A Construction of Blow up Solutions for Co-rotational Wave Maps

The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from \mathbbR²⁺¹ ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d ρ ² + g(ρ)² dθ², g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u _tt  + u _rr  + r ⁻¹ u _r  = r ⁻² g(u)g′(u), λ(t) = t ^−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0.     

Variation in the fluorescent background in Raman spectra of distilled water purified by different methods

The contribution of impurity fluorescence was determined in the water Raman spectra excited by the second harmonic (λ = 532 nm) of a pulsed Nd:YAG laser. Water samples prepared by different techniques (tap water (undistilled), distilled water, Milli-Q water, water for injections, and water subjected to cavitation treatment) were investigated. The Raman (bands at ν ₂ ∼ 1550 cm⁻¹ and ν ₃ ∼ 3400 cm⁻¹) and fluorescence (Stokes shift 2500 cm⁻¹) signals were separated spectrally and according to the differences in the emission kinetics. It was established that all investigated samples, including distilled and specially purified water for injections, exhibit afterglow. The highest sensitivity to the presence of impurities was revealed near ∼ 2500 cm⁻¹. The least contribution to the fluorescence signal was found in the water for injections.     

Thermal conductivity of crystalline fullerite C60 in the simple cubic phase

The behavior of the thermal conductivity k(T) of bulk faceted fullerite C₆₀ crystals is investigated at temperatures T=8–220 K. The samples are prepared by the gas-transport method from pure C₆₀, containing less than 0.01% impurities. It is found that as the temperature decreases, the thermal conductivity of the crystal increases, reaches a maximum at T=15–20 K, and drops by a factor of ∼2, proportional to the change in the specific heat, on cooling to 8 K. The effective phonon mean free path λ _p, estimated from the thermal conductivity and known from the published values of the specific heat of fullerite, is comparable to the lattice constant of the crystal λ _p∼d=1.4 nm at temperatures T>200 K and reaches values λ_p∼50d at T<15 K, i.e., the maximum phonon ranges are limited by scattering on defects in the volume of the sample in the simple cubic phase. In the range T=25−75 K the observed temperature dependence k(T) can be described by the expression k(T)∼exp(Θ/bT), characteristic for the behavior of the thermal conductivity of perfect nonconducting crystals at temperatures below the Debye temperature Θ (Θ=80 K in fullerite), where umklapp phonon-phonon scattering processes predominate in the volume of the sample. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 651–656 (25 April 1997)     

Coupling of tilting Gaussian beam with hybrid mode in the corrugated waveguide

The mode-conversion loss in the matching between the gaussian beam emanated from the gyrotron and the hybrid mode in the circular corrugated waveguide with the diameter of 2a is discussed. By numerical calculation, it is found that the loss considerably increases and optimum waist sizew ₀ changes when TEM₀₀ mode with the wavelength λ is injected with offset or tilt. By fitting numerical data to the polynomial function, it becomes evident that the scaling formulas of the losses for the off-axis shiftr _d and for the tilt angle θ are derived to be 2.3(r _d /a)² – 2.2(r _d /a)⁴ and 3.9(aα/λ)² – 5.6(aθ/λ)⁴ for fixedw ₀/a=0.643, respectively. To keep the mode-conversion loss ≤1% for the frequency of 168 GHz and 2a=88.9 mm, tilting angle and offset should be less than 0.1 degrees and 2.9 mm, respectively.     

Thermal conductivity of the diamond-paraffin wax composite

The thermal conductivity of diamond-paraffin wax composites prepared by infiltration of a hydrocarbon binder with the thermal conductivity λ _m = 0.2 W m⁻¹ K⁻¹ into a dense bed of diamond particles (λ _f ∼ 1500 W m⁻¹ K⁻¹) with sizes of 400 and 180 μm has been investigated. The calculations using universally accepted models considering isolated inclusions in a matrix have demonstrated that the best agreement with the measured values of the thermal conductivity of the composite λ = 10–12 W m⁻¹ K⁻¹ is achieved with the use of the differential effective medium model, the Maxwell mean field scheme gives a very underestimated calculated value of λ, and the effective medium theory leads to a very overestimated value. An agreement between the calculation and the experiment can be provided by constructing thermal conductivity functions. The calculation of the thermal conductivity at the percolation threshold has shown that the experimental thermal conductivity of the composites is higher than this critical value. It has been established that, for the composites with closely packed diamond particles (the volume fraction is ∼0.63 for a monodisperse binder), the use of the isolated particle model (Hasselman-Johnson and differential effective medium models) for calculating the thermal conductivity is not quite correct, because the model does not take into account the percolation component of the thermal conductivity. In particular, this holds true for the calculation of the heat conductance of diamond-matrix interfaces in diamond-metal composites with a high thermal conductivity.     

