arXiv subjects
Publications and source records attributed to Takashi Suzuki.
We study Smoluchowski-Poisson equation in two space dimensions provided with Dirichlet boundary condition for the Poisson part. For this equation several profiles of blowup solution have been noticed. Here we show the residual vanishing.
For bounded domains, eigenvalues and eigenfunctions of double layer potentials are considered. The aim of this paper is to establish some relationships between eigenvalues, eigenfunctions and the geometry of domain boundaries.
We study a variational functional of Trudinger-Moser type associated with one-sided Borel probability measure. Its boundedness at the extremal parameter holds when the residual vanishing occurs. In the proof we use a variant of the Y.Y. Li estimate.
We study a class of semilinear elliptic equations with constraints in higher dimension. It is known that several mathematical structures of the problem are closed to those of the Liouville equation in dimension two. In this paper, we establish a classification of entire solutions, the $\sup + \inf$ type inequality and the quantized blowup mechanism.
We consider finite volume effects on the electromagnetic form factor of the pion. We compute the peudoscalar-vector-pseudoscalar correlator in the $ε$ expansion of chiral perturbation theory up to the next-to-leading order and find a way to remove the dominant part, which comes from a contribution of the pion zero-mode. Inserting non-zero momentum to relevant operators (or taking a subtraction of the correlators at different time-slices), and taking an appropriate ratio of them, one can automatically cancel the zero-mode's contribution, which becomes non-perturbatively large $\sim \mathcal{O}(100 \%)$ in the $ε$ regime. The remaining finite volume dependence, which comes from the non-zero momentum modes, is shown to be perturbatively small even in such an extremal case. Since the zero-mode's dominance is universal in any finite volume scaling, and we do not rely on any particular feature of the $ε$ expansion, our method has a wide application to many other correlators of QCD.
Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Increasingly much evidence appears in favor of event-driven control hypothesis: human operators only start actively controlling the system when the discrepancy between the current and desired system states becomes large enough. The event-driven models based on the concept of threshold can explain many features of the experimentally observed dynamics. However, much still remains unclear about the dynamics of human-controlled systems, which likely indicates that humans employ more intricate control mechanisms. The present paper argues that control activation in humans may be not threshold-driven, but instead intrinsically stochastic, noise-driven. Specifically, we suggest that control activation stems from stochastic interplay between the operator's need to keep the controlled system near the goal state on one hand and the tendency to postpone interrupting the system dynamics on the other hand. We propose a model capturing this interplay and show that it matches the experimental data on human balancing of virtual overdamped stick. Our results illuminate that the noise-driven activation mechanism plays a crucial role at least in the considered task, and, hypothetically, in a broad range of human-controlled processes.
The antiferrodistortive (AFD) phase transition for a pseudotetragonal composition of Pb(Zr0.530Ti0.470)O3 (PZT) doped with 6% Sr has been investigated using sound velocity (4 to 320K), high resolution synchrotron X-ray powder diffraction (100 to 800K) and high resolution as well as high flux neutron powder diffraction measurements (4K) to settle the existing controversies about the true ground state of PZT in the morphotropic phase boundary (MPB) region. The multiplet character of the neutron diffraction profiles of (3/2 1/2 1/2)pc (pseudocubic or pc indices) and (3/2 3/2 1/2)pc superlattice peaks, appearing below the AFD transition temperature, rules out the rhombohedral R3c space group. The true ground state is confirmed to be monoclinic in the Cc space group in agreement with the predictions of the first principles calculations and earlier findings for pure PZT in the MPB region. 6% Sr2+ substitution and the use of high wavelength (λ=2.44Å) neutrons have played key role in settling the existing controversies about the true ground state of PZT in the MPB region.
The controversies about the structure of the true ground state of pseudorhombohedral compositions of Pb(ZrxTi1-x)O3 (PZT) are addressed using a 6% Sr2+ substituted sample with x=0.550. Sound velocity measurements reveal a phase transition at Tc~279K. The temperature dependence of FWHM of (h00)pc peaks and the unit cell volume also show anomalies around 279K even though there is no indication of any change of space group in the synchrotron X-ray powder diffraction (SXRD) patterns. The neutron powder diffraction patterns reveal appearance of superlattice peaks below Tc~279K confirming the existence of an antiferrodistortive phase transition. The Rietveld analysis of the room temperature and low temperature SXRD data below Tc shows that the structure corresponds to single monoclinic phase in the Cm space group while the analysis of neutron powder diffraction data reveals that the structure of the ground state phase below Tc corresponds to the Cc space group. Our analysis shows that the structural models for the ground state phase based on R3c space group with or without the coexistence of the room temperature monoclinic phase in the Cm space group can be rejected.
