Thomson Formula Research Articles

Digital acoustic model of an NPP pressurizer with WWER

It is experimentally proven that the main cause of vibration excitation of equipment and internals of the main circulation circuit (MCC) are acoustic standing waves (ASW) and main circulation pumps (MCP). Usage of an interdisciplinary approach made it possible to create a digital acoustic model of pressurizer system with pipelines attached to it and prove that it is a self-oscillating system capable of generating acoustic standing waves (ASW) similar to simultaneous operation of several Helmholtz resonators. Each Helmholtz resonator in pressurizer is able to suppress a certain frequency of ASW generated by the reactor, which depends on coolant temperature. Determination of natural frequencies of coolant pressure oscillations (NFCPO) in pressurizer using Thomson formula is based on method of electroacoustic analogy. Acoustic compliance of pressurizer and acoustic mass of various combinations of pipelines connected to it make it possible to calculate NFCPO, in the system under consideration, according to the formula presented in the form of acoustic analogues of inductance and capacitance. Acoustic parameters of a system of Helmholtz resonators formed by a pressurizer and a connecting pipeline with hot leg of the third loop in nominal operating mode of NPP with WWER-1000 are calculated. A technology has been developed and verified, advantage of which is usage of a pressurizer for damping ASW, frequencies of which fall within vibration bandwidth of primary circuit structural elements. Calculation and experimental proof of previously unknown ability of pressurizer to damp ASW generated by the reactor in a wide frequency range is given, and possibility of preventing resonances with vibrations of equipment and NPP structures is substantiated.

Phytochemical Analysis of Bulung Boni (Caulerpa cylindracea S.) N- Hexane Extract with Gc-Ms Method and Toxicity Test on Mice (Mus musculus L.)

One of the marine resource commodities owned by Indonesia is seaweed. Bulung boni is one type of seaweed that grown in Indonesia. Bulung boni is the regional name of Caulerpa cylindracea. Bulung boni is usually used as a food and medicine for most people in Bali. The purpose of this research is to study the content of phytochemical compounds in n-hexane extract of bulung boni and determine the toxicity effect on mice (Mus musculus). The methods used in this study were maceration, GC-MS (Gas Chromatography-Mass Spectrometry), observation, and calculation with the Thomson and Weil formula. This study used 24 mice as experimental animals. Mice were divided into 6 treatment groups, group 1 as control was given 1% Na-CMC solution, groups 2-6 were given test extracts with doses, 100, 200, 300, 400, 500 mg/30 g BW mice. The results showed the highest compound contained in the n-hexane extract of bulung boni was Hexadecanoic acid, methyl ester with an AUC value of 35.21%. Toxicity tests on mice showed no deaths experienced by mice, so the LD50 value determined was pseudo at 16.6 g/ kg BW and fell into the practically non-toxic category

Self-oscillations that cause the destruction of intermolecular bonds in the water coolant of a nuclear power plant

The digital acoustic model of a nuclear reactor (DAMNR) is presented as an auto-oscillatory system belonging to a special class of nonlinear dissipative systems capable of generating undamped oscillations. It is established that a water-water power reactor with a turbulent flow of a coolant is an open system of high complexity with a large number of elements, the connections between which are not predetermined, but probabilistic. Elements of the coolant circuit with negative dissipation (negative friction) are identified. It is shown that they self-organize chaotic turbulent pulsations and vortices into ordered wave oscillations, the frequency of which is determined by the Thomson (Kelvin) formula. In radio engineering circuits, an electronic self-oscillating generator with transformer feedback has similar properties. The presence of negative resistance in nonlinear dynamical systems leads to self-organization of chaotic turbulent perturbations and generation of self-oscillations in the form of acoustic standing waves (ASW). On the basis of theoretical and experimental data, the reliability of a previously unknown property of a reactor with connected pipelines - the ability to generate several ASW simultaneously-was confirmed. The use of DAMNR in the design and operation of nuclear power plants allows to identify the sources of ASW occurring in the coolant, the conditions for their occurrence and frequency.

A Comparative Analysis of the Size Dependence of the Melting and Crystallization Temperatures in Silver Nanoparticles via the Molecular Dynamics and Monte-Carlo Methods

The size dependences of the melting and crystallization temperatures of silver nanoparticles are obtained by two alternative atomistic simulation methods, such as the molecular dynamics and Monte-Carlo methods. The simulation results are analyzed and compared with available experimental values and a melting temperature calculated using the well-known Thomson formula. Atomistic simulation reveals good coincidence between the data and satisfactorily conforms to the Thomson formula. However, the melting temperatures predicted through atomistic simulations exceeds the available experimental data.

