Precise Phase Structure in Four-fermion Interaction Model on Torus

We investigate finite-size effects on chiral symmetry breaking in a four-fermion interaction model at a finite temperature and a chemical potential. Applying the imaginary time formalism, the thermal quantum field theory is constructed on an S1 in the imaginary time direction. In this paper, the finite-size effect is introduced by a compact S1 spatial direction with a U(1)-valued boundary condition. Thus, we study the model on a $\mathbb {R}^{D-2} \times S^{1} \times S^{1}$ torus. Phase diagrams are obtained by evaluating the local minima of the effective potential in the leading order of the 1/N expansion. From the grand potential, we calculate the particle number density and the pressure, then we illustrate the correspondence with the phase structure. We obtain a stable size for which the sign of the pressure flips from negative to positive as the size decreases. Furthermore, the finite chemical potential expands the parameter range that the stable size exists.

Distribution of Nanoparticles in a Turbulent Taylor–Couette Flow Considering Particle Coagulation and Breakage

In this paper, the dynamic evolution of nanoparticles in a turbulent Taylor–Couette flow was studied by means of a numerical simulation. The initial particle size was 200 nm, and the volume concentration was 1 × 10−5. The Reynolds-averaged N–S equation for Taylor–Couette flow was solved numerically using the realizable k-ε model combined with the standard wall function. The numerical result of the velocity distribution is in good agreement with the experimental results. Additionally, the dynamic equation for the particle number distribution function was solved numerically using the Taylor series expansion moment method (TEMOM). The variation characteristics of particle number density, diameter and polydispersity in the flow were analyzed. The results show that particle breakage is obvious in the region with strong vorticity due to the large shear strength, which leads to a significant change in the particle number density, diameter and polydispersity. Furthermore, the effects of the gap width between two cylinders and the Reynolds number on the distribution of the particle number density, size and polydispersity are discussed.

Gaussian integral by Taylor series and applications

In this paper, we present a solution for a specific Gaussian integral. Introducing a parameter that depends on a n index, we found out a general solution inspired by the Taylor series of a simple function. We demonstrated that this parameter represents the expansion coefficients of this function, a very interesting and new result. We also introduced some Theorems that are proved by mathematical induction. As a test for the solution presented here, we investigated a non-extensive version for the particle number density in Tsallis framework, which enabled us to evaluate the functionality of the method. Besides, solutions for a certain class of the gamma and factorial functions are derived. Moreover, we presented a simple application in fractional calculus. In conclusion, we believe in the relevance of this work because it presents a solution for the Gaussian integral from an unprecedented perspective.

An Improved Particle Number-Based Oil Spill Model Using Implicit Viscosity in Marine Simulator

Improving the physical realism of oil spill scenes in marine simulators can further enhance the emergency response capabilities of officials in charge and crew members and help reduce losses caused by oil spill disasters. In order to uniformly simulate the spreading, drift, breakup, and merging of oil spills at sea, we propose an improved divergence-free position-based fluid (DFPBF) framework based on the particle number density model. In our DFPBF framework, the governing equations for oil spills and ocean are discretized by Lagrangian particles, and the incompressibility of oil spills and ocean is ensured by solving the divergence-free velocity constraint solver and constant density constraint solver. In order to stably simulate the fate and transport of oil spills with higher viscosity, we introduce an implicit viscosity solution scheme for our DFPBF framework. The implicit solver uses a splitting concept to decouple viscosity solve and adopts an implicit scheme to discretize the integration of viscous force. Moreover, our DFPBF framework can ensure a divergence-free velocity field before applying the implicit viscosity scheme, which avoids the undesired bulk viscosity effects. The simulation results show that our DFPBF framework can stably simulate oil spills of various viscosities, especially high-viscosity crude oils.

CoFlame: A refined and validated numerical algorithm for modeling sooting laminar coflow diffusion flames

Mitigation of soot emissions from combustion devices is a global concern. For example, recent EURO 6 regulations for vehicles have placed stringent limits on soot emissions. In order to allow design engineers to achieve the goal of reduced soot emissions, they must have the tools to so. Due to the complex nature of soot formation, which includes growth and oxidation, detailed numerical models are required to gain fundamental insights into the mechanisms of soot formation. A detailed description of the CoFlame FORTRAN code which models sooting laminar coflow diffusion flames is given. The code solves axial and radial velocity, temperature, species conservation, and soot aggregate and primary particle number density equations. The sectional particle dynamics model includes nucleation, PAH condensation and HACA surface growth, surface oxidation, coagulation, fragmentation, particle diffusion, and thermophoresis. The code utilizes a distributed memory parallelization scheme with strip-domain decomposition. The public release of the CoFlame code, which has been refined in terms of coding structure, to the research community accompanies this paper. CoFlame is validated against experimental data for reattachment length in an axi-symmetric pipe with a sudden expansion, and ethylene–air and methane–air diffusion flames for multiple soot morphological parameters and gas-phase species. Finally, the parallel performance and computational costs of the code is investigated.

