 1 μ B per dimer are quite different from 0.11 μ B of another AF (AFII) state in (TMTTF) 2 Br with effective higher pressure. As a result, it is understood that the antiferromagnetic staggered spin order is stabilized on the CO state in the AFI phase of (TMTTF) 2 SbF 6 .

We performed $^{13}\mathrm{C}$ NMR measurements on the unconventional organic superconductor $\ensuremath{\lambda}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{GaCl}}_{4}$ to clarify its electronic properties in the paramagnetic state. We found that the spin-lattice relaxation rate divided by temperature $1/{T}_{1}T$ shows Curie-like enhancement above 55 K that arises from an antiferromagnetic fluctuation. In addition, we found additional enhancement of $1/{T}_{1}T$ below 10 K, where the Knight shift decreases and the linewidth of NMR spectra is broadened. The result could be understood by the magnetic fluctuation induced by the nesting of the Fermi surface. We discovered that $\ensuremath{\lambda}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{GaCl}}_{4}$ salt inherently exhibits the two different types of magnetic fluctuations.

A general topology optimization method, which is capable of simultaneous design of density and orientation of anisotropic material, is proposed by introducing orientation design variables in addition to the density design variable. In this work, the Cartesian components of the orientation vector are utilized as the orientation design variables. The proposed method supports continuous orientation design, which is out of the scope of discrete material optimization approaches, as well as design using discrete angle sets. The advantage of this approach is that vector element representation is less likely to fail into local optima because it depends less on designs of former steps, especially compared with using the angle as a design variable (Continuous Fiber Angle Optimization) by providing a flexible path from one angle to another with relaxation of orientation design space. An additional advantage is that it is compatible with various projection or filtering methods such as sensitivity filters and density filters because it is free from unphysical bound or discontinuity such as the one at theta = 2 pi and theta = 0 seen with direct angle representation. One complication of Cartesian component representation is the point-wise quadratic bound of the design variables; that is, each pair of element values has to reside in a given circular bound. To overcome this issue, we propose an isoparametric projection method, which transforms box bounds into circular bounds by a coordinate transformation with isoparametric shape functions without having the singular point that is seen at the origin with polar coordinate representation. A new topology optimization method is built by taking advantage of the aforementioned features and modern topology optimization techniques. Several numerical examples are provided to demonstrate its capability. Copyright (C) 2014 John Wiley & Sons, Ltd.

Summary This paper proposes a level-set based topology optimization method incorporating a boundary tracking mesh generating method and nonlinear programming. Because the boundary tracking mesh is always conformed to the structural boundary, good approximation to the boundary is maintained during optimization; therefore, structural design problems are solved completely without grayscale material. Previously, we introduced the boundary tracking mesh generating method into level-set based topology optimization and updated the design variables by solving the level-set equation. In order to adapt our previous method to general structural optimization frameworks, the incorporation of the method with nonlinear programming is investigated in this paper. To successfully incorporate nonlinear programming, the optimization problem is regularized using a double-well potential. Furthermore, the sensitivities with respect to the design variables are strictly derived to maintain consistency in mathematical programming. We expect the investigation to open up a new class of grayscale-free topology optimization. The usefulness of the proposed method is demonstrated using several numerical examples targeting two-dimensional compliant mechanism and metallic waveguide design problems. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we study inverse problems for multi-dimensional linear degenerate parabolic equations and strongly coupled systems. In particular we discuss the Lipschitz type stability results for the inverse source problems which determine a source term by boundary data on an appropriate sub-boundary and the data on any fixed time. Our arguments are based on the Carleman estimate. Here we prove and use the Carleman estimate with the x-independent weight function for linear degenerate parabolic equations and systems.

This paper deals with structural optimization for designing periodic structures in a hole array wavelength filter. The hole array wavelength filter that consists of metallic thin film and dielectric enables to transmit narrow bandwidth light. It is known that transmission spectrum can be changed not only by the periodicity of hole array but also by the shape of holes. For optimizing the hole shape, the level set method is used in this study. In the ordinary level set method, the boundaries are implicitly expressed by the zero level set of a scalar function, called the level set function, within a fixed mesh. Therefore, the material interpolation becomes numerically awkward within the elements across the implicit zero level set because those elements inevitably take on intermediate material properties even if the boundary of zero level set are mathematically clear. As the result, the optimization is likely to yield wrong solution. Here, a new level set optimization method incorporating Arbitrary Lagrangian Eulerian method is proposed to eliminate intermediate values on the interfaces perfectly. As a result, the proposed method can successfully perform the structural optimization of hole shape without intermediate values.

