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This study addresses a distributed controller design problem for discrete-time systems using linear matrix inequalities (LMIs). Sparsity constraints on control gains of distributed controllers result in conservatism via the convexification of the existing methods such as the extended LMI method. In order to mitigate the conservatism, we introduce a novel LMI formulation for this problem, utilizing the clique-wise decomposition method from our previous work on continuous-time systems. By reformulating the sparsity constraint on the gain matrix within cliques, this method achieves a broader solution set. Also, the analytical superiority of our method is confirmed through numerical examples.

Magneto-thermal switching (MTS) is a key technology for efficient thermal management. Recently, large MTS with nonvolatility has been observed in Sn-Pb solders [H. Arima et al., Commun. Mater. 5, 34 (2024)] where phase separation, different superconducting transition temperature (Tc) of Sn and Pb, and magnetic-flux trapping are the causes of the nonvolatile MTS. To further understand the mechanism and to obtain the strategy for enhancing switching ratio, exploration of new phase-separated superconductors with nonvolatile MTS is needed. Here, we show that the In52-Sn48 commercial solder is a phase-separated superconducting composite with two Tc and traps vortices after field cooling. A clear signature of nonvolatile MTS was observed at T = 2.5 K. From specific heat analyses, we conclude that the vortices are mainly trapped in the lower-Tc phase ({\gamma}-phase) after field cooling, which is the evidence that vortex trapping also works on achieving nonvolatile MTS in phase-separated superconducting composites., Comment: 14 pages, 5 figures

We examined the affection of the flux-trapped states of Sn60-Pb40 solders on superconducting properties of a Sn wire. The temperature dependence of electrical resistivity at H = 0 Oe after zero-field cooling (ZFC) showed a sharp superconducting transition at T = 3.7 K. In contrast, that after field cooling (FC) resulted in broadening of the transition. The difference between ZFC and FC data evidences critical affection of trapped fluxes at solders on superconducting states. We propose that, in electrical measurements where magnetic fields of several hundred Oe are critical, field experience should be seriously considered when using solders., Comment: 11 pages, 4 figures, supplementary data

The influence of annealing on the superconducting properties of eutectic high-entropy alloy NbScTiZr was examined by measuring magnetization, electrical resistivity, and zero-field specific heat. Additionally, the extent of lattice strain was assessed via the analysis of lattice parameters and Vickers microhardness. The greatest lattice strain was inferred in the sample annealed at 400 $^{\circ}$C. Field-dependent magnetization datasets indicate enhanced flux pinning in the as-cast, 400 $^{\circ}$C annealed, and 600 $^{\circ}$C annealed samples. The superconducting parameters such as upper critical field, Ginzburg-Landau coherence length, and magnetic penetration depth do not strongly depend on the annealing temperature. However, the Maki parameter shows a peak at 400 $^{\circ}$C annealing temperature and correlates with the magnitude of lattice strain. This suggests that greater lattice strain may enhance the Maki parameter by altering the orbital-limited field through the modification of flux pinning strength. Although the influence of lattice strain is less discernible in zero-field specific heat measurements, the superconducting parameters deduced from specific heat data suggest a potential for strong-coupled superconductivity in samples heat-treated above 600 $^{\circ}$C. Our investigation underscores the substantial impact of lattice strain on the Maki parameter of eutectic HEA superconductors, primarily through the modulation of flux pinning strength., Comment: to be published in Mater. Today Commun

Recently, huge uniaxial negative thermal expansion (NTE) along a $c$-axis has been observed in transition-metal ($Tr$) zirconides $Tr$Zr$_{2}$ with a tetragonal CuAl$_{2}$-type structure. In a recent study on FeZr$_{2}$ [M. Xu et al., Nat. Commun. 14, 4439 (2023)], the importance of optical phonons to the emergence of the $c$-axis NTE in FeZr$_{2}$ has been proposed. In this study, the physical properties of $Tr$Zr$_{2}$ ($Tr$ = Fe and Co$_{1-x}$Ni$_{x}$) have been studied by specific heat, sound velocity measurements, and theoretical phonon calculations to discuss the importance of optical phonons to the emergence of the $c$-axis NTE in CoZr$_{2}$ and FeZr$_{2}$. From analyses of lattice specific heat, we found that Ni substitution results in a systematic decrease in oscillator strength for the Einstein modes with 8.74 meV (CoZr$_{2}$). From phonon calculations, the low-energy optical phonon branches at the $\Gamma$ point were observed for CoZr$_{2}$ and FeZr$_{2}$ with $c$-axis NTE, but not in NiZr$_{2}$ with positive thermal expansion. The enhancement of phonon density of states near the above-mentioned optical phonon energy in CoZr$_{2}$ and FeZr$_{2}$ is consistent with the specific heat analyses. We propose the importance of the low-energy optical phonons to the emergence of the $c$-axis NTE in TrZr$_{2}$., Comment: 14 pages, 9 figures, and 3 tables

