Coarsely grained stochastic Boltzmann equation and its moment equations

The stochastic Boltzmann equation is coarsely grained. The coarsely grained stochastic (CGS) Boltzmann equation has fluctuating terms in its collision term. On the basis of the CGS Boltzmann equation, reduced Grad’s 26 moment equations are derived. Coarsely grained moment equations obtained from the CGS Boltzmann equation show that fluctuating terms remain as nonvanishing terms owing to the nonlinearity in the collision term of the CGS Boltzmann equation. The Navier-Stokes-Fourier law obtained using the CGS Boltzmann equation indicates that the pressure deviator and heat flux include fluctuations of their one-order higher moments.     

Defining a randomness notion via another

To compare two randomness notions with each other, we ask whether a given randomness notion can be defined via another randomness notion. Inspired by Yu's pioneering study, we formalize our question using the concept of relativization of randomness. We give some solutions to our formalized questions. Also, our results include the affirmative answer to the problem asked by Yu in a discussion with the second author, i.e., whether Schnorr randomness relative to the halting problem is equivalent to Martin‐Löf randomness relative to all low 1‐generic reals.     

Weak theories of concatenation and minimal essentially undecidable theories

We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation \({\mathsf{WTC}^{-\varepsilon}}\) , which is a weak subtheory of Grzegorczyk’s theory \({\mathsf{TC}^{-\varepsilon}}\) , is a minimal essentially undecidable theory, that is, the theory \({\mathsf{WTC}^{-\varepsilon}}\) is essentially undecidable and if one omits an axiom scheme from \({\mathsf{WTC}^{-\varepsilon}}\) , then the resulting theory is no longer essentially undecidable. Moreover, we give a positive answer to Grzegorczyk and Zdanowski’s conjecture that ‘The theory \({\mathsf{TC}^{-\varepsilon}}\) is a minimal essentially undecidable theory’. For the alternative theories \({\mathsf{WTC}}\) and \({\mathsf{TC}}\) which have the empty string, we also prove that the each theory without the neutrality of \({\varepsilon}\) is to be such a theory too.     

Fast Calculation of Computer-Generated Fresnel Hologram Utilizing Distributed Parallel Processing and Array Operation

Fresnel CGH for a three-dimensional (3-D) object is generated by calculating the Fresnel diffraction, but it requires a huge amount of calculation. This is one reason for the difficulty in realizing real-time holography. We propose fast calculation method of computer-generated Fresnel hologram (Fresnel CGH) utilizing distributed parallel processing and array operation. In our method, a projected image with depth information of the 3-D object is prepared to calculate the Fresnel diffraction. The Fresnel diffraction of the projected image is then calculated with depth information by array operation and distributed parallel processing. Parallel processing is realized using JavaSpaces and many standard computers. In our array operation, calculation error in phase distribution on a hologram occurs more than the strict Fresnel diffraction. However, it was confirmed by experiments that the influence of an error can be controlled and ignored. In this paper, our proposed method and some experimental results are shown.     

High-speed driving of multi-color LED panel for subjective super-resolution display

Optical Review - We have developed a new high-speed driving circuit of a multi-color LED panel by the use of FPGA for subjective super-resolution display. In the subjective super-resolution...     

Frequency measurement of pure rotational transitions in the v2 = 1 state of H2O

Frequencies of pure rotational transitions in the v₂ = 1 vibrationally excited state of H₂¹⁶O were measured with a tunable far-infrared spectrometer in the frequency range of 0.5-5 THz. Molecular parameters of Watson’s A-reduced Hamiltonian have been obtained to reproduce the observed frequencies.     

First underground results with NEWAGE-0.3a direction-sensitive dark matter detector

A direction-sensitive dark matter search experiment at Kamioka underground laboratory with the NEWAGE-0.3a detector was performed. The NEWAGE-0.3a detector is a gaseous micro-time-projection chamber filled with CF₄ gas at 152 Torr. The fiducial volume and target mass are 20×25×31 cm³$20\times 25\times 31{\text{cm}}^3$ and 0.0115 kg, respectively. With an exposure of 0.524 kg days, improved spin-dependent weakly interacting massive particle (WIMP)-proton cross section limits by a direction-sensitive method were achieved including a new record of 5400 pb for 150 GeV/c²$/c^2$ WIMPs. We studied the remaining background and found that ambient γ-rays contributed about one-fifth of the remaining background and radioactive contaminants inside the gas chamber contributed the rest.     

Symmetry limit theory for cantilever beam-columns subjected to cyclic reversed bending

The behavior of a linear strain-hardening cantilever beam-column subjected to completely reversed plastic bending of a new idealized program under constant axial compression consists of three stages: a sequence of symmetric steady states, a subsequent sequence of asymmetric steady states and a divergent behavior involving unbounded growth of an anti-symmetric deflection mode. A new concept “symmetry limit” is introduced here as the smallest critical value of the tip-deflection amplitude at which transition from a symmetric steady state to an asymmetric steady state can occur in the response of a beam-column. A new theory is presented for predicting the symmetry limits. Although this transition phenomenon is phenomenologically and conceptually different from the branching phenomenon on an equilibrium path, it is shown that a symmetry limit may theoretically be regarded as a branching point on a “steady-state path” defined anew. The symmetry limit theory and the fundamental hypotheses are verified through numerical analysis of hysteretic responses of discretized beam-column models.     

Automated micro stopped-flow/continuous-flow apparatus for serial measurement of enzyme reactions and its application as a real-time analyser for column chromatography

By functional combination of two modes of stopped-flow (SF) and flow-injection analysis (FIA), an automated micro apparatus is constructed for serial measurement of enzyme reactions. The complete operation of the apparatus, including kinetic data aquisition, is controlled by a personal computer. The apparatus has three specific features: (a) the volume required per measurement of a time course in an enzyme reaction is as small as 30 μl for each of enzyme and assay solution; (b) the time course can be traced by sampling ten observation points in a maximum of 1 s; and (c) the serial measurement of such a time course can be performed with automated cyclic operation (10 s per operating cycle as the lower limit). In addition to enzymatic activity, simultaneous monitoring of protein concentration, pH and conductivity in the enzyme solution can be sequentially conducted by the automated micro SF/FIA apparatus equipped with appropriate detectors. The successful application of such a four-channel apparatus to ion-exchange and affinity column chromatography of calf bone alkaline phosphatase proves that it is useful as a practical real-time analyser for enzyme activity together with other parameters to be monitored in liquid chromatography.