Determining White Noise Forcing From Eulerian Observations in the Navier Stokes Equation

The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to and the state of a system of interest given noisy observations. Herein we consider the forward problem of the forced 2D Navier Stokes equation. The inverse problem is inference of the forcing, and possibly the initial condition, given noisy observations of the velocity field. We place a prior on the forcing which is in the form of a spatially correlated temporally white Gaussian process, and formulate the inverse problem for the posterior distribution. Given appropriate spatial regularity conditions, we show that the solution is a continuous function of the forcing. Hence, for appropriately chosen spatial regularity in the prior, the posterior distribution on the forcing is absolutely continuous with respect to the prior and is hence well-defined. Furthermore, the posterior distribution is a continuous function of the data. We complement this theoretical result with numerical simulation of the posterior distribution

Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions

The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a long-range power-law interaction is studied by extensive Monte Carlo simulations, with particular attention to the issue of the spin-chirality decoupling/coupling. Large system sizes up to $L=4096$ are studied. With varying the exponent $\sigma$ describing the power-law interaction, we observe three distinct types of ordering regimes. For smaller $\sigma$, the spin and the chirality order at a common finite temperature with a common correlation-length exponent, exhibiting the standard spin-chirality coupling behavior. For intermediate $\sigma$, the chirality orders at a temperature higher than the spin, exhibiting the spin-chirality decoupling behavior. For larger $\sigma$, both the spin and the chirality order at zero temperature. We construct a phase diagram in the $\sigma$ versus the temperature plane, and discuss implications of the results. Critical properties associated with both the chiral-glass and the spin-glass transitions are also determined.Comment: 28 pages, 26 figures, to appear in J. Phys. Soc. Jp

A digital twin framework for Industry 4.0 enabling next-gen manufacturing

Digital twins offer a framework to support the ever-rising demands in the fast-paced industrial evolution. This technology not only adds to the reliability of industrial processes but also offers an insight in to long-term behaviors and pattern during the aging of the industrial equipment. In this paper, a digital twin framework is presented to replicate the processes of a real production line for product assembly. The proposed work implements a digital/graphical replica of Festo Cyber Physical Factory (CPF) for Industry 4.0 (I4.0). The implemented system allows to schedule orders and specify product configuration which embodies the actions of CPF in digital world. In addition, the paper also presents a viable framework to interlink the physical system with the digital instance to offer extended services and a pathway towards realization of fully functional digital twins

Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet

Ordering of the classical Heisenberg antiferromagnet on the triangular lattice is studied by means of a mean-field calculation, a scaling argument and a Monte Carlo simulation, with special attention to its vortex degree of freedom. The model exhibits a thermodynamic transition driven by the Z_2-vortex binding-unbinding, at which various thermodynamic quantities exhibit an essential singularity. The low-temperature state is a "spin-gel" state with a long but finite spin correlation length where the ergodicity is broken topologically. Implications to recent experiments on triangular-lattice Heisenberg antiferromagnets are discussed

Pulse Shape Discrimination of CsI(Tl) with a Photomultiplier Tube and MPPCs

In this study, we evaluate and compare the pulse shape discrimination (PSD) performance of multipixel photon counters (MPPCs, also known as silicon photomultiphers - SiPMs) with that of a typical photomultiplier tube (PMT) when testing using CsI(Tl) scintillators. We use the charge comparison method, whereby we discriminate different types of particles by the ratio of charges integrated within two time-gates (the delayed part and the entire digitized waveform). For a satisfactory PSD performance, a setup should generate many photoelectrons (p.e.) and collect their charges efficiently. The PMT setup generates more p.e. than the MPPC setup does. With the same digitizer and the same long time-gate (the entire digitized waveform), the PMT setup is also better in charge collection. Therefore, the PMT setup demonstrates better PSD performance. We subsequently test the MPPC setup using a new data acquisition (DAQ) system. Using this new DAQ, the long time-gate is extended by nearly four times the length when using the previous digitizer. With this longer time-gate, we collect more p.e. at the tail part of the pulse and almost all the charges of the total collected p.e. Thus, the PSD performance of the MPPC setup is improved significantly. This study also provides an estimation of the short time-gate (the delayed part of the digitized waveform) that can give a satisfactory PSD performance without an extensive analysis to optimize this gate