For over a century, the Hall effect, a transverse effect under out-of-plane magnetic field or magnetization, has been a cornerstone for magnetotransport studies and applications. Modern theoretical formulation based on the Berry curvature has revealed the potential that even in-plane magnetic field can induce anomalous Hall effect, but its experimental demonstration has remained difficult due to its potentially small magnitude and strict symmetry requirements. Here we report observation of the in-plane anomalous Hall effect by measuring low-carrier density films of magnetic Weyl semimetal EuCd$_2$Sb$_2$. Anomalous Hall resistance exhibits distinct three-fold rotational symmetry for changes in the in-plane field component, and this can be understood in terms of out-of-plane Weyl points splitting or orbital magnetization induced by in-plane field, as also confirmed by model calculation. Our findings demonstrate the importance of in-plane field to control the Hall effect, accelerating materials development and further exploration of various in-plane field induced phenomena., Comment: 14 pages, 4 figures

CuAl2-type transition-metal (Tr) zirconides are superconductor family, and the Tr-site element substitution largely modifies its transition temperature (Tc). Here, we synthesized polycrystalline samples of Fe1-xNixZr2 by arc melting. From magnetic susceptibility measurements, bulk superconductivity was observed for 0.4 < x < 0.8, and the highest Tc of 2.8 K was observed for x = 0.6. Specific heat measurements were also performed, bulk superconductivity was observed for 0.4 < x < 0.8, and the highest Tc of 2.6 K was observed for x = 0.6. The obtained superconductivity phase diagram exhibits dome-shaped trend, which is similar to unconventional superconductors, where magnetic fluctuations are essential for superconductivity. In addition, from the c/a lattice constant ratio analysis, we show the possible relationship between the suppression of bulk superconductivity in the Ni-rich compositions and a collapsed tetragonal transition., Comment: 16 pages, 8 figures, SI

We report the results of the CO $\textit J$=1-0 and SiO $\textit J$=2-1 mapping observations towards the broad-velocity-width molecular feature CO 16.134-0.553 with the Nobeyama Radio Observatory 45 m telescope. The high quality CO map shows that the 5-pc size broad-velocity-width feature bridges two separate velocity components at $\textit V_{\rm{LSR}}$$\quad$$\simeq$ 40 km s$^{-1}$ and 65 km s$^{-1}$ in the position-velocity space. The kinetic power of CO 16.134-0.553 amounts to $7.8\times10^2$ $\textit L$$_\odot$ whereas no apparent driving sources were identified. Prominent SiO emission was detected from the broad-velocity-width feature and its root in the $\textit V_{\rm{LSR}}$$\quad$$\simeq$ 40 km s$^{-1}$ component. In the CO Galactic plane survey data, CO 16.134-0.553 appears to correspond to the Galactic eastern rim of a 15-pc diameter expanding CO shell. An $1\deg$-diameter H I emission void and $4\deg$-long vertical H I filament were also found above and below the CO shell, respectively. We propose that the high-velocity plunge of a dark matter subhalo with a clump of baryonic matter was responsible for the formation of the H I void, CO 16.134-0.553/CO shell, and the H I filament., Comment: 7 pages, 6 figures, 2 table, accepted for publication in ApJ

This study addresses a distributed state feedback controller design problem for continuous-time linear time-invariant systems by means of linear matrix inequalities (LMI). As the exact convexification is still open, the block-diagonal relaxation of Lyapunov functions has been prevalent despite its conservatism. In this work, we target a class of non-block-diagonal Lyapunov functions that has the same sparsity as distributed controllers. By leveraging a block-diagonal factorization of sparse matrices and Finsler's lemma, we first present a (nonlinear) matrix inequality for stabilizing distributed controllers with such Lyapunov functions, which boils down to a necessary and sufficient condition for such controllers if the sparsity pattern is chordal. As a relaxation of the inequality, we derive an LMI that completely covers the conventional relaxation and then provide analogous results for $H_\infty$ control. Lastly, numerical examples underscore the efficacy of our results., Comment: 8 pages