This paper presents a topology optimization method which is capable of designing both topology and orientation distribution of anisotropic composite material simultaneously. Topology optimization is a well established structural optimization framework which optimizes the material distribution, i.e. density, in a given design domain for maximum performance. However, a method for structures made of inhomogeneously distributed anisotropic composite material is still under research. In this paper, a topology optimization method is extended to handle orientation distribution together with density distribution. A tensor field design variable is used for modeling orientation based on the idea of the orientation tensor. All tensor components are updated in similar manner to the Free Material Optimization technique while maintaining the physical feasibility by using the existing material tensor for interpolation. Thanks to the tensor representation, the method is free from complications derived from three-dimensional rotation. At the same time, the method works well with common non-linear programming algorithms because the tensor invariants are kept constant by multi-variable projection without point-wise constraints. The proposed method is built upon a modern topology optimization technique, thus, it is versatile and flexible enough to solve multi-load problems. Single loaded and multiply loaded stiffness maximization problems are provided as numerical examples, and characteristics of concurrent density and fiber orientation optimization are investigated.

Angle-resolved heat capacity (ARHC) measurements with multi-directional magnetic fields for an organic superconductor λ-(BETS)2GaCl4 are performed to investigate the out-of-plane (polar angle) and ...

We performed the STM Spectroscopy (STS) measurement on organic superconductor deuterated κ-(ET-d[3,3])2Cu[N(CN) 2 ]Br to clarify the mechanism of superconductivity. The mechanism of superconductivity in κ-ET2X is predicted as the spin fluctuation mechanism where the gap symmetry changes from d x 2 − y 2 to dxy with increasing the electron correlation. In previous STS measurements, we found that d[2,2]-Br, d[0,0]-Br and Cu(NCS)2 were d-wave superconductors and the symmetry was described by the d x 2 − y 2 . The electron correlation of these salts is still weak in the frame of the spin fluctuation model. So, we investigated the d[3,3]-Br which located at stronger electron correlation region than the previously studied salts by the STS. We also investigated the STS on the cut lateral surfaces by the focused ion beam (FIB) method to measure the in-plane anisotropy of superconducting gap in more detail as well as the as-grown surfaces. It was found from the result that d[3,3]-Br was d -wave superconductor and the gap symmetry was d x 2 − y 2 as well as the previously studied ET salts. Therefore, d[3,3]-Br is also still weak in spite of stronger electron correlation than other ET salts. On the other hand, we also observed the two-type superconducting gaps which are the nodal and anti-nodal type gaps at the same angle surface. This suggests the coexistence of d x 2 − y 2 and dxy. It may be the evidence of the change from d x 2 − y 2 to dxy caused by the locally stronger electron correlation around the anti-ferromagnetic insulating region.

This paper deals with density-based topology optimization considering fluid and thermal interactions, in which the Navier---Stokes and heat transport equations are coupled. We particularly focus on designing heat exchangers. In the engineering context, heat exchangers are designed while considering a certain amount of input power. Therefore it is important to maximize the performance of a heat exchanger under a constant input power. In this paper we propose a way to control the input power by introducing an extra integral equation. To be more precise, in the fluid analysis, the inlet pressure is determined by solving the extra integral equation together with the Navier---Stokes equation. By doing this we can keep the inlet power constant even when the flow channels are changed in the optimization process. Consequently, the system of equations of the fluid field takes an integrodifferential form. On the other hand, in the heat transport analysis, a single governing equation is defined for simultaneously modeling both the solid and fluid parts. The design variable is a fluid fraction whose distribution represents the topology of the solid and fluid domains. When designing heat exchangers, two different heat conditions are considered in the formulation of the optimization problems, namely temperature-dependent and temperature-independent heat sources. Through the numerical examples for designing flow channels in a heat exchanger, it is shown that distinct topologies can be obtained according to the input power and the heat source conditions.