Theory of Exciton Recombination from the Magnetically Induced Wigner Crystal

We study the theory of itinerant-hole photoluminescence of two-dimensional electron systems in the regime of the magnetically induced Wigner crystal. We show that the exciton recombination transition develops structure related to the presence of the Wigner crystal. The form of this structure depends strongly on the separation $d$ between the photo-excited hole and the plane of the two-dimensional electron gas. When $d$ is small compared to the magnetic length, additional peaks appear in the spectrum due to the recombination of exciton states with wavevectors equal to the reciprocal lattice vectors of the crystal. For $d$ larger than the magnetic length, the exciton becomes strongly confined to an interstitial site of the lattice, and the structure in the spectrum reflects the short-range correlations of the Wigner crystal. We derive expressions for the energies and the radiative lifetimes of the states contributing to photoluminescence, and discuss how the results of our analysis compare with experimental observations.Comment: 10 pages, no figures, uses Revtex and multicol.st

The novel method to reduce the silica content in lignin recovered from black liquor originating from rice straw

Difficulties in the production of lignin from rice straw because of high silica content in the recovered lignin reduce its recovery yield and applications as bio-fuel and aromatic chemicals. Therefore, the objective of this study is to develop a novel method to reduce the silica content in lignin from rice straw more effectively and selectively. The method is established by monitoring the precipitation behavior as well as the chemical structure of precipitate by single-stage acidification at different pH values of black liquor collected from the alkaline treatment of rice straw. The result illustrates the significant influence of pH on the physical and chemical properties of the precipitate and the supernatant. The simple two-step acidification of the black liquor at pilot-scale by sulfuric acid 20w/v% is applied to recover lignin at pH 9 and pH 3 and gives a percentage of silica removal as high as 94.38%. Following the developed process, the high-quality lignin could be produced from abundant rice straw at the industrial-scale

Dynamics and deposition of sediment-bearing multi-pulsed flows and geological implication

Previous studies on dilute, multi-pulsed, subaqueous saline flows have demonstrated that pulses will inevitably advect forwards to merge with the flow front. On the assumption that pulse merging occurs in natural-scale turbidity currents, it was suggested that multi-pulsed turbidites that display vertical cycles of coarsening and fining would transition laterally to single-pulsed, normally graded turbidites beyond the point of pulse merging. In this study, experiments of dilute, single- and multi-pulsed sediment-bearing flows (turbidity currents) are conducted to test the linkages between downstream flow evolution and associated deposit structure. Experimental data confirm that pulse merging occurs in laboratory-scale turbidity currents. However, only a weak correspondence was seen between longitudinal variations in the internal flow dynamics and the vertical structure of deposits; multi-pulsed deposits were documented, but transitioned to single-pulsed deposits before the pulse merging point. This early transition is attributed to rapid sedimentation-related depletion of the coarser-grained suspended fraction in the laboratory setting, whose absence may have prevented the distal development of multi-pulsed deposits; this factor complicates estimation of the transition point in natural-scale turbidite systems

Blow-up profile of rotating 2D focusing Bose gases

We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation $\Omega$. First we study the behavior of the ground state when the coupling constant approaches $a\_*$ , the critical strength of the cubic nonlinearity for the focusing nonlinear Schr{\"o}dinger equation. We prove that blow-up always happens at the center of the trap, with the blow-up profile given by the Gagliardo-Nirenberg solution. In particular, the blow-up scenario is independent of $\Omega$, to leading order. This generalizes results obtained by Guo and Seiringer (Lett. Math. Phys., 2014, vol. 104, p. 141--156) in the non-rotating case. In a second part we consider the many-particle Hamiltonian for $N$ bosons, interacting with a potential rescaled in the mean-field manner $--a\_N N^{2\beta--1} w(N^{\beta} x), with$w$a positive function such that$\int\_{\mathbb{R}^2} w(x) dx = 1$. Assuming that$\beta < 1/2$and that$a\_N \to a\_*$sufficiently slowly, we prove that the many-body system is fully condensed on the Gross-Pitaevskii ground state in the limit$N \to \infty$

Chirality scenario of the spin-glass ordering

Detailed account is given of the chirality scenario of experimental spin-glass transitions. In this scenario, the spin glass order of weakly anisotropic Heisenberg-like spin-glass magnets including canonical spin glasses are essentially chirality driven. Recent numerical and experimental results are discussed in conjunction with this scenario.Comment: Submitted to J. Phys. Soc. Japan "Special Issue on Frustration