Size dependence of the melting temperature of metallic nanoclusters from the viewpoint of the thermodynamic theory of similarity

The generalized Thomson formula Tm = Tm(∞)(1-δ)R for the melting point of small objects Tm has been analyzed from the viewpoint of the thermodynamic theory of similarity, where R is the radius of the particle and Tm(∞) is the melting point of the corresponding large crystal. According to this formula, the parameter δ corresponds to the value of the radius of the Tm(R-1) particle obtained by the linear extrapolation of the dependence to the melting point of the particle equal to 0 K. It has been shown that δ = αδ0, where α is the factor of the asphericity of the particle (shape factor). In turn, the redefined characteristic length δ0 is expressed through the interphase tension σsl at the boundary of the crystal with its own melt, the specific volume of the solid phase vs and the macroscopic value of the heat of fusion λ∞:δ0 = 2σslvs/λ∞. If we go from the reduced radius of the particle R/δ to the redefined reduced radius R/r1 or R/d, where r1 is the radius of the first coordination shell and d ≈r1 is the effective atomic diameter, then the simplex δ/r1 or δ/d will play the role of the characteristic criterion of thermodynamic similarity. At a given value of α, this role will be played by the simplex Estimates of the parameters δ0 and δ0/d have been carried out for ten metals with different lattice types. It has been shown that the values of the characteristic length δ0 are close to 1 nm and that the simplex δ0/d is close to unity. In turn, the calculated values of the parameter δ agree on the order of magnitude with existing experimental data.

Defect of the well-known (classical) expression for the ionization rate in gas-discharge plasma and its modification

A critical analysis is given of the well-known expression for the electron-impact ionization rate constant αi of neutral atoms and ions, derived by linearization of the ionization cross section σi(e) as a function of the electron energy near the threshold I and containing the characteristic factor (I + 2kT). Using the classical Thomson expression for the ionization cross section, it is shown that in addition to the linear slope of σi(e), it is also necessary to take into account the large negative curvature of this function near the threshold. In this case, the second term in parentheses changes its sign, which means that the commonly used expression for αi (∼4kT/I) already at moderate values of the temperature (kT/I ∼ 0.1). The source of this error lies in a mathematical mistake in the original approach and is related to the incorrect choice of the sequential orders of terms small in the parameter kT/I. On the basis of a large amount of experimental data and considerations similar to the Gryzinski theory, a universal two-parameter modification of the Thomson formula (as well as the Bethe—Born formula) is proposed and a new simple expression for the ionization rate constant for arbitrary values of kT/I is derived.

On the size distribution in three-dimensional quantum-dot crystals

The size distribution function of nanodots in artificial three-dimensional (Si)Ge/Si and In(Ga)As/GaAs quantum dot crystals grown using templates with perfect periodicity is calculated. Pyramidal nanodots were modeled by cone-shaped clusters for which the Thomson formula was derived, which is necessary to determine the growth (dissolution) rate of clusters during Ostwald ripening. A comparison of the calculated curve with experimental histograms shows that the size distribution itself is formed during Ostwald ripening and is caused by features of Ge and InAs quantum-dot formation on preliminarily textured Si and GaAs substrates.

Linear attenuation coefficients of tissues from 1 keV to 150 keV

The linear attenuation coefficients and three interaction processes have been computed for liver, kidney, muscle, fat and for a range of x-ray energies from 1keV to 150keV. Molecular photoelectric absorption cross sections were calculated from atomic cross section data. Total coherent (Rayleigh) and incoherent (Compton) scattering cross sections were obtained by numerical integration over combinations of F2m(x) with the Thomson formula and Sm(x) with the Klein–Nishina formula, respectively. For the coherent (Rayleigh) scattering cross section calculations, molecular form factors were obtained from recent experimental data in the literature for values of x<1Å−1 and from the relativistic modified atomic form factors for values of x≥1Å−1. With the inclusion of molecular interference effects in the coherent (Rayleigh) scattering, more accurate knowledge of the scatter from these tissues will be provided. The number of elements involved in tissue composition is 5 for liver, 47 for kidney, 44 for muscle and 3 for fat. The results are compared with previously published experimental and theoretical linear attenuation coefficients. In general, good agreement is obtained. The molecular form factors and scattering functions and cross sections are incorporated into a Monte Carlo program. The energy distributions of x-ray photons scattered from tissues have been simulated and the results are presented.

Dimensional dependences of the interfacial tension at a solid—liquid interface and the melting temperature of metal nanoparticles

New coordinating relationships are obtained for the dimensional dependences of melting temperature T(r) and interfacial tension σSL(r) of a solid spherical nanoparticle at the boundary with its own melt. The Thomson formula for T(r) and the Tolman formula for σSL(r) follow from the expressions obtained at large radii of curvature. Numerical calculations are performed for metals. Results from calculations on the dimensional dependences of the melting temperature for Pt, Au, and Al that conform fairly well with experimental data are given as examples.