We consider finite volume effects on the electro-magnetic pion form factor near the chiral limit, in the so-called $ε$ regime. The pseudoscalar-vector-pseudoscalar three-point function is calculated in the $ε$ expansion of chiral perturbation theory to the next-to-leading order. In the $ε$ regime, finite volume effects are non-perturbatively large in general. However, we find a way to remove its dominant part, by inserting momenta to the correlators, and taking an appropriate ratio of them. The subleading contribution is, then, shown to be perturbatively small, and one can extract the form factor as in a similar way to that in the $p$ regime.
We study Smoluchowski-Poisson equation in two space dimensions provided with Dirichlet boundary condition for the Poisson part. For this equation several profiles of blowup solution have been noticed. Here we show collapse mass quantization with possible vanishing term.
We give a new approach for the local class field theory of Serre and Hazewinkel. We also discuss two-dimensional local class field theory in this framework.
We completely determine which extension of local fields satisfies Fontaine's property (Pm) for a given real number m. A key ingredient of the proof is the local class field theory of Serre and Hazewinkel.
Recently, application of electric field (E-field) has received considerable attention as a new method to induce novel quantum phenomena since application of E-field can tune the electronic states directly with obvious scientific and industrial advantages over other turning methods. However, E-field-induced Mott transitions are rare and typically require high E-field and low temperature. Here we report that the multiband Mott insulator Ca2RuO4 shows unique insulator-metal switching induced by applying a dry-battery level voltage at room temperature. The threshold field Eth ~40 V/cm is much weaker than the Mott gap energy. Moreover, the switching is accompanied by a bulk structural transition. Perhaps the most peculiar of the present findings is that the induced metal can be maintained to low temperature by a weak current.
Blow-up solutions to the two-dimensional Gel'fand problem are studied. It is known that the location of the blow-up points of these solutions is related to a Hamiltonian function involving the Green function of the domain. We show that this implies an equivalence between the Morse indices of the solutions and the associated critical points of the Hamiltonian.
We give a refinement of the local class field theory of Serre and Hazewinkel. This refinement allows the theory to treat extensions that are not necessarily totally ramified. Such a refinement was obtained and used in the authors' paper on Fontaine's property (Pm), where the explanation had to be rather brief. In this paper, we give a complete account, from necessary knowledge of an appropriate Grothendieck site to the details of the proof. We start by reviewing the local class field theory of Serre and Hazewinkel.
We have carried out dc magnetic susceptibility, magnetization and specific heat measurements on thiospinel CuCrZrS$_{4}$. Below $T_{\rm C}^{*} =$ 58 K, dc magnetic susceptibility and magnetization data show ferromagnetic behavior with a small spontaneous magnetization 0.27 $μ_{\rm B}/$f. u.. In dc magnetic susceptibility, large and weak irreversibilities are observed below $T_{\rm f} =$ 6 K and in the range $T_{\rm f}< T < T_{\rm C}^{*}$ respectively. We found that there is no anomaly as a peak or step in the specific heat at $T_{\rm C}^{*}$.
A new electron-doped superconductor Li_x_Sr_2_CuO_2_Br_2_ with x = 0.15 has successfully been synthesized by an electrochemical Li-intercalation technique. The magnetic susceptibility shows superconductivity of bulk with the superconducting transition temperature Tc = 8 K. This compound is the first electron-doped superconducting cuprate with the K_2_NiF_4_ structure.
We report the transport and thermodynamic properties under hydrostatic pressure in the antiferromagnetic Kondo compound CeMg2Cu9 with a two-dimensional arrangement of Ce atoms. Magnetic specific heat Cmag(T) shows a Schottky-type anomaly around 30 K originating from the crystal electric field (CEF) splitting of the 4f state with the first excited level at Δ_{1}/kB = 58 K and the second excited level at Δ_{2}/kB = 136 K from the ground state. Electric resistivity shows a two-peaks structure due to the Kondo effect on each CEF level around T_{1}^{max} = 3 K and T_{2}^{max} = 40 K. These peaks merge around 1.9 GPa with compression. With increasing pressure, Neel temperature TN initially increases and then change to decrease. TN finally disappears at the quantum critical point Pc = 2.4 GPa.