Here we study nonmonotonic features which appear both in magnetoresistivity and anomalous Hall resistivity during the simple magnetization process, by systematically measuring type-II magnetic Weyl semimetal EuCd$_2$Sb$_2$ films over a wide carrier density range. We find that a positive magnetoresistivity hump can be explained as manifestation of a field-linear term in the generalized magnetoconductivity formula including the Berry curvature. As also confirmed by model calculation, the term can be negative and pronounced near the Weyl point energy in the case that the Weyl cones are heavily tilted. Our findings demonstrate extensive effects of the Berry curvature on various magnetotransport in magnetic Weyl semimetals beyond the anomalous Hall effect., Comment: 17 pages, 4 figures

Formation of vortices is a typical phenomenon of type-II superconductors under magnetic fields (H). In contrast, type-I superconductors do not host vortices because of their Meissner state. As rare cases, vortices have been observed in intermediate states of type-I superconductors; in addition, the recent observation of type-II superconductivity with vortices in a (originally type-I) Pb crystal film at extremely low temperature (T) under H has opened new pathway to study vortex physics. However, thermodynamic characteristics of such type-II-like superconducting states with vortices in originally type-I element superconductors have not been detected because of the lack of bulk example. In this study, we investigated superconducting states of phase-separated Sn-Pb solders using specific heat and magnetization to reveal magnetic-flux-trapping mechanisms. Here, we show that Sn islands in the Sn-Pb solders exhibit type-II-like superconducting states with vortices when the solders host extremely high magnetic fluxes after field cooling. Furthermore, with increasing T, the amount of trapped flux decreases, and the driving force of the magnetic flux changes from type-II superconducting states of Sn to supercurrent of Pb regions surrounding the Sn islands. The field-cooled Sn-Pb solders are rich in physics of bulk vortex formation and anomalously enhanced supercurrent in element (originally type-I) superconductors., Comment: We found a problem on the analysis of specific heat data because of possible self-heating of the measured solders when flux reduction. We will resubmit the data after careful analyses

Searching for an ideal magnetic Weyl semimetal hosting only a single pair of Weyl points has been a focal point for systematic clarification of its unique magnetotransport derived from the interplay between topology and magnetization. Among the candidates, triangular-lattice antiferromagnet EuCd$_2$As$_2$ has been attracting special attention due to the prediction of the ideal Weyl semimetal phase in the ferromagnetic state, however, transport properties of low-carrier density samples have remained elusive. Here we report molecular beam epitaxy growth of EuCd$_2$As$_2$ films, achieving low-hole density in the range of $10^{15}$-$10^{16}$ cm$^{-3}$ at low temperature. Transport measurements of such low-carrier density films reveal an insulating behavior with an activation gap of about 200 meV, which persists even in the field-induced ferromagnetic state. Our work provides an important experimental clue that EuCd$_2$As$_2$ is intrinsically insulating, contrary to the previous prediction., Comment: 12 pages, 3 figures

We report the first observation of bulk superconductivity of a ${\eta}$-carbide-type oxide Zr$_{4}$Pd$_{2}$O. The crystal structure and the superconducting properties were studied through synchrotron X-ray diffraction, magnetization, electrical resistivity, and specific heat measurement. The superconducting transition was observed at $T_{\mathrm{c}}$ = 2.73 K. Our measurement revealed that the ${\eta}$-carbide-type oxide superconductor Zr$_{4}$Pd$_{2}$O shows an enhanced upper critical field ${\mu_{\mathrm{0}}H_{\mathrm{c2}}\mathrm{(0)}}$ = 6.72 T, which violates the Pauli-Clogston limit ${\mu_{\mathrm{0}}H_{\mathrm{P}}}$ = 5.29 T. On the other hand, we found that the enhanced upper critical field is absent in a Rh analogue Zr$_{4}$Rh$_{2}$O. The large ${\mu_{\mathrm{0}}H_{\mathrm{c2}}\mathrm{(0)}}$ of Zr$_{4}$Pd$_{2}$O would be raised from strong spin-orbit coupling with Pd-4$d$ electrons. The discovery of new superconducting properties for Zr$_{4}$Pd$_{2}$O would shed light on the further development of ${\eta}$-carbide-type oxide superconductors., Comment: 12 pages, 4 figures, 3 tables

