Deformation of viscoelastic coating in a turbulent flow

The rate and amplitude of compliant coating deformation by turbulent pressure pulsations were calculated. Complex compliance determined by a 2D model has two components: along and across the coating. Dependence of the components of dimensionless compliance on the wavelength — coating thickness ratio was determined for 0.3 < λ/H < 30 and dependence of these components on the ratio of flow velocity to velocity of wave propagation was determined for 0.1 < V/C < 10. Deformation amplitude and rate of surface displacement for the hard compliant coatings which can be used in practice were calculated within the range of 5–55 m/s for the water and air turbulent flow. The effects of the loss tangent and Poisson’s ratio of the coating material were also studied. It is shown that the mean-square displacement of their surface does not exceed the thickness of a viscous sublayer. However, the velocity of surface motion is comparable with velocity pulsations in a boundary layer near a wall. This can be a reason for drag reduction on a compliant wall. The calculated value of ratio between energy absorbed by the wall and energy dissipated within the flow because of drag was 10⁻⁴ for water and 10⁻⁶ for air. This estimate does not confirm the hypothesis explaining drag reduction by energy takeoff from the flow.     

Boundary conditions on a compliant wall in the turbulent flow

It is shown that with an increase in elasticity modulus of the coating material from 0.01 MPa to 100 MPa the pulsation velocity of coating surface changes not more than by 30 % and equals 0.17–0.24 of the value of dynamic flow velocity, and this can change significantly Reynolds stresses in the near-wall area. According to performed analysis, it was found out that the deformation value of the compliant coatings within the velocity range, optimal for their interaction with the turbulent flow, is only several units of the viscous scale. Moreover, these deformations are very gentle: the ratio of amplitude of deformation to wavelength is less than 10^?3. It is assumed that while modeling the interaction between the compliant coating and turbulent flow it is not necessary to transfer the boundary conditions to the moving coating surface. Perhaps, it will be sufficient to determine the velocity of wall motion over the undisturbed coating surface.     

Polynomial deformations of enveloping algebra U(sl(2,2102))

We define the polynomial deformation, U _t ^p, of enveloping algebra U(sl(2,)) as an analogue of quantum group and construct a nice set D _p ^even of parameters on which we described irreducible representations and classify the irreducible ones in terms of the highest weights. Also, we construct the Casimir elements and using them we see that every finite dimensional U _t ^p-module is semisimple.     

Dynamic compliance of multilayer coatings

The algorithm for calculation of dynamic compliance of multilayer coatings was developed. The compliance modulus and phase lag of coating surface motion vs. the current pressure depend on viscoelastic properties of materials, ratio of wavelength to layer thickness λ/H, and ratio of wave velocity to propagation velocity of shear vibrations in the base layer V / C _t,2 ⁰ Dynamic compliance of the two-layer coating consisting of a thick base layer and thin durable outer layer was calculated. The elasticity modulus of the outer layer ranged up to eight values of elastic modulus of the inner layer; the density of the outer layer either remained equal to the density of the inner layer or increased proportionally to the elastic modulus. Depending on V / C _t,2 ⁰ two scenarios of compliant coating interaction with the turbulent flow were distinguished: resonant and broadband ones. It is shown that the vibration properties of two-layer coatings can be significantly better than the properties of the monolayer coatings. This makes it possible either to increase the coating strength or to work efficiently at lower velocities.     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

Wei Hua’s four-parameter potential: Comments and computation of molecular constants αe and εeXe

The value of adjustable parameterC in the four-parameter potentialU(r) =D _e [(1 - exp[-b(r -r _e)])/(1 -C exp[-b(r -r _e)])]² has been expressed in terms of molecular parameters and its significance has been brought out. The potential so constructed, withC derived from the molecular parameters, has been applied to ten electronic states in addition to the states studied by Wei Hua. Average mean deviation for these 25 states has been found to be 3.47 as compared to 6.93, 6.95 and 9.72 obtained from Levine, Varshni and Morse potentials, respectively. Also Dunham’s method has been used to express rotation-vibration interaction constant (α_e) and anharmonicity constant (ω_ex_e) in terms ofC and other molecular constants. These relations have been employed to determine these quantities for 37 electronic states. For α_e, the average mean deviation is 7.2% compared to 19.7% for Lippincott’s potential which is known to be the best to predict these values. Average mean deviation for (ω_ex_e) turns out to be 17.4% which is almost the same as found from Lippincott’s potential function.     

