1,605,291 research outputs found
Existence of a critical point in the phase diagram of the ideal relativistic neutral Bose gas
We explore the phase transitions of the ideal relativistic neutral Bose gas
confined in a cubic box, without assuming the thermodynamic limit nor
continuous approximation. While the corresponding non-relativistic canonical
partition function is essentially a one-variable function depending on a
particular combination of temperature and volume, the relativistic canonical
partition function is genuinely a two-variable function of them. Based on an
exact expression of the canonical partition function, we performed numerical
computations for up to hundred thousand particles. We report that if the number
of particles is equal to or greater than a critical value, which amounts to
7616, the ideal relativistic neutral Bose gas features a spinodal curve with a
critical point. This enables us to depict the phase diagram of the ideal Bose
gas. The consequent phase transition is first-order below the critical pressure
or second-order at the critical pressure. The exponents corresponding to the
singularities are 1/2 and 2/3 respectively. We also verify the recently
observed `Widom line' in the supercritical region.Comment: 1+25 pages, 6 B/W figures: Comment on the Widom line added. Minor
improvement. Version to appear in `New Journal of Physics
Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class
The probability P(alpha, N) that search algorithms for random Satisfiability
problems successfully find a solution is studied as a function of the ratio
alpha of constraints per variable and the number N of variables. P is shown to
be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and
exponentially small in N above. The critical behaviour is universal for all
algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon)
alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to
the critical behaviour of random graphs, and the scaling function Phi is
exactly calculated through a mapping onto a diffusion-and-death problem.Comment: 7 pages; 3 figure
Nonlinear evolution and saturation for heavy nuclei in DIS
The nonlinear evolution equation for the scattering amplitude of colour
dipole off the heavy nucleus is solved in the double logarithmic approximation.
It is found that if the initial parton density in a nucleus is smaller then
some critical value, then the scattering amplitude is a function of one scaling
variable inside the saturation region, whereas if it is greater then the
critical value, then the scaling behaviour breaks down. Dependence of the
saturation scale on the number of nucleons is discussed as well.Comment: 12 pages, 1 figur
Effects of Variable Viscosity and Temperature Modulation on Linear Rayleigh-BĂ©nard Convection in Newtonian Dielectric Liquid
The linear Rayleigh-BĂ©nard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied
Effects of Variable Viscosity and Temperature Modulation on Linear Rayleigh-BĂ©nard Convection in Newtonian Dielectric Liquid
The linear Rayleigh-BĂ©nard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied
- …