The exponent λ (x, Q2) of the proton structure functionF2(x, Q2) at lowx

The exponent λ of the structure function F₂ ∼x ^−λ is calculated using the solution of the DGLAP equation for gluon at lowx reported recently by the present authors. The quantity λ is calculated both as a function ofx at fixedQ ² and as a function ofQ ² at fixedx and compared with the most recent data from H1     

Re-evaluation of the LHC potential for the measurement of <Emphasis Type="Italic">m</Emphasis><Subscript><Emphasis Type="Italic">W</Emphasis></Subscript>

We present a study of the LHC sensitivity to the W boson mass based on simulation studies. We find that both experimental and phenomenological sources of systematic uncertainties can be strongly constrained with Z measurements: the lineshape, dσ _Z /dm, is robustly predicted, and its analysis provides an accurate measurement of the detector resolution and absolute scale, while the differential cross-section analysis, d² σ _Z /dydp _T , absorbs the strong interaction uncertainties. A sensitivity δ m _W ∼7 MeV for each decay channel (W→e ν, W→μ ν), and for an integrated luminosity of 10 fb⁻¹, appears as a reasonable goal.     

Quasi-long-range order in the random anisotropy Heisenberg model

The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r ₁)m(r ₂)〉∼|r ₁−r ₂|^{− 0.62ε}. The magnetic susceptibility diverges at low fields as χ∼H ^−1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Experimental study of optical gas-dynamic processes of polymeric material ablation by ultrashort laser pulses

Optical gas-dynamic processes occurring in polymeric targets ((CH₂O) _n , (C₂F₄) _n ) exposed to ultrashort laser pulses (τ _0.5 ∼ 45 − 70 fs; λ _I,II,III = 266, 400, 800 nm; and E/S ∼ 0.1 − 40 J/cm² at r ₀ ∼ 20 μm) were studied under normal conditions and in vacuum (p ∼ 10⁻² Pa). The dynamics of the mass flow from the target surface (m′ ∼ 10⁻⁵ − 10⁻⁴ g/J) was studied and the spectral-energy thresholds of laser ablation, the electron density distribution (n _e ∼ 10¹⁴ − 10¹⁸ cm⁻³), the mass-averaged velocity of the material flow from the target surface (∼ 10³ m/s), and the chemical composition and average temperature in the near-surface plasma formation (T ∼ 5000 K) were determined using interference microscopy, emission spectroscopy, and shadowgraphy.     

Effect of plasmon-phonon excitations on the coefficient of reflection from the surface of hexagonal silicon carbide

The coefficient R(ν) of reflection from the surface of 6H-SiC single crystals is studied in the case in which the long-wavelength optical vibrations of the lattice are coupled with the electron plasma. It is shown for the first time that the anisotropy of the properties of electrons and phonons in 6H-SiC gives rise to special features in the spectrum of the coupled vibrations and the transparency regions. It is found, in particular, that if the axis of the crystal lies in the polarization plane of the incident radiation (0<θ<90°), for 30 cm⁻¹⩽ν _p⊥<320 cm⁻¹ the spectrum of R(ν) acquires three regions of transparency and opacity, and for ν _p⊥⩾320 cm⁻¹ four such regions, which are absent in an isotropic medium. The width of these regions is found to depend on the electron concentration in the conduction band and on the angle θ. Zh. éksp. Teor. Fiz. 116, 646–654 (August 1999)     

Hypervirial perturbation theory for eigenenergies for two types of atomic potentials

Eigenenergies are calculated for the potentialsV ₁(r)=−(a/r)[1+(1+br)e^−2br ] andV ₂(r)=−(v/r)[1 −λr(1−Z ⁻¹)(1+λr)⁻¹], using renormalized series technique. Accurate results produced here for various eigenstates agree with those available in the literature.     

Experimental determination of the difference of the beta-decay constants for atomic and molecular tritium

The results of an experiment measuring the difference Δλ=λ_a−λ _m of the beta-decay constants of atomic and molecular tritium are reported. The difference Δλ is determined by comparing the rates of growth of the relative content of radiogenic helium-3 in samples containing atomic and molecular tritium. The result Δλ=(4.6±0.8)×10⁻¹²s⁻¹ corresponds to a relative change of the decay constant by ∼0.26%. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 167–170 (10 August 1998)     

Monte-Carlo optimization of correlated helium wave function

A new type of correlated wave function for the normal helium is proposed in the form:ψ(r₁, r₂)=Σc _mφ_m withφ _m=exp]−α(r ₁+r ₂)]/(br ₁₂+a) ^m wherea, b, α are non-linear variational parameters. Optimizing these parameters by the Monte-Carlo technique, an energy eigen-value of −2.903645(a.u.) is obtained withonly three terms in the basis expansion alongwith satisfactory cusp condition, compared to the essentially exact non-relativistic value of −2.903724 as given by Freundet al (Phys. Rev. A29, 980 (1984)).     