Anharmonic force constants of GaSb from the measured third order elastic constants at 300°K

The third-order elastic constants of single crystal GaSb are determined using ultrasonic pulse interferometer at 10 MHz. The constants at 300°K, in units of 10¹¹ N.m.⁻², are C_l11 = ™ 4 ·75 ± 0·06 C₁₄₄ = + 0·50 ± 0·25 C₁₁₃ = ™ 3 ·08 ± 0·02 C₁₆₆ = ™ 2·16 ± 0·13 C₁₂₃ = ™ 0 ·44 ± 0·29 C₄₅₆ = ™ 0·25 ± 0·15 These constants are used to evaluate the three anharmonic first and second neighbour force constants based on modified Keating’s model. The constants are (in units of 10¹¹ N.m⁻²)γ=− 2·406;δ=0·407;ε=−0·222.     

Theory of drift step-recovery diodes

A theory of drift step-recovery diodes as current interrupters in inductive-storage generators is elaborated. The theory includes the nonlinear dependence of the base resistance and barrier capacitance on the current passing through the diodes. Simple relationships are obtained for the diode parameters (the thickness and doping level of the base, the charge of nonequilibrium holes extracted from the base for the time T _B of high-reverse-conductivity phase, and the surface area and number m of series-connected diodes) and parameters of the loop (the capacitance and inductance of the energy storage and the initial voltage U C ₀ across the capacitance) that provide the generation of a voltage pulse with a desired rise time t _B and amplitude U _m on the load. For a given diode efficiency k, the maximal values of the overvoltage factor U _m/U C ₀ and pulse sharpening coefficient T _B/t _B are shown to depend on a factor proportional to

Thermal expansion of thin C60 films

The thermal expansion coefficient a and structure of C₆₀ films with thickness t∼3–10 nm were investigated in the temperature interval from room to liquid-nitrogen temperature by electron-optical methods. The thermal expansion coefficient was determined from the temperature shift of the diffraction maxima in the electron diffraction patterns. The objects of investigation were epitaxial C₆₀ films condensed in vacuum on a (100) NaCl cleavage surface and oriented in the (111) plane. A surface-induced size effect in the thermal expansion coefficient was observed. It was established that as t decreases α _f increases and is described well by the relation α _f=17·10⁻⁶ K⁻¹+8.3·10⁻⁵ nm K⁻¹ t ⁻¹. This relation was used to estimate the linear expansion coefficient α _s of the C₆₀ surface in the (111) plane as α _s=60·10⁻⁶K⁻¹, which is several times larger than the bulk value. The experimental results agree satisfactorily with the theoretical calculations of the mean-square displacements of molecules located in a region near the surface. Zh. éksp. Teor. Fiz. 114, 1868–1875 (November 1998)     

Growth of crystallites consisting of C60 molecules on heated (100)Mo

The initial stages of growth of films of C₆₀ molecules on a (100)Mo surface are studied by high-resolution Auger spectroscopy and atomic force microscopy under ultrahigh vacuum conditions. It is shown that at T<750 K, after a specific coating with molecular density 1.5×310¹⁴ cm⁻², which the authors term a high-temperature (HT) monolayer, has formed on the surface, crystallites in the form of “towers” with flat tops grow on the surface. The fraction of the area occupied by towers depends strongly on the substrate temperature and the flux density of the molecules on the surface but is virtually independent of the exposure time. At temperatures _T>760 K the C₆₀ molecules making up the crystallites desorb, while the molecules making up the HT monolayer decompose, and the carbon released is dissolved in the interior of the substrate. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 969–972 (25 June 1998)     

Asymptotic behavior of orbits of C 0-semigroups and solutions of linear and semilinear abstract differential equations

In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t ⁿ f(t, u(t)), where A is the generator of a C ₀-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C ₀-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S ^p-A defined similarly to the case of S ^p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A _u:= A ∩ BUC(ℝ, X) if n = 0 and to t ⁿ A _u ⊕ w _n C ₀ (ℝ, X) if n ∈ ℕ, where w _n(t) = (1 + |t|)ⁿ. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0. Dedicated to the memory of B. M. Levitan     

Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a “spring-backed” plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (Λ_t) required for unstable fluctuations is proportional to the wavenumber k ( Λ _t∼k) in the plate membrane type of wall while it scales as k² in the viscoelastic membrane type of wall ( Λ _t∼k ²) in the limit k→ 0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number. Received 8 November 2000 and Received in final form 20 March 2001     

Instability of gravity flows on a slope

A Hamiltonian version of contour dynamics is formulated for the model of a potential slope flow of homogeneous incompressible fluid. The particle-like solutions that play the role of structural elements in the disintegration of strongly perturbed slope flows are studied in terms of this approach. Investigation of the solution instability mechanism has shown that two collapse scenarios are realized, depending on the slope steepness. The singularity for the surface shape develops according to the law (t − t ₀)^−1/3 on a vertical slope and slightly more slowly, according to the law (t − t ₀)^−2/7, where t ₀ is the collapse time, on a nonvertical slope. A sufficient collapse criterion that allows this effect to be judged from the first three integrals of motion has been established.     

Stability of naked singularity arising in gravitational collapse of Type I matter fields

Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary C²-mass functionM(r, v) and a C¹-functionh(r, v) (through the corresponding C¹-metric functionν(t, r)), there exist infinitely many choices of energy distribution functionb(r) such that the ’true’ initial data(M, h(r,v)) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole (BH) and naked singularity (NS) form a ’big’ subset of the true initial data set, their occurrence is not generic. The terms ’stability’ and ’genericity’ are appropriately defined following the theory of dynamical systems. The particular case of radial pressurep _r (r) has been illustrated in details to get a clear picture of how naked singularity is formed and how, it is stable with respect to initial data.     

On the effective Debye temperatures of the C60 fullerite

The effective Debye temperatures Θ_eff determined for solids by different physical methods have been analyzed and compared. Attention has been focused on the original parameter of the Debye theory of heat capacity, i.e., the translational calorimetric Debye temperature Θ _c ^t (0), and the X-ray Debye temperature Θ _x in the framework of the Debye-Waller theory for the C₆₀ fullerite. It has been established that the true Debye law T ³ is satisfied for the C₆₀ fullerite over a very narrow range of temperatures: 0.4 K ≤ T ≤ 1.8 K. For this reason, the experimental Debye temperatures Θ _c ^t (0) obtained for the C₆₀ fullerite by different authors in the range T > 4.2 K are characterized by a large scatter (by a factor of ∼5). It has been revealed that the value Θ _c ^t (0) = 77.12 K calculated in this paper with the use of the six-term Betts formula from the harmonic elastic constants $ \tilde C_{ijkl} $ \tilde C_{ijkl} of the C₆₀ single crystal in the limit T = 0 K is closest to the true Debye temperature. It has been demonstrated using the method of equivalent moments that the real spectral frequency distribution of translational lattice vibrations g(ω) for the C₆₀ fullerite deviates from a parabolic distribution. The effective Debye temperatures Θ_eff involved in applied problems of thermodynamics of crystals and elastic scattering of different radiations from lattice vibrations have been determined. The quantitative measure of anharmonicity of translational and librational lattice vibrations of the C₆₀ fullerite has been determined. This has made it possible to empirically evaluate the lattice thermal conductivity κ of the C₆₀ fullerite at T ≈ 300 K: κ(300) = 0.80 W (m/K), which is in good agreement with the experimental thermal conductivity κ_exp = 0.78 W (m/K) at T ≈ 250 K.     

Microwave and far-infra-red dielectric absorption inn-alkanes

Summary The power absorption coefficient (α) forn-hexane (C₆),n-heptane (C₇),n-dodecane (C₁₂) andn-tetradecane (C₁₄), benzene and cyclohexane has been studied at 20 °C, in the wave number range 20 to 300 cm⁻¹ within an accuracy of 2%. The power absorption measurements onn-alkanes (C₅−C₁₄ except for C₈, C₁₁ and C₁₃) are discussed in conjunction with the dielectric loss in the frequency range (9⋎140) GHz. The results indicate that, unlike other nonpolar liquids,n-alkanes show a broad dielectric dispersion in the microwave frequency range followed by a second dispersion in the far infra-red. The results are interpreted in terms of a dipole moment of 0.09 D in alkanes. A possible explanation for the origin of the dipole moment is discussed. A reference is also made to measurements of the dielectric loss and the Stark effect on the lower-series alkanes in the gas phase.