In this study, we explore distributed optimization problems with clique-wise coupling through the lens of operator splitting. This framework of clique-wise coupling extends beyond conventional pairwise coupled problems, encompassing consensus optimization and formation control, and is applicable to a wide array of examples. We first introduce a matrix, called the clique-wise duplication (CD) matrix, which enables decoupled reformulations for operator splitting methods and distributed computation. Leveraging this matrix, we propose a new distributed optimization algorithm via Davis-Yin splitting (DYS), a versatile three-operator splitting method. We then delve into the properties of this method and demonstrate how existing consensus optimization methods (NIDS, Exact Diffusion, and Diffusion) can be derived from our proposed method. Furthermore, being inspired by this observation, we derive a Diffusion-like method, the clique-based projected gradient descent (CPGD), and present Nesterov's acceleration and in-depth convergence analysis for various step sizes. The paper concludes with numerical examples that underscore the efficacy of our proposed method., Comment: 16pages

We investigate the thermal expansion and superconducting properties of a CuAl2-type (tetragonal) superconductor CoZr2 under high pressures. We perform high-pressure synchrotron X-ray diffraction in a pressure range of 2.9 GPa < P < 10.4 GPa and discover that CoZr2 exhibits volumetric negative thermal expansion under high pressures. Although the uniaxial positive thermal expansion (PTE) along the a-axis is observed under ambient pressure, that is suppressed by pressure, while the large uniaxial negative thermal expansion (NTE) along the c-axis is maintained under the pressure regime. As a result of a combination of the suppressed uniaxial PTE along the a-axis and uniaxial NTE along the c-axis, volumetric negative thermal expansion is achieved under high pressure in CoZr2. The mechanisms of volumetric NTE would be based on the flexible crystal structure caused by the soft Co-Co bond as seen in the iso-structural compound FeZr2, which exhibits uniaxial NTE along the c-axis. We also perform high-pressure electrical resistance measurements of CoZr2 to confirm the presence of superconductivity under the examined pressure regime in the range of 0.03 GPa < P < 41.9 GPa. We confirm the presence of superconductivity under all pressures and observe dome-like shape pressure dependence of superconducting transition temperature. Because of the coexistence of two phenomena, which are volumetric NTE and superconductivity, in CoZr2 under high pressure, the coexistence would be achievable under ambient pressure by tuning chemical compositions after our present observation., Comment: 22 pages, 7 figures, supporting information

We explored quinary body-centered cubic (bcc) high-entropy alloy (HEA) superconductors with valence electron concentrations (VECs) ranging from 4.6 to 5.0, a domain that has received limited attention in prior research. Our search has led to the discovery of new bcc Ti-Hf-Nb-Ta-Re superconducting alloys, which exhibit an interesting phenomenon of phase segregation into two bcc phases with slightly different chemical compositions, as the VEC increases. The enthalpy of the formation of each binary compound explains the phase segregation. All the alloys investigated were categorized as type-II superconductors, with superconducting critical temperatures ($T_\mathrm{c}$) ranging from 3.25 K to 4.38 K. We measured the Vickers microhardness, which positively correlated with the Debye temperature, and compared it with the hardness values of other bcc HEA superconductors. Our results indicate that $T_\mathrm{c}$ systematically decreases with an increase in hardness beyond a threshold of approximately 350 HV. Additionally, we plotted $T_\mathrm{c}$ vs. VEC for representative quinary bcc HEAs. The plot revealed the asymmetric VEC dependence. The correlation between the hardness and $T_\mathrm{c}$, as well as the asymmetric dependence of $T_\mathrm{c}$ on VEC can be attributed to the simultaneous effects of the electronic density of states at the Fermi level and electron-phonon coupling under the uncertainty principle, especially in the higher VEC region., Comment: to appear in Journal of Alloys and Metallurgical Systems

In this study, we propose a design methodology of distributed controllers for multi-agent systems on a class of directed interaction networks by extending the gradient-flow method. Although the gradient-flow method is a common design tool for distributed controllers, it is inapplicable to directed networks. First, we demonstrate how to construct a distributed controller for systems over a class of time-invariant directed graphs. Subsequently, we establish better convergence properties and performance enhancement than the conventional gradient-flow method. To illustrate its application in time-varying networks, we address the dynamic matching problem of two distinct groups of agents with different sensing ranges. This problem is a novel coordination task that involves pairing agents from two distinct groups to achieve a convergence of the paired agents' states to the same value. Accordingly, we apply the proposed method to this problem and provide sufficient conditions for successful matching. Lastly, numerical examples for systems on both time-invariant and time-varying networks demonstrate the effectiveness of the proposed method., Comment: 13 pages. https://ieeexplore.ieee.org/document/10453999

