Modern Physics Letters B

Steady state solutions of a heat balance equation modeling a thermal explosion in a cylindrical vessel are obtained. The heat balance equation reduces to a Lane–Emden equation of the second-kind when steady state solutions are investigated. Analytical solutions to this Lane–Emden equation of the second-kind are obtained by implementation of the Lie group method. The classical Lie group method is used to obtain the well-known solution of Frank-Kamenetskii for the temperature distribution in a cylindrical vessel. Using an extension of the classical Lie group method a non-local symmetry is obtained and a new solution describing the temperature distribution after blow-up is obtained.

Q-switched fiber lasers are very attractive sources in many applications such as military affairs, surgical operation, laser machining, laser marking, nonlinear frequency conversion, range finding, remote sensing and optical time domain reflectometer. To improve the peak power of Q-switched fiber laser is what we pursue, and to know the factors that influence the peak power is what we should make clear first. In this paper, certain essential factors that influence the peak power are presented, with their theoretical basis clarified, which may be helpful to the design of the kindred Q-switched fiber lasers.

We present the bosonic operator Hamiltonian models of two Josephson junctions which are connected in series and in parallel, respectively. By introducing the entangled state representations (|η〉 representation and Cooper pairs representation) and projecting the operator Hamiltonian onto the |η〉 representation we obtain the correct Josephson current and phase equations consistent with the classical Hamiltonian cases.

Self-assembled InAs/AlAs quantum dots embedded in a resonant tunneling diode device structure are grown by molecular beam epitaxy. Through the selective etching in a C₆H₈O₇ · H₂O-K₃C₆H₅O₇ · H₂O-H₂O₂ buffer solution, 310 nm GaAs capping layers are removed and the InAs/AlAs quantum dots are observed by field-emission scanning electron microscopy. It is shown that as-fabricated quantum dots have a diameter of several tens of nanometers and a density of 10¹⁰ cm^-2 order. The images taken by this means are comparable or slightly better than those of transmission electron microscopy. The undercut of the InAs/AlAs layer near the edges of mesas is detected and that verifies the reliability of the quantum dot images. The inhomogeneous oxidation of the upper AlAs barrier in H₂O₂ is also observed. By comparing the morphologies of the mesa edge adjacent regions and the rest areas of the sample, it is concluded that the physicochemical reaction introduced in this letter is diffusion limited.

By exploiting the fermionic qubit parity measurement, we present a scheme to realize quantum non-demolition (QND) measurement of Bell states and generate n-party GHZ state in quantum dot. Compared with the original protocol, the required electron transfer before and after parity measurement can be nonadiabatic, which may speed up the operation speed and make the omitting of spin-orbit interaction more reasonable. This may help us to construct CNOT gate without highly precise control of coupling as the way of D. Gottesman and I. L. Chuang.

Bulk polycrystalline samples of nano-Mo doped MgB₂ were synthesized by Fe tube encapsulation at ambient pressure under argon annealing (850°C). Mo substitution takes place successfully at the Mg site in Mg_1-xMo_xB₂ only till x=0.2. For higher (x>0.2) Mo content the same did not enter the MgB₂ lattice but rather forms an isomorphic lattice in the host with decreased c but an increased a-parameter. The ρ(T) measurements showed superconducting transition temperature (T_c) of around 36 K for all the samples till x=0.3 and slightly decreased values of 35 and 34 K for x=0.4 and 0.5 samples, respectively. Resistivity under magnetic field [R(T)H] experiments showed distinct single peaks in dρ/dT for all applied fields up to 8 Tesla. The estimated upper critical field H_c2 is 8 Tesla for pristine and x=0.2 samples at 15.6 and 19 K, respectively. Thus H_c2 increases up to x=0.20 samples and decreases afterwards. Magnetic susceptibility measurements exhibited sharp transition to superconducting state with a sizeable diamagnetic signal at 38 K (T_c) in zero field-cooled measurements. Commendable current density (J_c) of up to 10⁵ A/cm² in 1–2 T (Tesla) fields at temperatures (T) of up to 10 K is seen from magnetization measurements invoking the Bean's critical state model for pristine samples. For higher fields above 2.5 Tesla the J_c(H) characteristics of x=0.1 and 0.2 samples were found to be slightly superior to that for pristine samples with enhanced H_irr (irreversibility field).

We have applied the Rigid Ion Model (RIM) to study the cohesive and thermal properties of binary intermetallic BeB₂ and TiB₂. The paper reports the calculated results on cohesive energy (ϕ), compressibility (β), molecular force constant (f), Restrahalen frequency (ν₀), Debye temperature (Θ_D) and Gruneisen parameter (γ) for the temperature range 50 K ≤ T ≤ 300 K and the effect of van der Waal interaction on these properties are also shown. Our results on Debye temperature are closer to the experimental data. In addition, we have computed the specific heats for BeB₂ and TiB₂ and compared them with the available experimental data.