Conservation laws for classical and relativistic collisions. II

On the basis of elementary symmetry arguments it is shown that (1) if in classical mechanics there exists a quantity λ+Σ_iμ_iυ_i+1/2νυ ² that is conserved, where λ,μ _i, andν are particle parameters, then theμ _i andν are all proportional to a single parameterμ and the quantityAμ+Σ_iB_iμυ_i+C(λ+ 1/2Dμυ ²), whereD ≡ν/μ, is conserved for all values ofA, B _i, andC; (2) if in relativistic mechanics there exists a quantity λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc[1−(υ ²/c ²)]^−1/2 that is conserved, then theμ _i andν are all proportional to a single parameterμ and the quantityAλ+Σ_iB_iμν_i[1−(υ ²/c ²)]^−1/2+Cμc [1−(υ ²/c ²)]^−1/2 is conserved for all values ofA, B _i, andC.     

Bound states and critical behavior of the Yukawa potential

We investigate the bound states of the Yukawa potential V (r)=−λexp(−αr)/r, using different algorithms: solving the Schr?dinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = α_C, above which no bound state exists. We study the relation between α_C and λ for various angular momentum quantum number l, and find in atomic units, α_C(l) = λ[A ₁ exp(−l/B ₁) + A ₂ exp(−l/B ₂)], with A ₁ = 1.020(18), B ₁ = 0.443(14), A ₂ = 0.170(17), and B ₂ = 2.490(180).     

Determination of absorption cross sections for oxygen molecules in the Schumann-Runge band region at high temperatures

We have measured the absorption cross sections of oxygen molecules in oxygen and in an oxygen-argon mixture heated by a shock wave, in the wavelength range 190–250 nm at temperatures of 1500–7000 K, for thermal equilibrium conditions behind the shock wave front. Analysis of the absorption cross sections obtained allowed us to select a data set that adequately describes the absorption characteristics of the electronic transition X³Σ _g ⁻ → B³Σ _u ⁻ for the oxygen molecule. In order to approximate the temperature dependence of these cross sections at a temperature of 1500–4500 K, we chose the function σ(λ, T) = σ₀(λ)(1 − exp (−θ/T)) exp (− n*θ/T) where θ₀ = 1.4·10⁻¹⁷, 1.4·10⁻¹⁷, 1.2·10^{− 17}, and 1.3·10⁻¹⁷ cm², n* = 3.1, 4.1, 5.6, and 7.47 for wavelengths 190, 210, 230, and 250 nm, respectively; θ = 2240 K is the characteristic temperature of the O₂ molecules. The approximation error was 19–25% and did not exceed the experimental error. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 1, pp. 13–17, January–February, 2006.     

Conservation laws for classical and relativistic collisions. I

On the basis of simple kinematic arguments it is shown that any quantity, depending only on the nature and velocity of a particle, that is conserved in a collision must, in classical mechanics, be of the form λ+Σ_iμ_iυ_i+1/2vυ ² or in relativistic mechanics of the form λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc [1−(υ ²/c ²)]^−1/2 where λ,μ _i, andν are particle parameters.     

Sub-THz radiation room temperature sensitivity of long-channel silicon field effect transistors

Room temperature operating n-MOSFETs (n-type metal-oxide silicon field effect transistors) used for registration of sub-THz (sub-terahertz) radiation in the frequency range ν = 53−145 GHz are considered. n-MOSFETs were manufactured by 1-μm Si CMOS technology applied to epitaxial Si-layers (d ≈15 μm) deposited on thick Si substrates (d = 640 μm). It was shown that for transistors with the channel width to length ratio W/L = 20/3 μm without any special antennas used for radiation input, the noise equivalent power (NEP) for radiation frequency ν ≈76 GHz can reach NEP ∼6×10⁻¹⁰ W/Hz^1/2. With estimated frequency dependent antenna effective area S_est for contact wires considered as antennas, the estimated possible noise equivalent power NEP_pos for n-MOSFET structures themselves can be from ∼15 to ∼10³ times better in the specral range of ν ∼55–78 GHz reaching NEP_pos ≈10⁻¹² W/Hz^1/2.     

Electrical transport properties of CuWO4

The temperature dependence of the electrical conductivity, thermoelectric power and dielectric constant of the antiferromagnetic CuWO₄ have been studied in the temperature range 300–1000 K. The conductivity results can be summarised by the equations σ_I=6.31 × 10⁻³ exp (−0.29 eV/kT) ohm⁻¹ cm⁻¹ in the temperature range 300–600 K and σ_II=3.16 × 10⁵ exp (−1.48 eV/kT) ohm⁻¹ cm⁻¹ between 600 K and 1000 K. The thermoelectric power can be expressed byθ=[− 1.25 (10³/T) + 3.9] mV/K. Initially dielectric constant increases slowly but for high temperatures its increase is fast.     

On the Boltzmann Equation for Fermi–Dirac Particles with Very Soft Potentials: Averaging Compactness of Weak Solutions

The paper considers macroscopic behavior of a Fermi–Dirac particle system. We prove the L ¹-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi–Dirac particles in a periodic box with the collision kernel b(cos θ)|ρ−ρ _*|^γ, which corresponds to very soft potentials: −5 < γ ≤ −3 with a weak angular cutoff: ∫₀ ^π b(cos θ)sin ³θ dθ < ∞. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff–Young inequality, the L ^∞-bounds of the solutions, and a specific property of the value-range of the exponent γ. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy.