Efficient prediction of the quality factors of micromechanical resonators

A high quality factor (Q-factor) is one of the major requirements of high-performance resonators. An understanding of the dissipation mechanism is crucial for maximizing the quality factor by reducing the energy loss. Thermoelastic damping has been well-known as the important intrinsic dissipation that affects the quality factor of micro-resonators. In this study, a finite element formulation based on the weak form of fully coupled thermoelastic problems is suggested. The coupled thermoelastic equation usually leads to a large-size complex eigenvalue problem, which is very massive and time-consuming to solve. Therefore, we also applied the model order reduction (MOR) scheme to this coupled multiphysical problem in order to achieve computational efficiency. The present approach is validated by comparing the numerical results and analytical solutions.     

First measurement of inclusive B→Xsη decays

We report a first measurement of inclusive B→Xsη decays, where Xs is a charmless state with unit strangeness. The measurement is based on a pseudoinclusive reconstruction technique and uses a sample of 657×10(6)BB pairs accumulated with the Belle detector at the KEKB e+e- collider. For MXs < 2.6 GeV/c2, we measure a branching fraction of [26.1±3.0(stat)-2.1+1.9(syst)-7.1+4.0(model)]×10(-5) and a direct CP asymmetry of ACP=-0.13±0.04-0.03+0.02. Over half of the signal occurs in the range MXs > 1.8 GeV/c2.     

Observation of B(s)(0) → D(s)(*)+ D(s)(*)- using e+ e- collisions and a determination of the B(s)-B(s) width difference ΔΓ(s)

We have made the first observation of B(s)(0)→D(s)(*)+ D(s)(*)- decays using 23.6 fb(-1) of data recorded by the Belle experiment running on the Υ(5S) resonance. The branching fractions are measured to be B(B(s)(0)→D(s)+ D(s)-)=(1.03(-0.32-0.25)(+0.39+0.26))%, B(B(s)(0)→D(s)(*±) D(s)(?))=(2.75(-0.71)(+0.83)±0.69)%, and B(B(s)(0)→D(s)*+ D(s)*-)=(3.08(-1.04-0.86)(+1.22+0.85))%; the sum is B[B(s)(0)→D(s)(*)+ D(s)(*)-]=(6.85(-1.30-1.80)(+1.53+1.79))%. Assuming B(s)(0)→D(s)(*)+ D(s)(*)- saturates decays to CP-even final states, the branching fraction determines the ratio ΔΓ(s)/cosφ, where ΔΓ(s) is the difference in widths between the two B(s)-B(s) mass eigenstates, and φ is a CP-violating weak phase. Taking CP violation to be negligibly small, we obtain ΔΓ(s)/Γ(s)=0.147(-0.030)(+0.036)(stat)(-0.041)(+0.042)(syst), where Γ(s) is the mean decay width.     

Pressure-tunable guided-mode resonance sensor for single-wavelength characterization

A method of tuning a one-dimensional guided-mode resonance grating through the use of an air-pressure-responsive membrane is demonstrated here using finite-element method simulation. The device consists of a titanium dioxide (TiO(2)) grating structure embedded in a flexible polydimethylsiloxane membrane. This grating has a resonant response to TM-polarized light at a wavelength dependent upon the refractive index of the surrounding medium. By varying the pressure by 5500 Pa, lateral strain may be applied to the grating; this allows resonances to be produced for medium refractive indices ranging from 1.33 to 1.50 for a fixed-wavelength 850 nm light source.     

Classification of solutions of elliptic equations arising from a gravitational O(3) gauge field model

In this paper, we study an elliptic equation arising from the self-dual Maxwell gauged $O(3)$ sigma model coupled with gravity. When the parameter τ equals 1 and there is only one singular source, we consider radially symmetric solutions. There appear three important constants: a positive parameter a representing a scaled gravitational constant, a nonnegative integer $N_1$ representing the total string number, and a nonnegative integer $N_2$ representing the total anti-string number. The values of the products $a{N}_1,a{N}_2\in [0,\infty )$ play a crucial role in classifying radial solutions. By using the decay rates of solutions at infinity, we provide a complete classification of solutions for all possible values of $a{N}_1$ and $a{N}_2$. This improves previously known results.     

Ground States and Phase Transition of the λ Model on the Cayley Tree

We consider the λ model, a generalization of the Potts model, with spin values {1, 2, 3} on the order-two Cayley tree. We describe the model ground states and prove that translation-invariant Gibb measures exist, which means that a phase transition exists. We establish that two-periodic Gibbs measures exist.     

Inequalities related to partial trace and block Hadamard product

In this paper, we present inequalities related to partial trace and block Hadamard product for positive semidefinite matrices. Some interesting results involving block matrices will be also derived.     

Congruences involving the $$U_{\ell }$$Uℓ operator for weakly holomorphic modular forms

The Ramanujan Journal - Let $$\lambda $$ be an integer, and $$f(z)=\sum _{n\gg -\infty } a(n)q^n$$ be a weakly holomorphic modular form of weight$$\lambda +\frac{1}{2}$$ on $$\Gamma _0(4)$$ with...     

Uniqueness and symmetry of ground states for higher-order equations

We establish uniqueness and radial symmetry of ground states for higher-order nonlinear Schrödinger and Hartree equations whose higher-order differentials have small coefficients. As an application, we obtain error estimates for higher-order approximations to the pseudo-relativistic ground state. Our proof adapts the strategy of Lenzmann (Anal PDE 2:1–27, 2009) using local uniqueness near the limit of ground states in a variational problem. However, in order to bypass difficulties from lack of symmetrization tools for higher-order differential operators, we employ the contraction mapping argument in our earlier work (Choi et al. 2017. arXiv:1705.09068) to construct radially symmetric real-valued solutions, as well as improving local uniqueness near the limit.