Accurate Collisional Cross-Sections: Important Non-Lte Input Data

Non-LTE modelling for a particular atom requires accurate collisional excitation and ionization cross-sections for the entire system of transitions in the atom. This review concerns with inelastic collisions with electrons and neutral hydrogen atoms. For the selected atoms, H i and Ca ii, comparisons are made between electron impact excitation rates from ab initio calculations and various theoretical approximations. The effect of the use of modern data on non-LTE modelling is shown. For most transitions and most atoms, hydrogen collisional rates are calculated using a semi-empirical modification of the classical Thomson formula for ionization by electrons. Approaches used to estimate empirically the efficiency of hydrogenic collisions in the statistical equilibrium of atoms are reviewed.

On the size dependence of the melting temperature of nanoparticles

The size dependence of the melting temperature of nanocrystals has been investigated within the thermodynamic approach. A formula is obtained, which, in contrast to the classical Thomson formula, takes into account the metastable character of equilibrium between the crystal core and melt shell. Comparative investigation of the size dependence of the melting temperature, disregarding and taking into account the size dependences of the surface tension of the solid and liquid phases and the interface tension, has been performed by the example of aluminum, tin, and copper nanoparticles.

A Proof of the Gibbs–Thomson Formula in the Droplet Formation Regime

We study equilibrium droplets in two-phase systems at parameter values corresponding to phase coexistence. Specifically, we give a self-contained microscopic derivation of the Gibbs–Thomson formula for the deviation of the pressure and the density away from their equilibrium values which, according to the interpretation of the classical thermodynamics, appears due to the presence of a curved interface. The general—albeit heuristic—reasoning is corroborated by a rigorous proof in the case of the two-dimensional Ising lattice gas.

Calculation of the radiative opacity of laser-produced plasmas using a relativistic-screened hydrogenic model

In this work, we use a relativistic-screened hydrogenic model to compute the radiative opacity of laser-produced plasmas. The model is based on a set of screening charges which allow one to easily calculate atomic properties of isolated ions. These screened charges have been fitted to a fourth-order polynomial depending on the nuclear charge Z for ground and single excited states of ions belonging to the isoelectronic sequences comprised between He-like to U-like. In the opacity model used, ionic populations are obtained by solving the Saha equation including degeneracy corrections. Bound–bound transitions are determined using a Voigt profile for line shape, which includes natural, collisional, Doppler and UTA widths. Bound–free and free–free opacities are evaluated using the Kramer cross-sections with appropriate corrections. Scattering processes are computed through the use of the Thomson formula with corrections. The results are compared with other screened hydrogenic models and more sophisticated self-consistent codes.

Electromagnetic dipole radiation of oscillating D-branes

I emphasize analogy between Dp-branes in string theories and solitons in gauge theories comparing their common properties and showing differences. In string theory we do not have the full set of equations which define the theory in all orders of coupling constant as it was in gauge theories, nevertheless such solutions have been found as solutions of low energy superstring effective action carrying the RR charges. The existence of dynamical RR charged extended objects in string theory has been deduced also by considering string theory with mixed boundary conditions, when type II closed superstring theory is enriched by open strings with Neumann boundary conditions on p + 1 directions and Dirichlet conditions on the remaining 9-p transverse directions. We will show that for certain excitations of the string/D3-brane system Neumann boundary conditions emerge from the Born-Infeld dynamics. Here the excitations which are coming down the string with a polarization along a direction parallel to the brane are almost completely reflected just as in the case of all-normal Dirichlet excitations considered by Callan and Maldacena, but now the end of the string moves freely on the 3-brane realizing Polchinski's open string Neumann boundary condition dynamically. In the low energy limit ω → 0, i.e. for wavelengths much larger than the string scale only a small fraction ∼ ω 4 of the energy escapes in the form of dipole radiation. The physical interpretation is that a string attached to the 3-brane manifests itself as an electric charge, and waves on the string cause the end point of the string to freely oscillate and produce e.m. dipole radiation in the asymptotic outer region. The magnitude of emitted power is in fact exactly equal to the one given by Thomson formula in electrodynamics.

Classical coarsening theory in heteroepitaxial systems

Classical coarsening theory, originally developed by Lifshitz, Slyozov, and Wagner (LSW), describes the growth of grains or islands and predicts time-independent self-similar island-size distribution functions. This dynamic scaling is reconsidered here to include island–island elastic interactions, line tension of the islands, and diffusion barriers for adatoms due to the strained substrate with a simple model that preserves self-similarity. These effects significantly modify the size distribution of islands. In particular, the size distribution becomes narrower than originally predicted by LSW theory as derived from the Gibbs–Thomson formula. However, the time dependence of the average island size is described by usual power law formula.

