Packing triangles in low degree graphs and indifference graphs

We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation ratio known so far for these problems has ratio 3/2+?, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver [On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM J. Discrete Math. 2(1) (1989) 68-72]. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs.     

Liquid crystal formation in suspensions of hard rodlike colloidal particles: direct observation of particle arrangement and self-ordering behavior

We successfully prepared monodisperse, hard rodlike colloidal particles with a wide range of length-to-width ratios (L/W). In their suspensions liquid crystals, or nematic (N) and smectic (Sm) phases, spontaneously appeared. The size of the particles made it possible to directly observe their arrangement and dynamics with an optical microscope. The phase behavior observed exhibited an I (isotropic)-Sm transition for L/W=3.5-8.0 and I-N-Sm transitions for L/W=10-35. In pre-Sm transition regions, lateral clustering of the particles and subsequent layering of the clusters were observed exactly.     

Photonic molecule lasing

Lasing at resonantly coupled whispering-gallery mode frequencies is observed in photonic molecules consisting of bispheres of 4.2 and 5.1 microm in diameter placed in a silicon V-groove. We examine spatial profiles of photonic molecule modes by use of frequency-resolved imaging and reveal bonding and antibonding mode features. From the lasing threshold characteristics, we quantitatively measure the quality factor and the spontaneous-emission coupling ratio of the photonic molecule modes and confirm that strong coherent coupling leads to photonic molecule modes.     

Exact dynamical structure factor of the degenerate haldane-shastry model

The dynamical structure factor S(q,omega) of the K-component ( K = 2, 3, 4) spin chain with a 1/r(2) interaction is derived exactly at zero temperature for the arbitrary size of the system. The result is interpreted in terms of a free quasiparticle picture which is a generalization of the spinon picture in the SU(2) case. The excited states consist of K quasiparticles each of which is characterized by a set of K-1 quantum numbers. Divergent singularities of S(q,omega) at the spectral edges are derived analytically. The analytic result is checked numerically for finite systems.     

Microwave spectrum of cis-thiopropionic acid

The microwave spectrum of cis-thiopropionic acid in the ground vibrational state has been observed in the frequency range between 10 and 35 GHz. The rotational and centrifugal distortion constants, and the dipole moments have been determined. The conformation of this molecule is discussed on the basis of the observed results.     

Microscopic evidence for a new type of ordering of spin components in a random mixture with competing magnetic anisotropies

The Mössbauer spectroscopy was applied on a random mixture of two kinds of magnetic ions with competing anisotropies, Fe_1?xCo_xCl₂·2H₂O. The Mössbauer spectra observed in the Co(Fe)-rich antiferromagnetic (AF) phase near the tetracritical point show that, although the m₂(m₁) spin component parallel to the easy axis of pure FeCl₂·2H₂O(CoCl₂·2H₂O) has no long-range order in this phase (from the neutron diffraction experiment), the m₂(m₁) spin component contributes to the magnetic hyperfine field at ⁵⁷Fe nuclei as well as the m₁(m₂) spin component (which has a long-range order). This fact indicates that the m₂(m₁) spin components exists in the Co(Fe)-rich AF phase near the tetra-critical point at least in a time scale of ～ 10^?8s. This result predicts that the antiferromagnetic ordering in the Co(Fe)-rich AF phase is a new type one. The new phase observed in the intermediate concentration region is demonstrated as the “mixed ordering” phase.     

Growth kinetics and morphology of self-assembled monolayers formed by contact printing 7-octenyltrichlorosilane and octadecyltrichlorosilane on Si(100) wafers

The growth kinetics and morphologies of self-assembled monolayers deposited by contact printing 7-octenyltrichlorosilane (OCT) and octadecyltrichlorosilane (OTS) on Si(100) were studied by ellipsometry and atomic force microscopy. We found that, for both OCT and OTS, full monolayers could be obtained at room temperature after printing times of 120-180 s; the printing-based monolayer assembly processes follow apparent Langmuir adsorption kinetics, with the measured film growth rates increasing both with the ambient humidity and with concentration of the ink used to load the stamp. At a dew point of 10 degrees C and an ink concentration (in toluene) of 50 mM, the observed film growth rate constant is 0.05 s(-)(1). When the printing was carried out at a lower ambient humidity (dew points of 1-3 degrees C), the measured rates of assembly were approximately a factor of 2 slower. Increasing the deposition temperature from 25 to 45 degrees C under these conditions increased the film growth rate only slightly. The morphology of the films depends on the identity of the ink. Uniform, high-coverage films could be obtained readily from the eight-carbon chain length adsorbate OCT, provided that the stamp was not overloaded with the ink; for high concentrations outside of the optimal range, the surface presented significant numbers of adsorbed particles ascribed, in part, to siloxane polymers formed by hydrolysis of the ink on the stamp before printing. In marked contrast, for the 18-carbon adsorbate OTS, the printed films always consisted of a mixture of a uniform monolayer plus adsorbed polysiloxane particles. The different film morphologies seen for OCT and OTS are proposed to result from the different transfer efficiencies of the organotrichlorosilane relative to polysiloxane hydrolysis products formed during the printing process. These transfer efficiencies exhibit sensitivities related to the permeation of the poly(dimethylsiloxane) (PDMS) stamp by the silane reagents. Short-chain inks such as OCT evidently permeate the PDMS stamp more deeply than longer-chain inks such as OTS. This difference, and the different diffusion rates of ink vs oligomeric silane hydrolysis products, determines the film morphology obtained by contact printing. The mass transfer dynamics of the process thus yield surface layers derived from varying quantities of siloxane oligomers, which subsequently transfer to the substrate along with unhydrolyzed silane adsorbate during the printing step. The structural evolution of the contact-printed films so obtained is strikingly different from that of SAMs prepared by immersion.