By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynami...By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some specJal first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.展开更多
High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of...High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second-order at a high temperature T; however at T = 0 they are first- or second-order, depending on whether A/m(0), the ratio of the momentum cutoff A in the fermion-loop integrals to the dynamicalfermion mass m(0) at zero temperature, is less than 3.387 or not. The former condition cannot be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence.展开更多
We have proven the general relations between the gap equations obeyed by dynamical fermion mass and thecorresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion inte...We have proven the general relations between the gap equations obeyed by dynamical fermion mass and thecorresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion interactionmodels. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicitexpressions for the effective potentials at zero temperature in the cases of D = 2,3, and 4 for practical use.展开更多
Numerical investigations of the Darmstadt transonic single stage compressor (DTC), in the Rotor1-Stator1 configuration, aimed at advancing the understanding of the effect of different rotor tip gaps and transition mod...Numerical investigations of the Darmstadt transonic single stage compressor (DTC), in the Rotor1-Stator1 configuration, aimed at advancing the understanding of the effect of different rotor tip gaps and transition modelling on the blade surfaces are presented. Steady three dimensional Reynolds Averaged Navier Stokes (RANS) simulations were performed to obtain the flow fields for the different configurations at different operating conditions using the RANS-Solver TRACE. The stage geometry and the multi-block structured grid were generated by G3DMESH and a grid sensitivity analysis was conducted. For the clearance gap region, a fully gridded special H-grid was chosen. Comparisons were made between the flow characteristic at design speed, representative for a transonic flow regime, and at 65% speed, representative for a subsonic flow regime. The computations were used to analyse the flow phenomena through the tip clearance region for the different configurations and their impact on the performance of the compressor stage.展开更多
The blade tip clearance flow in axial-flow pump is simulated based on three-dimensional N-S equations, RNG k -e turbulence model, and SIMPLEC algorithm. It shows that numerical results agree well with experiment data ...The blade tip clearance flow in axial-flow pump is simulated based on three-dimensional N-S equations, RNG k -e turbulence model, and SIMPLEC algorithm. It shows that numerical results agree well with experiment data measured by 5-hole probe through validation. Flow fields at the blade tip and velocity distribution at the exit of rotor are analyzed in detail. The numerical results show that the increase in tip clearance reduces hydro-head, especially at small flow rate. Experiment equipment is also introduced.展开更多
The author proves that for initial data in a set S ? (H2(?) ∩ H0(?)) × H0(?), 1 1 unbounded in H0(?) × L2(?), the solut...The author proves that for initial data in a set S ? (H2(?) ∩ H0(?)) × H0(?), 1 1 unbounded in H0(?) × L2(?), the solutions of the Cauchy-Dirichlet problem for the 1 dissipative Kirchho? equation Z ?t u ? ν + L 2 | x u|2dx xu + δ?tu = 0 (x ∈ ?, t > 0), ? are global in [0,+∞) and decay exponentially. The functions in S do not satisfy any additional regularity assumption, instead they must satisfy a condition relating their energy with the largest lacuna in their Fourier expansion. The larger is the lacuna the larger is the energy allowed.展开更多
Extensive numerical investigations of the performance and flow structure in an unshrouded tandem-bladed centrifugal compressor are presented in comparison to a conventional compressor.Stage characteristics are explore...Extensive numerical investigations of the performance and flow structure in an unshrouded tandem-bladed centrifugal compressor are presented in comparison to a conventional compressor.Stage characteristics are explored for various tip clearance levels,axial spacings and circumferential clockings.Conventional impeller was modified to tandem-bladed design with no modifications in backsweep angle,meridional gas passage and camber distributions in order to have a true comparison with conventional design.Performance degradation is observed for both the conventional and tandem designs with increase in tip clearance.Linear-equation models for correlating stage characteristics with tip clearance are proposed.Comparing two designs,it is clearly evident that the conventional design shows better performance at moderate flow rates.However;near choke flow,tandem design gives better results primarily because of the increase in throat area.Surge point flow rate also seems to drop for tandem compressor resulting in increased range of operation.展开更多
文摘By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some specJal first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.
文摘High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second-order at a high temperature T; however at T = 0 they are first- or second-order, depending on whether A/m(0), the ratio of the momentum cutoff A in the fermion-loop integrals to the dynamicalfermion mass m(0) at zero temperature, is less than 3.387 or not. The former condition cannot be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence.
文摘We have proven the general relations between the gap equations obeyed by dynamical fermion mass and thecorresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion interactionmodels. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicitexpressions for the effective potentials at zero temperature in the cases of D = 2,3, and 4 for practical use.
基金a part of the Deutsche Forschungsgemeinschaft Joint Research Project FOR-1066
文摘Numerical investigations of the Darmstadt transonic single stage compressor (DTC), in the Rotor1-Stator1 configuration, aimed at advancing the understanding of the effect of different rotor tip gaps and transition modelling on the blade surfaces are presented. Steady three dimensional Reynolds Averaged Navier Stokes (RANS) simulations were performed to obtain the flow fields for the different configurations at different operating conditions using the RANS-Solver TRACE. The stage geometry and the multi-block structured grid were generated by G3DMESH and a grid sensitivity analysis was conducted. For the clearance gap region, a fully gridded special H-grid was chosen. Comparisons were made between the flow characteristic at design speed, representative for a transonic flow regime, and at 65% speed, representative for a subsonic flow regime. The computations were used to analyse the flow phenomena through the tip clearance region for the different configurations and their impact on the performance of the compressor stage.
文摘The blade tip clearance flow in axial-flow pump is simulated based on three-dimensional N-S equations, RNG k -e turbulence model, and SIMPLEC algorithm. It shows that numerical results agree well with experiment data measured by 5-hole probe through validation. Flow fields at the blade tip and velocity distribution at the exit of rotor are analyzed in detail. The numerical results show that the increase in tip clearance reduces hydro-head, especially at small flow rate. Experiment equipment is also introduced.
基金the Funds of the "Italian Ministero della Universit`a e della Ricerca Scientifica eTecnologica"
文摘The author proves that for initial data in a set S ? (H2(?) ∩ H0(?)) × H0(?), 1 1 unbounded in H0(?) × L2(?), the solutions of the Cauchy-Dirichlet problem for the 1 dissipative Kirchho? equation Z ?t u ? ν + L 2 | x u|2dx xu + δ?tu = 0 (x ∈ ?, t > 0), ? are global in [0,+∞) and decay exponentially. The functions in S do not satisfy any additional regularity assumption, instead they must satisfy a condition relating their energy with the largest lacuna in their Fourier expansion. The larger is the lacuna the larger is the energy allowed.
基金the Deanship of Scientific Research,Research Center of College of Engineering, King Saud University for the financial support
文摘Extensive numerical investigations of the performance and flow structure in an unshrouded tandem-bladed centrifugal compressor are presented in comparison to a conventional compressor.Stage characteristics are explored for various tip clearance levels,axial spacings and circumferential clockings.Conventional impeller was modified to tandem-bladed design with no modifications in backsweep angle,meridional gas passage and camber distributions in order to have a true comparison with conventional design.Performance degradation is observed for both the conventional and tandem designs with increase in tip clearance.Linear-equation models for correlating stage characteristics with tip clearance are proposed.Comparing two designs,it is clearly evident that the conventional design shows better performance at moderate flow rates.However;near choke flow,tandem design gives better results primarily because of the increase in throat area.Surge point flow rate also seems to drop for tandem compressor resulting in increased range of operation.