We consider a fractional radiative transport equation, where the time derivative is of half order in the Caputo sense. By establishing Carleman estimates, we prove the global Lipschitz stability in determining the coefficients of the one-dimensional time-fractional radiative transport equation of half-order.

We present the results of $^{13}\mathrm{C}$ NMR experiments in an organic superconductor with localized Fe spins ${\ensuremath{\beta}}^{\ensuremath{''}}\ensuremath{-}{(\text{BEDT-}\mathrm{TTF})}_{4}[({\mathrm{H}}_{3}\mathrm{O})\mathrm{Fe}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{3}]\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{C}}_{6}{\mathrm{H}}_{5}\mathrm{Br}$. We reveal the antiferromagnetic coupling between Fe $d$ spins and $\ensuremath{\pi}$ spins, which creates an exchange field antiparallel to the external field direction at the $\ensuremath{\pi}$ electrons. In addition to the static effects of Fe spins, we show from the nuclear spin-lattice relaxation rate measurement that the magnetic fluctuations generated by Fe spins are suppressed at low temperatures and high magnetic fields. These conditions are suitable to stabilize the field-induced superconductivity by the field compensation mechanism. After the suppression of Fe-spin dynamics by a magnetic field of 19 T, we observed the underlying $\ensuremath{\pi}$-electron contribution. We discuss a possible anomaly in the $\ensuremath{\pi}$-electron system.

SUMMARY Most topology optimization problems are formulated as constrained optimization problems; thus, mathematical programming has been the mainstream. On the other hand, solving topology optimization problems using time evolution equations, seen in the level set-based and the phase field-based methods, is yet another approach. One issue is the treatment of multiple constraints, which is difficult to incorporate within time evolution equations. Another issue is the extra re-initialization steps that interrupt the time integration from time to time. This paper proposes a way to describe, using a Heaviside projection-based representation, a time-dependent diffusion equation that addresses these two issues. The constraints are treated using a modified augmented Lagrangian approach in which the Lagrange multipliers are updated by simple ordinary differential equations. The proposed method is easy to implement using a high-level finite element code. Also, it is very practical in the sense that one can fully utilize the existing framework of the code: GUI, parallelized solvers, animations, data imports/exports, and so on. The effectiveness of the proposed method is demonstrated through numerical examples in both the planar and spatial cases. Copyright © 2012 John Wiley & Sons, Ltd.

This study presents optimization methods for the design of rotor poles in interior permanent magnet machines, which aim to effectively obtain a sinusoidal distribution of the air-gap flux density. A sinusoidal field in the air-gap offers several advantages, such as reduction of torque ripple when using sinusoidal phase currents, and reduction in cogging torque and higher harmonic components of back electromotive force. In this study, the optimization process is achieved based on a phase field method using an Allen-Cahn equation. For the optimization problem we address, regions with meaningful design sensitivity values may exist outside the interfacial layer, which makes design variable updating impossible. To resolve this problem, the design sensitivities are diffused in the radial direction, using a diffusion equation. The time evolution of the design variables is based on the implicit finite element method, and the augmented Lagrangian method is used to deal with the volume constraint.

This paper deals with continuum-based compliant mechanism design. In topology optimization, filtering techniques are used for the regularization of the design space. In the density design representation, convolution-type filters inherently produce gray transition regions between solids and voids. In order to reduce the gray transition regions, projection schemes have recently been proposed. Binarization, however, still leads to one-node connected hinges in compliant mechanism design. In this paper, we propose a method that incorporates the level set and arbitrary Lagrangian Eulerian methods so that the gray transition regions are completely excluded and one-node connected hinges are not formed.

This paper deals with topology optimization of body shapes in fluid flows, where some new ideas for drag minimization and lift maximization problems are proposed. For drag minimization problems, the objective function is expressed as a body force integration in the flow domain. Also a similar expression of objective function is given for lift maximization problems. Employing those objective function expressions, optimum shapes of bodies in incompressible axisymmetric and two-dimensional flows are numerically investigated.