Low-energy BO and BO 2 emission from H 2BO 3 sputtered in a low-pressure high-frequency SNMS plasma

Background corrected secondary neutral energy spectra derived from Cu powder pellets with H 3BO 3, MgO, Al 2O 3, TiO 2, Y 2O 3 and ZrO 2, show energy distributions being more or less typical for collision cascades in the cases of the metal ions M +, of O + at energies >5 eV above the ion generation potential, and of the molecules Cu 2 +, AlO +, TiO +, YO + and ZrO +, whereas the larger parts of the energy distributions of BO +and BO 2 +exhibit a similar shape as the Ar +plasma gas ions. From this, and from the background of the low decomposition and melting temperatures of H 3BO 3 and B 2O 3, respectively, we conclude that the detected BO and BO 2 molecules have been emitted with thermal energies in processes implying lower energies than collision cascades. Evidence was found that the same holds for HBO 2 and H 2BO 2. In order to obtain relative correction factors for MO + molecular ion intensities, electron impact ionization cross sections have been calculated for the light MO molecules using the binary-encounter Bethe (BEB) formula, and for the respective metal M atoms by means of the semiempirical Lotz formula. For the heavy MO molecules YO and ZrO, cross sections have been estimated using the Thomson formula. The comparison of corrected relative MO/M and M/Cu intensities yields evidence that thermal (H)BO x emission amounts to the same order of magnitude as B emission from collision cascades, and that this situation is comparable to the high yield of MO molecules emitted in collision cascades from oxides with high M masses. Since the normal energy window of an HF-plasma secondary neutral mass spectrometer does not accept particles with originally thermal energies, it is concluded that these findings are relevant for quantification.

Mechanical behavior of Al 2O 3 ceramics under cyclic tension-compression loading

During cyclic deformation, temperature measurements were carried out with thermocouples. On the basis of the thermoelastic effect, a thermometric method is described which allows the determination of the elastic part of the total deformation. Thus effective stress changes can be determined. The system is quite sensitive and makes it possible to characterize the behavior of a small volume unit during cyclic deformation. The temperature change ΔT is directly related to the stress change Δσ according to Thomson's formula. Notched Al 2O 3 specimens were tested under direct tension-compression loading. Cyclic tests with a stepwise load increase were carried out using a tensile tester and a servohydraulic test system. The test frequency was 0.5 and 5 Hz and the stress ratio was R = −1. Load differences and corresponding changes of temperature were measured. By means of the temperature measurements, the notch factor can be determined. It can be shown that the calculated stress concentration in the notched area is much higher than the measured value. This indicates that the stress reduction in Al 2O 3 is higher than in non-brittle materials. The predominant mechanism causing reduction of the stress concentration is microcracking. Fractographic studies with the scanning electron microscope show damage of Al 2O 3 under cyclic loading conditions.

Size and surface effect in nematic-isotropic phase transition of a liquid crystal

The size and surface effects on the nematic-isotropic phase transition of a liquid crystal are analyzed using a functional form of the surface energy proportional to the square of the scalar order parameter. The evaluated temperature shift agrees with the published experimental observations. This form seems confirmed by experimental data of the anchoring energy versus temperature, determined by means of the Freedericksz technique. The obtained formula for the temperature shift is similar to the well-known Thomson formula, usually considered in the classical phase transitions.

Special melting behaviour of highly oriented polyethylene

The DSC method has been applied for the study of melting behaviour of polyethylene [PE] films in dependence on the number of repeated stretching λ. Some samples have been subjected to annealing and etching by nitric acid. The melting process characteristics have been correlated with structural parameters. It was found that the longitudinal dimension of a crystallite l, calculated from the value of long period and degree of crystallinity, had increased slightly with increasing λ. A rise in the melting point temperature Tm with increasing λ has not been caused so much by the value of l but has been related to the decrease of σe values—the specific free surface energy of the edges of crystallites. The values of σe, calculated according to the Thomson formula, have significantly decreased with increasing λ and have increased after annealing of the samples. The etching process has been accompanied by increase of σe. The structural changes, occuring during stretching, annealing and etching of PE samples, have had their significance presumably in amorphous zones and the end facets of crystallites, affecting also σe and, consequently, Tm values.

The nature of the muon

A quarklike model of the muon based upon the Thomson formula for the electron is correlated with a recent account of the muong-factor and shown to determine the muon-electron mass ratio. The theory indicates that this is 206.7687, in close accord with its measured value. The model involves a resonance governed by the period at which a disturbance propagates around the electron charge, the radius of which is the same as that of the de Sitter microuniverse model of the electron suggested by Caldirola.