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Riassunto Si è studiato il coefficiente di assorbimento di potenza (α) pern-esano (C₆),n-eptano (C₇),n-dodecano (C₁₂) en-tetradecano (C₁₄), nel benzene e nel cicloensano a 20 °C nell’intervallo di numeri d’onda da 20 a 300 cm⁻¹ con un’accuratezza del 2%. Le misurazioni dell’assorbimento di potenza neglin-alcani (C₅−C₁₄, eccetto che per C₈, C₁₁ e C₁₃) sono discusse insieme alla perdita dielettrica nell’intervallo di frequenza (9⋎140) GHz. I risultati indicano che, diversamente da altri liquidi non polari, glin-alcani mostrano un’ampia dispersione dielettrica nell’intervallo di frequenza delle microonde, seguíta da una seconda dispersione nel lontano infrarosso. I risultati sono interpretati in termini di un momento dipolare di 0.09 D negli alcani. Si discute una possibile spiegazione dell’origine del momento dipolare. Si fa anche un accenno alle misurazioni della perdita dielettrica e dell’effetto di Stark sugli alcani della serie inferiore in fase gassosa.

     

Electrolyte interaction with DPPC vesicles: An ESR study

Summary The partition of the spin probe TEMPO between the fluid lipid phase of single-walled vesicles of dipalmitoylphosphatidylcholine and the aqueous bulk solution have been used to investigate the interaction of monovalent ions with polar head of neutral phospholipids. The study has been performed by electron spin resonance (ESR) spectroscopy in the temperature range of (20÷60)°C and in the presence of (0÷3) M 1∶1 electrolyte. In the absence of electrolyte the spin probe TEMPO reveals the characteristic order→disorder DPPC main phase transition atT _m≈37°C, while the pretransition occurs atT _p≈27.5°C. On increasing the ionic strength of the dispersion medium it results for the partition coefficient,P _C, that, at each temperature,P _C(3)>P _C(2)>P _C(1)>P _C(0). Correspondingly, the pretransition disappears and theT _m value downshifts from ≈37°C with 0 M electrolyte to ≈34°C with 3M salt in the order:T _m(3)>T _m(2)>T _m(1)>T _m(0). The results suggest an increase in the net surface charge density of vesicles due to high ionic-strength values. The alteration of the electric interactions occurring into the polar zone of DPPC bilayer reduces the hindrances which, in turn, favour the enhancement of TEMPO partitioning in the hydrophobic core of phospholipid bilayers. The authors of this paper have agreed to not receive the proofs for correction.     

Moduli Space of BPS Walls in Supersymmetric Gauge Theories

Existence and uniqueness of the solution are proved for the ‘master equation’ derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with N _F charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V-equivalence relation for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(N _C) gauge theory with N _F hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(N _C) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.     

Determination of nonlinear σ-ω-ρ model parameters in the relativistic mean-field theory by nuclear-matter properties

The parameters of the σ-ω-ρ model in the relativistic mean-field theory with nonlinear σ-meson self-interaction are determined by nuclear-matter properties, which are taken as those extracted by fits to data based on nonrelativistic nuclear models. The values of the relevant parameters are C _σ ²∼ 94, C _ω ²∼ 32, C _ρ ²∼ 26, b∼ - 0.09, c∼ 1, and the σ-meson mass m _σ∼ 370 MeV, while the value of the calculated nuclear- surface thickness is t∼ 1.4 fm. The field system is shown to be stable, since the σ-meson self-interaction energy is a lower bound in this whole parameter region with positive c. On the other hand, the effective nucleon mass M^* is larger than 0.73M, if the symmetry incompressibility K_s is assumed to be negative and the nuclear-matter incompressibility K₀ is kept less than 300 MeV. Received: 27 June 2001 / Accepted: 5 October 2001