SUMMARY In the last decade, metamaterials have been gaining attention and have been investigated because of their unique characteristics, which conventional materials do not have, such as negative refraction indexes. However, it is sometimes difficult to design metamaterials on the basis of experience and theoretical considerations because the relationship between their electromagnetic characteristics and structure is often vague. A mathematical structural design methodology targeting metamaterials may therefore be useful for expanding the engineering applications of metamaterials in industry. In this paper, a new level set-based topology optimization method is proposed for designing composite right- and left-handed transmission lines, each of which consists of a waveguide and periodically located dielectric resonators. Such transmission lines function as a fundamental metamaterial. In the proposed method, the shape and topology of the dielectric resonators are represented by the level set function, and topology optimization problems are formulated on the basis of the level set-based representation. Copyright © 2011 John Wiley & Sons, Ltd.

This study presents a topology optimization method to reduce cogging torque, applied to the design of the stator core of an interior permanent magnet motor. The proposed method uses a reaction-diffusion equation and optimization is separately performed based on two objective functions: 1) minimization of the cogging torque itself, for a number of rotor positions; and 2) minimization of the magnetic energy variation. The optimization results show that configurations having dummy slots are desirable, but the number of dummy slots differs according to the objective function used.

In this paper, we propose a level set-based topology optimization method targeting metallic waveguide design problems, where the skin effect must be taken into account since the metallic waveguides are generally used in the high-frequency range where this effect critically affects performance. One of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal. To implement this approach, we develop a boundary-tracking scheme for the arbitrary Lagrangian Eulerian (ALE) mesh pertaining to the zero iso-contour of the level set function that is given in an Eulerian mesh, and impose Dirichlet boundary conditions at the nodes on the zero iso-contour in the ALE mesh to compute the electric field. Since the ALE mesh accurately tracks the zero iso-contour at every optimization iteration, the electric field is always appropriately computed during optimization. For the sensitivity analysis, we compute the nodal coordinate sensitivities in the ALE mesh and smooth them by solving a Helmholtz-type partial differential equation. The obtained smoothed sensitivities are used to compute the normal velocity in the level set equation that is solved using the Eulerian mesh, and the level set function is updated based on the computed normal velocity. Finally, the utility of the proposed method is discussed through several numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.

A coupling calculation method using dynamics and lubrication for a rotor and floating bush bearing system has been developed to predict self-excited oscillations and unbalance oscillations using a flexible multibody dynamics technique with hydrodynamic lubrication theory. Based on experimental results using a floating bush bearing, an accurate and numerically efficient lubrication model is proposed to calculate the hydrodynamic force, the bush rotating speed and the temperature of the oil film. In the multibody dynamics analysis, the rotor was modeled using the finite element method to include bending elasticity and the gyroscopic effect. The bearing bush was modeled by a rigid body. The coupling analysis between the rotordynamics and the oil film force of the bearing was performed by an in-house flexible multibody dynamics solver. Subsequently, the detailed mechanism of the rotor oscillation and the influence of some design parameters were investigated by numerical simulations and experiments.

We have investigated the magnetic properties of λ-(BEDT-STF)2FeCl4 by Mossbauer measurement to reveal the origin of the paramagnetic-like behavior of the 3d spin system observed in λ-(BETS)2FeCl4 u...

The kinetic energy of α′-(BEDT-TTF)2IBr2, α-(BEDT-TTF)2I3, and α-(BEDT-TTF)2NH4Hg(SCN)4 was estimated from the room-temperature optical conductivity measured from 50 to 30 000 cm−1. The kinetic energy of α′-(BEDT-TTF)2IBr2 was significantly smaller than that of α-(BEDT-TTF)2I3 that shows metal–insulator phase transition. A clear hysteresis was found in the magnetic susceptibility near the phase transition at around 30 K.

The low temperature phase in (EDT-TTF)2AuBr2 was investigated by 1H NMR and magnetic susceptibility measurements for protonated and partially deuterated single crystals. Two sharp peaks were observed in the temperature dependence of T 1 − 1 for both salts, associated with the SDW transition TSDW and the sub-phase transition T* common in the incommensurate SDW phase. The values of TSDW determined as 15 and 19 K for h- and d-salts, respectively, indicate the negative chemical pressure effect. The obtained ratios T*/TSDW 0.37 and 0.43 for h- and d-salts, respectively, are slightly larger than the common value T*/TSDW≅0.3 observed in (TMTCF)2X. The ratio T*/TSDW increases for larger TSDW and the low temperature sub-phase becomes more stable.

