Acoustoelastic analysis of reflected waves in nearly incompressible, hyper-elastic materials: forward and inverse problems

Many materials (e.g., rubber or biologic tissues) are "nearly" incompressible and often assumed to be incompressible in their constitutive equations. This assumption hinders realistic analyses of wave motion including acoustoelasticity. In this study, this constraint is relaxed and the reflected waves from nearly incompressible, hyper-elastic materials are examined. Specifically, reflection coefficients are considered from the interface of water and uni-axially prestretched rubber. Both forward and inverse problems are experimentally and analytically studied with the incident wave perpendicular to the interface. In the forward problem, the wave reflection coefficient at the interface is evaluated with strain energy functions for nearly incompressible materials in order to compute applied strain. For the general inverse problem, mathematical relations are derived that identify both uni-axial strains and normalized material constants from reflected wave data. The validity of this method of analysis is demonstrated via an experiment with stretched rubber. Results demonstrate that applied strains and normalized material coefficients can be simultaneously determined from the reflected wave data alone if they are collected at several different (but unknown) levels of strain. This study therefore indicates that acoustoelasticity, with an appropriate constitutive formulation, can determine strain and material properties in hyper-elastic, nearly incompressible materials.     

Phase-locked laser system for a metastable states qubit in 40 Ca+

We describe the development of a phase-locked laser system tailored to an ion-trap-based quantum information processor with (40)Ca(+). Laser outputs from an extended cavity diode laser and a Ti:sapphire laser with output laser wavelengths of approximately 850 and 854 nm, respectively, were phase locked and used to excite a Raman transition between the D(3/2) and D(5/2) metastable states qubit. Development and the performance of the laser system are described. We also compare the characteristics and the benefits of the developed qubit coupling with those in the conventional approaches.     

Branching ratio and L2 + L3 intensities of 3d-transition metals in phthalocyanines and the amine complexes

L(2,3) inner-shell excitation spectra were obtained by electron energy-loss spectroscopy (EELS) for the divalent first transition series metals in phthalocyanine complexes (MPc) such as titanium oxide phthalocyanine (TiOPc), fluoro-chromium phthalocyanine (CrFPc), manganese phthalocyanine (MnPc), iron phthalocyanine (FePc), cobalt phthalocyanine (CoPc), nickel phthalocyanine (NiPc) and copper phthalocyanine (CuPc). It was found that the value of normalized total intensity of I(L2 + L3) was nearly proportional to the formal electron vacancies of each 3d-state, and the values of the branching ratio, I(L3)/I((L2 + L3), represented a high-spin-state rather than low-spin-state for MnPc, FePc and NiPc. EELS was also applied to charge-transfer complexes of FePc with an amine such as pyridine or gamma-picoline. It was concluded that their I(L2 + L3) intensity of Fe showed the decrease in vacancies of 3d-states on the formation of the charge-transfer complex with these amines, which suggests some electron transfer from the amine to Fe in phthalocyanine. The EELS study provides beneficial information for investigating the electronic states of the specific metal sites in organic materials.     

Anomalous nuclear spin relaxation in liquid 3He4He mixtures

The longitudinal relaxation time, T₁, was measured in liquid ³He⁴He mixtures with molar concentrations of ³He of 0.12, 0.20 and 0.45 under saturated vapor pressure. λ-anomaly was clearly observed in the temperature dependence of T₁.     

Constructing finitely presented monoids which have no finite complete presentation

Squier (1987) showed that if a monoid is defined by a finite complete rewriting system, then it satisfies the homological finiteness condition FP₃, and using this fact he gave monoids (groups) which have solvable word problems but cannot be presented by finite complete systems. In the present paper we show that a monoid cannot have a finite complete presentation if it contains certain special elements. This observation enables us to construct monoids without finite complete presentation in a direct and elementary way. We give a finitely presented monoid which has (1) a word problem solvable in linear time and (2) linear growth but (3) no finite complete presentation. We also give a finitely presented monoid which has (1) a word problem solvable in linear time, (2) finite derivation type in the sense of Squier and (3) the property FP_∞, but (4) no finite complete presentation.     

