Fast generation of stability charts for time-delay systems using continuation of characteristic roots

Many dynamic processes involve time delays, thus their dynamics are governed by delay differential equations (DDEs). Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging because DDEs are infinite-dimensional. We propose a new approach to quickly generate stability charts for DDEs using continuation of characteristic roots (CCR). In our CCR method, the roots of the characteristic equation of a DDE are written as implicit functions of the parameters of interest, and the continuation equations are derived in the form of ordinary differential equations (ODEs). Numerical continuation is then employed to determine the characteristic roots at all points in a parametric space; the stability of the original DDE can then be easily determined. A key advantage of the proposed method is that a system of linearly independent ODEs is solved rather than the typical strategy of solving a large eigenvalue problem at each grid point in the domain. Thus, the CCR method significantly reduces the computational effort required to determine the stability of DDEs. As we demonstrate with several examples, the CCR method generates highly accurate stability charts, and does so up to 10 times faster than the Galerkin approximation method.Comment: 12 pages, 6 figure

Seebeck Effect in Magnetic Tunnel Junctions

Creating temperature gradients in magnetic nanostructures has resulted in a new research direction, i.e., the combination of magneto- and thermoelectric effects. Here, we demonstrate the observation of one important effect of this class: the magneto-Seebeck effect. It is observed when a magnetic configuration changes the charge based Seebeck coefficient. In particular, the Seebeck coefficient changes during the transition from a parallel to an antiparallel magnetic configuration in a tunnel junction. In that respect, it is the analog to the tunneling magnetoresistance. The Seebeck coefficients in parallel and antiparallel configuration are in the order of the voltages known from the charge-Seebeck effect. The size and sign of the effect can be controlled by the composition of the electrodes' atomic layers adjacent to the barrier and the temperature. Experimentally, we realized 8.8 % magneto-Seebeck effect, which results from a voltage change of about -8.7 {\mu}V/K from the antiparallel to the parallel direction close to the predicted value of -12.1 {\mu}V/K.Comment: 16 pages, 7 figures, 2 table

Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement

Parameter Identification in Nonlinear Mechanical Systems with Noisy Partial State Measurement Using PID-Controller Penalty Functions

Dynamic models of physical systems often contain parameters that must be estimated from experimental data. In this work, we consider the identification of parameters in nonlinear mechanical systems given noisy measurements of only some states. The resulting nonlinear optimization problem can be solved efficiently with a gradient-based optimizer, but convergence to a local optimum rather than the global optimum is common. We augment the dynamic equations with a morphing parameter and a proportional-integral-derivative (PID) controller to transform the objective function into a convex function; the global optimum can then be found using a gradient-based optimizer. The morphing parameter is used to gradually remove the PID controller in a sequence of steps, ultimately returning the model to its original form. An optimization problem is solved at each step, using the solution from the previous step as the initial guess. This strategy enables use of a gradient-based optimizer while avoiding convergence to a local optimum. The efficacy of the proposed approach is demonstrated by identifying parameters in the van der Pol-Duffing oscillator, a hydraulic engine mount system, and a magnetorheological damper system. Our method outperforms genetic algorithm and particle swarm optimization strategies, and demonstrates robustness to measurement noise

Polaron Formation in the Three-Band Peierls-Hubbard Model for Cuprate Superconductors

Exact diagonalization calculations show a continuous transition from delocalized to small polaron behavior as a function of intersite electron-lattice coupling. A transition, found previously at Hartree-Fock level [Yonemitsu et al., Phys. Rev. Lett. {\bf 69}, 965 (1992)], between a magnetic and a non magnetic state does not subsist when fluctuations are included. Local phonon modes become softer close to the polaron and by comparison with optical measurements of doped cuprates we conclude that they are close to the transition region between polaronic and non-polaronic behavior. The barrier to adiabatically move a hole vanishes in that region suggesting large mobilities.Comment: 7 pages + 3 poscript figures, Revtex 3.0, MSC-199