It is said that the quasi-two dimensional organic conductor ( BEDT-TTF ) 2 X forming two columns structure like α or θ salts, shows charge order (CO) state at low temperature. To confirm the existence of the CO state and the electron magnetism in α ′ phase whose symmetry is different from that of α and θ phases, we investigated 13 C-NMR on α ′ ‐ ( BEDT-TTF ) 2 IBr 2 , in which one-sided central carbon on BEDT-TTF molecules is substituted with 13 C. As a result, the change of spectrum was observed at 200 K which corresponds to CO transition and the angular dependence of spectrum at 15 K indicated that the charge ordering pattern was intra-column separating type. The spectrum in paramagnetic state can be examined by not only the difference of the charge density on on-site molecule but also the contribution from off-site molecules. This result suggested that the hyperfine coupling tensor changes after CO transition in which the charge separates extremely.

The ground state of $\lambda$-(BEDT-TTF)$_2$GaCl$_4$, which has the same structure as the organic superconductor $\lambda$-(BETS)$_2$GaCl$_4$, was investigated by magnetic susceptibility and $^{13}$C NMR measurements. The temperature dependence of the magnetic susceptibility revealed an antiferromagnetic (AF) correlation with $J/k_{\rm B} \simeq$ 98 K. NMR spectrum splitting and the divergence of $1/T_1$ were observed at approximately 13 K, which is associated with the AF transition. We found that the AF structure is commensurate according to discrete NMR peak splitting, suggesting that the ground state of $\lambda$-(BEDT-TTF)$_2$GaCl$_4$ is an AF dimer-Mott insulating state. Our results suggest that the superconducting phase of $\lambda$-type salts would be located near the AF insulating phase., Comment: 5 pages, 4 figures

This paper deals with formulation of dynamics of a moving flexible body in a local frame of reference. In a conventional approach the local frame is normally fixed to the corresponding body and always represents the positions and angles of the body: the positions and angles are represented by Cartesian coordinates and Euler angles or Euler parameters, respectively. The elastic degrees of freedom are expressed by, e.g. nodal coordinates in a finite element analysis, modal coordinates, etc. However, the choice of these variables as the generalized coordinates makes the resulting equations of motion extremely complicated. This is because the representation of the rotation of a body is highly non-linear and this non-linearity makes the coefficient matrices dependent on the coordinates themselves. In this paper, we propose an alternative way of treating the issue by explicitly predicting the body motions and regularly updating the local frame. First, the motion of the local frame is assumed to explicitly follow the associated moving body. Then, the equations of motion are derived in a set of generalized coordinates that express both rigid-body and elastic degrees of freedom in the local frame. These equations are solved by a time integration with a given time interval. The motion of the local frame in the interval is estimated from a prediction of the rigid-body motions. Then, the gap between the predicted and the actual motions is evaluated. Finally, the predictions are iteratively corrected by the obtained responses in the rigid-body motions so that the gap should remain within an imposed tolerance. Copyright © 2009 John Wiley & Sons, Ltd.

This paper deals with a new type of shock absorbing device that cooperates between two colliding objects. The new device utilizes a four-bar-chain-like articulated mechanism with some possible actuations. The devices are assumed to be deployed in the pre-crash phase (by sensing and identifying unavoidable collisions) so as to provide an extended deformable region between the two objects. Moreover, by functioning like a four-bar-chain mechanism, they produce a repulsive effect by pushing each other and sliding in the opposite lateral direction. To investigate the capacity of the proposed articulated shock absorbing mechanism, a standard numerical optimization technique called SQP and a new optimization technique called ALPSO are applied. ALPSO is an attractive method for solving multimodal optimization problems based on Particle Swarm Optimization and constraint treatment using an Augmented Lagrange Method. We demonstrate ALPSO and show its applicability to this problem. The optimization process automatically determines the mode of the operation and gives an estimation of the development potential of the new device.