Pushing exercise program to correct glottal incompetence

A voice therapy program using pushing exercises to correct glottal incompetence is described. The program utilizes various types of instrumentation to determine whether or not a given patient is likely to benefit from the treatment. The program also provides feedback of target voices. Three cases with incomplete glottal closure and subsequent vocal dysphonia characterized by an asthenic breathy quality are used to illustrate the program. Details of the program, termination criteria, and problems and precautions learned from treating 29 patients over a 3-year period are presented.     

Study of latent and etched tracks by a charged particle transmission technique

A recently suggested technique for non-destructive investigation of inhomogeneities in thin objects, which is based on the measurement of the energy spectra of charged particles transmitted through the object, is used for the study of thermal annealing of 10–20 μm thick polyethylene terephtalate, polypropylene and polycarbonate foils irradiated with 1–10 MeV/amu heavy ions. At elevated temperature a foil linear contraction is observed on pristine and irradiated material. Also the foil roughness increases with increasing temperature. On the same foils with etched pores 0.5–1.0 μm in diameter, the thermal annealing results in gradual closing of the pores up to about 30% of their initial diameter at the temperatures of 150–175°C. At higher temperatures the pore diameter increases and achieves its initial value.     

Disk Noise Measurement System for Optical Disks

We developed a system to measure disk noise as a function of both radial and angular position. In order to obtain an accurate disk noise measurement, crosstalk and intersymbol interference were avoided by recording regularly repeating pit patterns and the influence of electronic and laser noise was removed by averaging techniques. We found the system’s mapping ability and its high sensitivity to be very useful in investigating disk noise phenomena in the mastering process. We used the system to assess the accuracy and reproducibility of the photopolymerization replication and Al vapor deposition processes. Also, we investigated the choice of photoresist and found that photoresists with the combination of the narrowest molecular weight distribution and the highest photo-active compound content resulted in the lowest disk noise levels. Our system can, in principle, be adapted to evaluate magneto-optical and phase change disks.     

Singular values of some modular functions

For an integer N greater than 5 and a triple \({\mathfrak{a}}=[a_{1},a_{2},a_{3}]\) of integers with the properties 0<a _i ≤N/2 and a _i ≠a _j for i≠j, we consider a modular function \(W_{\mathfrak{a}}(\tau)=\frac{\wp (a_{1}/N;L_{\tau})-\wp (a_{3}/N;L_{\tau})}{\wp (a_{2}/N;L_{\tau})-\wp(a_{3}/N;L_{\tau})}\) for the modular group Γ ₁(N), where ?(z;L _τ ) is the Weierstrass ?-function relative to the lattice L _τ generated by 1 and a complex number τ with positive imaginary part. For a pair of such triples \({\mathfrak{A}}=[{\mathfrak{a}},{\mathfrak{b}}]\) and a pair of non-negative integers F=[m,n], we define a modular function \(T_{{\mathfrak{A}},F}\) for the group Γ ₀(N) as the trace of the product \(W_{\mathfrak{a}}^{m}W_{\mathfrak{b}}^{n}\) to the modular function field of Γ ₀(N). In this article, we study the integrality of singular values of the functions \(W_{\mathfrak{a}}\) and \(T_{{\mathfrak{A}},F}\) by using their modular equations. We prove that the functions \(T_{{\mathfrak{A}},F}\) for suitably chosen \({\mathfrak{A}}\) and F generate the modular function field of Γ ₀(N), and from Shimura reciprocity and Gee–Stevenhagen method we obtain that singular values \(T_{{\mathfrak{A}},F}(\tau)\) for suitably chosen \({\mathfrak{A}}\) and F generate ring class fields. Further, we study the class polynomial of \(T_{{\mathfrak{A}},F}\) for Schertz N-system.