CoFlame: A refined and validated numerical algorithm for modeling sooting laminar coflow diffusion flames

Mitigation of soot emissions from combustion devices is a global concern. For example, recent EURO 6 regulations for vehicles have placed stringent limits on soot emissions. In order to allow design engineers to achieve the goal of reduced soot emissions, they must have the tools to so. Due to the complex nature of soot formation, which includes growth and oxidation, detailed numerical models are required to gain fundamental insights into the mechanisms of soot formation. A detailed description of the CoFlame FORTRAN code which models sooting laminar coflow diffusion flames is given. The code solves axial and radial velocity, temperature, species conservation, and soot aggregate and primary particle number density equations. The sectional particle dynamics model includes nucleation, PAH condensation and HACA surface growth, surface oxidation, coagulation, fragmentation, particle diffusion, and thermophoresis. The code utilizes a distributed memory parallelization scheme with strip-domain decomposition. The public release of the CoFlame code, which has been refined in terms of coding structure, to the research community accompanies this paper. CoFlame is validated against experimental data for reattachment length in an axi-symmetric pipe with a sudden expansion, and ethylene–air and methane–air diffusion flames for multiple soot morphological parameters and gas-phase species. Finally, the parallel performance and computational costs of the code is investigated.

Assessing relative contributions of PAHs to soot mass by reversible heterogeneous nucleation and condensation

Given the recent EURO 6 regulations, which include limits on particle number density (and hence size) for soot emissions from land vehicles, soot models must be capable of accurately predicting soot particle sizes. Previous modeling work has demonstrated the importance of the relative strengths of nucleation and condensation in predicting soot primary particle size. Due to this importance, a fundamental reversible model for nucleation and condensation, called the reversible PAH clustering (RPC) model, was developed in previous work through the use of statistical mechanics and the results from several recent works. In the present work, the RPC model is enhanced to include multiple nucleation (or dimerization) events from 6 different PAH size groups, resulting in 21 unique dimer pairs. In addition, a soot PAH tracking model is developed to track the amount of each PAH size group within soot particles. The addition of this model resulted in reduced computation times and the ability to investigate PAH-PAH reactions within soot particles. The results of the enhanced RPC model demonstrate that smaller PAHs are most important for the nucleation process, while small and large PAHs are important for the condensation process. These results are shown to be due to the relatively lower reversibility of condensation versus the nucleation process. These findings are discussed in light of recent experimental results in the literature and are shown to be well supported. Keywords: reversibility, PAH nucleation, PAH condensation, laminar diffusion flame, soot model

Assessing relative contributions of PAHs to soot mass by reversible heterogeneous nucleation and condensation

Given the recent EURO 6 regulations, which include limits on particle number density (and hence size) for soot emissions from land vehicles, soot models must be capable of accurately predicting soot particle sizes. Previous modeling work has demonstrated the importance of the relative strengths of nucleation and condensation in predicting soot primary particle size. Due to this importance, a fundamental reversible model for nucleation and condensation, called the reversible PAH clustering (RPC) model, was developed in previous work through the use of statistical mechanics and the results from several recent works. In the present work, the RPC model is enhanced to include multiple nucleation (or dimerization) events from 6 different PAH size groups, resulting in 21 unique dimer pairs. In addition, a soot PAH tracking model is developed to track the amount of each PAH size group within soot particles. The addition of this model resulted in reduced computation times and the ability to investigate PAH-PAH reactions within soot particles. The results of the enhanced RPC model demonstrate that smaller PAHs are most important for the nucleation process, while small and large PAHs are important for the condensation process. These results are shown to be due to the relatively lower reversibility of condensation versus the nucleation process. These findings are discussed in light of recent experimental results in the literature and are shown to be well supported. Keywords: reversibility, PAH nucleation, PAH condensation, laminar diffusion flame, soot model