Polaronic optical absorption in electron-doped and hole-doped cuprates

Polaronic features similar to those previously observed in the photoinduced spectra of cuprates have been detected in the reflectivity spectra of chemically doped parent compounds of high-critical-temperature superconductors, both $n$-type and $p$-type. In Nd$_2$CuO$_{4-y}$ these features, whose intensities depend both on doping and temperature, include local vibrational modes in the far infrared and a broad band centered at $\sim$ 1000 cm$^{-1}$. The latter band is produced by the overtones of two (or three) local modes and is well described in terms of a small-polaron model, with a binding energy of about 500 cm$^{-1}$. Most of the above infrared features are shown to survive in the metallic phase of Nd$_{2-x}$Ce$_x$Cu0$_{4-y}$, Bi$_2$Sr$_2$CuO$_6$, and YBa$_2$Cu$_3$O$_{7-y}$, where they appear as extra-Drude peaks. The occurrence of polarons is attributed to local modes strongly coupled to carriers, as shown by a comparison with tunneling results.Comment: File latex, 31 p., submitted to Physical Review B. Figures may be faxed upon reques

Preoperative risk stratification of lymph node metastasis for non-functional pancreatic neuroendocrine neoplasm: An international dual-institutional study

BACKGROUND: /Objectives: Although the presence of lymph node metastasis (LNM) defines malignant potential, preoperative prediction of LNM has not been established for non-functional pancreatic neuroendocrine neoplasm (NF-PNEN). We sought to develop a prediction system using only preoperatively available factors that would stratify the risk of LNM for NF-PNEN. METHODS: We retrospectively reviewed patients who underwent R0/1 resection of NF-PNEN at Kyoto University (2007-2019) and the University of California, San Francisco (2010-2019). Risk stratification of LNM was developed using preoperative factors by the logistic regression analysis. Long-term outcomes were compared across the risk groups. RESULTS: A total of 131 patients were included in this study. Lymph nodes were pathologically examined in 116 patients, 23 (20%) of whom had LNM. Radiological tumor size [1.5-3.5 cm (odds ratio: 13.5, 95% confidence interval: 1.77-398) and >3.5 cm (72.4, 9.06-2257) against ≤1.5 cm], <50% cystic component (8.46 × 10^6, 1.68 × 10^106-), and dilatation of main pancreatic duct ≥5 mm (31.2, 3.94-702) were independently associated with LNM. When patients were classified as the low-risk (43 patients), intermediate-risk (44 patients), and high-risk groups (29 patients), proportions of LNM differed significantly across the groups (0%, 14%, and 59%, respectively). Recurrence-free survival (RFS) of the low- and intermediate-risk groups were significantly better than that of the high-risk group (5-year RFS rates of 92.2%, 85.4%, and 47.1%, respectively). CONCLUSIONS: The prediction system using preoperative radiological factors stratifies the risk of LNM for NF-PNEN. This stratification helps to predict malignant potential and determine the surgical procedure and necessity of regional lymphadenectomy

Frequency dependent relaxation rate in the superconducting YBa2Cu3O{6+delta}

The submillimeter-wave 3 cm{-1} < nu < 35 cm{-1} complex conductivity of the reduced YBa2Cu3O{6+delta} film (Tc=56.5 K) was investigated for temperatures 4 K < T < 300 K and compared to the properties of the same film in the optimally doped state. The frequency dependence of the effective quasiparticle scattering rate 1/tau*(nu) was extracted from the spectra. 1/tau*(nu) is shown to be frequency independent at low frequencies and high temperatures. A gradual change to 1/tau*~nu^{1.5} law is observed as temperature decreases. In order to explain the observed temperature dependence of the low frequency spectral weight above Tc, the quasiparticle effective mass is supposed to be temperature dependent for T>Tc.Comment: 4 pages, 4 figure

Optical conductivity of the nonsuperconducting cuprate La(8-x)Sr(x)Cu(8)O(20)

La(8-x)Sr(x)Cu(8)O(20) is a non-superconducting cuprate, which exhibits a doubling of the elementary cell along the c axis. Its optical conductivity sigma (omega) has been first measured here, down to 20 K, in two single crystals with x = 1.56 and x = 2.24. Along c, sigma (omega) shows, in both samples, bands due to strongly bound charges, thus confirming that the cell doubling is due to charge ordering. In the ab plane, in addition to the Drude term one observes an infrared peak at 0.1 eV and a midinfrared band at 0.7 eV. The 0.1 eV peak hardens considerably below 200 K, in correspondence of an anomalous increase in the sample dc resistivity, in agreement with its polaronic origin. This study allows one to establish relevant similarities and differences with respect to the spectrum of the ab plane of the superconducting cuprates.Comment: Revised version submitted to Phys. Rev. B, including the elimination of Fig. 1 and changes to Figs. 4 and