This study addresses a distributed optimization with a novel class of coupling of variables, called clique-wise coupling. A clique is a node set of a complete subgraph of an undirected graph. This setup is an extension of pairwise coupled optimization problems (e.g., consensus optimization) and allows us to handle coupling of variables consisting of more than two agents systematically. To solve this problem, we propose a clique-based linearized ADMM algorithm, which is proved to be distributed. Additionally, we consider objective functions given as a sum of nonsmooth and smooth convex functions and present a more flexible algorithm based on the FLiP-ADMM algorithm. Moreover, we provide convergence theorems of these algorithms. Notably, all the algorithmic parameters and the derived condition in the theorems depend only on local information, which means that each agent can choose the parameters in a distributed manner. Finally, we apply the proposed methods to a consensus optimization problem and demonstrate their effectiveness via numerical experiments.

This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed gradient-based algorithm with a novel operator inspired by the convex projection, called the clique-based projection. Next, we scrutinize the convergence properties for both diminishing and fixed step sizes. For diminishing ones, we show the convergence to an optimal solution under the assumptions of the smoothness of an objective function and the compactness of the constraint set. Additionally, when the objective function is strongly monotone, the strict convergence to the unique solution is proved without the assumption of compactness. For fixed step sizes, we prove the non-ergodic convergence rate of O(1/k) concerning the objective residual under the assumption of the smoothness of the objective function. Furthermore, we apply Nesterov's acceleration method to the proposed algorithm and establish the convergence rate of O(1/k^2). Numerical experiments illustrate the effectiveness of the proposed method., Comment: 8 pages, 5 figures

We investigated the structural, electronic, and superconducting properties of Co1-xNixZr2, in which c-axis thermal expansion is systematically controlled. At x (smaller than) 0.3, c-axis negative thermal expansion (NTE) was observed, and the thermal expansion constant {\alpha}c approached zero with increasing x. At x = 0.4-0.6, zero thermal expansion was observed, and positive thermal expansion (PTE) appeared for x (greater than) 0.7. By analyzing the c/a ratio, we observed a possible collapsed transition in the tetragonal lattice at around x = 0.6-0.8. The lattice collapse results in c-axis PTE and the suppression of bulk superconductivity., Comment: 16 pages, 5 figures, 1 table, Supporting materials

This study developed an automated identification procedure for compact clouds with broad velocity widths in the spectral line data cubes of highly crowded regions. The procedure was applied to the CO J=3-2 line data, obtained using the James Clerk Maxwell Telescope, to identify 184 high velocity dispersion compact clouds (HVCCs), which is a category of peculiar molecular clouds found in the central molecular zone of our galaxy. A list of HVCCs in the area -1.4{\deg}

The $l\!=\!+1.\!\!^\circ3$ region in the Galactic center is characterized by multiple shell-like structures and their extremely broad velocity widths. We revisit the molecular superbubble hypothesis for this region, based on high resolution maps of CO {\it J}=1--0, $^{13}$CO {\it J}=1--0, H$^{13}$CN {\it J}=1--0, H$^{13}$CO$^{+}$ {\it J}=1--0, SiO {\it J}=2--1, and CS {\it J}=2--1 lines obtained from the Nobeyama radio observatory 45-m telescope, as well as CO {\it J}=3--2 maps obtained from the James Clerk Maxwell telescope. We identified eleven expanding shells with total kinetic energy and typical expansion time $E_{\rm kin}\!\sim\! 10^{51.9}$ erg and $t_{\rm exp}\!\sim\! 10^{4.9}$ yr, respectively. In addition, the $l\!=\!+1.\!\!^\circ3$ region exhibited high SiO {\it J}=2--1/H$^{13}$CN {\it J}=1--0 and SiO {\it J}=2--1/H$^{13}$CO$^{+}$ {\it J}=1--0 intensity ratios, indicating that the region has experienced dissociative shocks in the past. These new findings confirm the molecular superbubble hypothesis for the $l\!=\!+1.\!\!^\circ3$ region. The nature of the embedded star cluster, which may have supplied 20--70 supernova explosions within 10$^5$ yr, is discussed. This work also show the importance of compact broad-velocity-width features in searching for localized energy sources hidden behind severe interstellar extinction and stellar contamination.