We analyze the characteristic features of jam formation on a circular
one-lane road. We have applied an optimal velocity model including stochastic noise, where cars are treated as moving and interacting particles. The motion of <i>N</i> cars is described by the system of 2<i>N</i> stochastic differential equations with multiplicative white noise. Our system of cars behaves in qualitatively different ways depending on the values of control parameters <i>c</i> (dimensionless density), <i>b</i> (sensitivity parameter characterising the fastness of relaxation), and α (dimensionless noise intensity). In analogy to the gas-liquid phase transition in supersaturated vapour at low enough temperatures, we observe three different regimes of traffic flow at small enough values of <i>b</i> < <i>b</i><sub><i>cr</i></sub>. There is the free flow regime (like gaseous phase) at small densities of cars, the coexistence of a jam and free flow (like liquid and gas) at
intermediate densities, and homogeneous dense traffic (like liquid phase) at large densities. The transition from free flow to congested traffic occurs when the homogeneous solution becomes unstable and evolves into the limit cycle. The opposite process takes place at a different density, so that we have a hysteresis effect and phase transition of the first order. A phase transition of second order, characterised by critical exponents, takes place at a certain critical density <i>c</i> = <i>c</i><i><sub>cr</sub></i>.
Inclusion of the stochastic noise allows us to calculate the distribution of headway distances and time headways between the successive cars, as well as the distribution of jam (car cluster) sizes in a congested traffic.
We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat <i>C<sub>v</sub></i> based on the finite-size scaling of its maximal values <i>C</i><sub><i>v</i></sub><sup>max</sup> depending on the linear size of the lattice <i>L</i>. An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of <i>C</i><sub><i>v</i></sub>. The simulations made up to <i>L</i> ≤ 128 with application of the Wolff's cluster algorithm allowed us to verify the possible power-like as well as logarithmic singularity of the specific heat predicted by different theoretical treatments. The most challenging and interesting result we have obtained is that the finite-size scaling of <i>C<sub>v</sub></i><sup>max</sup> in 3D Ising model is well described by a logarithmic rather than power-like ansatz, just like in 2D case. Another modification of our iterative method has been considered to estimate the critical coupling of 3D Ising model from the Binder cumulant data within <i>L</i> ε [96; 384]. Furthermore, the critical exponent β has been evaluated from the simulated magnetization data within the range of reduced temperatures <i>t</i> ≥ 0.000086 and system sizes <i>L</i> ≤ 410.
Intensive light emission (photoluminescence) from silicon nanocrystals has been interpreted in literature as recombinative emission. It has been supposed that the band structure is "pseidodirect." The literature analysis presented in our paper shows that the band structure is indirect and therefore intensive recombinative emission is not possible. According to new aspect, a part of electrons reaches the second conduction subband due to Auger recombination. Then the intensive visible radiation could be caused by transitions of these electrons from the second to the first conduction subband. We have constructed continuity equations for the electron concentration in the first and the second conduction subbands. This system of equations has been solved numerically with two adjustable parameters. At suitable values of these parameters our theoretical curve of the photoluminescence decay well coincides with experimental one.
We present a comparison of nucleation in an isothermal-isochoric container with traffic congestion on a one-lane freeway. The analysis is based, in both cases, on the probabilistic description by stochastic master equations. Further we analyze the characteristic features of traffic breakdowns. To describe this phenomenon we apply the stochastic model regarding the jam emergence to the formation of a large car cluster on the highway.
We present in this paper results of investigation of optical properties of SiO<SUB>2</SUB>-(Co plus Si)-SiO<SUB>2</SUB>-Si structures under laser treatment with Q-switched YAG:Nd and carbon dioxide lasers. The photo-thermo-chemical reaction of Co with Si has a threshold character. No changes in optical properties of (Co plus Si) mixture was observed up to intensities of carbon dioxide laser radiation 2 MW/cm<SUP>2</SUP>. At larger intensities the reflection coefficient R decreases from 70% to 45% with increasing of the intensity up to 8 MW/cm<SUP>2</SUP>. When this multilayer structure is irradiated with Q-switched YAG:Nd laser with radiation intensity from 14 MW/cm<SUP>2</SUP> to 53 MW/cm<SUP>2</SUP>, the magnitude of reflection coefficient returns to its initial value 70%. It means that the information recorded by carbon-dioxide laser is erased. Calculations of the temperature field during irradiation with carbon-dioxide and YAG:Nd laser showed that the phase transition from mixture (Co plus Si) to CoSi<SUB>2</SUB> caused by irradiation with carbon-dioxide laser results in recording of information, whereas the thermal impact caused by irradiation with YAG:Nd laser results in amorphization of CoSi<SUB>2</SUB> and erasing of information.
The optical properties of SiO<SUB>2</SUB>-(Co plus Si)-SiO<SUB>2</SUB>-Si structures studied by treatment with Q-switched YAG:Nd and carbon dioxide lasers are presented. The photo-thermo- chemical reaction of Co with Si has a threshold character. No change in optical properties of (Co plus Si) mixture was observed up to 2 MW/cm<SUP>2</SUP> intensities of carbon dioxide laser radiation. A decrease of the reflection coefficient R from 70% to 45% is observed as the intensity is increased up to 8 MW/cm<SUP>2</SUP>. When this multilayer structure is subject to Q-switched YAG:Nd laser radiation of the intensity from 14 MW/cm<SUP>2</SUP> to 53 MW/cm<SUP>2</SUP>, the magnitude of the reflection coefficient returns to its initial value 70%. It means that information recorded by carbon dioxide laser is erased. Calculations of the temperature field during irradiation with carbon dioxide and YAG:Nd laser showed that the phase transition from mixture (Co plus Si) to CoSi<SUB>2</SUB> caused by carbon dioxide laser irradiation results in recording of information, whereas the thermal impact caused by YAG:Nd laser irradiation results in amorphization of CoSi<SUB>2</SUB> and erasing of information.
The present paper contains theoretical investigation or the possibili iy 'oritr:'1i1n, the impurity concentration distribution iribLue ci JI!t £1e1.d—rrn u t,iit tLL.it1L(Jfl equin is aen into account . The Three , acting on impar ty atoms , results roii the temperature gradient or the crystalline lattice. The expression ror heat or transport Is obtained rrorn rnicroscopc theory. Calculations ror concrete impurities show that concentration of impurities near maximum temperature can either increase (0, In, Sb) or decrease (B, P3 C) , deieni.rig on the erfeotive S1ZCS 01° the impurity atois and on their interaction With crystal lattice. Calculation UP B and Sb Iflipurities ifl • SiliCOfl at Ufliroflhl fld equal their initial concentration IS perrorned. Redistribution or these impurltles arter temperature 1eld With maximal temperature at the crystal sarrce 1s appli ed resui ts In creation or p—n junction near the surrace. Similarly, the p—n—p structure ifl volume of the crystal is created w:er tb temperature maximum is located there . Strongly absorbed laser radiation can be used to reach appropriate temperature gradient near the surrace.