This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin model...This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin models.DSR extends Einstein's special relativity by introducing an additional invariant scale—the Planck energy—leading to modified energy-momentum relations that encode potential quantum-gravitational effects at ultra-high energies.In this context,we derive the modified Dirac equations for both DSR scenarios and analytically determine the corresponding energy spectra.These spectra are subsequently used to compute the partition function and key thermodynamic quantities,including specific heat,by employing the Euler-Maclaurin formula to facilitate an efficient approximation of the partition function.The analysis is restricted to the positive-energy sector,enabled by the exact Foldy-Wouthuysen transformation,which effectively decouples positive and negative energy states.The findings reveal that Planck-scale deformation parameters induce significant modifications in the energy spectrum and thermodynamic behavior of the Dirac oscillator in each DSR framework,thereby offering valuable insights into possible observable imprints of quantum gravitational phenomena in relativistic quantum systems.展开更多
In the context of advancing towards dual carbon goals,numerous factories are actively engaging in energy efficiency upgrades and transformations.To accurately pinpoint energy efficiency bottlenecks within factories an...In the context of advancing towards dual carbon goals,numerous factories are actively engaging in energy efficiency upgrades and transformations.To accurately pinpoint energy efficiency bottlenecks within factories and prioritize renovation sequences,it is crucial to conduct comprehensive evaluations of the energy performance across various workshops.Therefore,this paper proposes an evaluation model for workshop energy efficiency based on the drive-state-response(DSR)framework combined with the fuzzy BORDA method.Firstly,an in-depth analysis of the relationships between different energy efficiency indicators was conducted.Based on the DSR model,evaluation criteria were selected from three dimensions-drive factors,state characteristics,and response measures-to establish a robust energy efficiency indicator system.Secondly,three distinct assessment techniques were selected:Grey Relational Analysis(GRA),Entropy Weight Method(EWM),and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)forming a diversified set of evaluation methods.Subsequently,by introducing the fuzzy BORDA method,a comprehensive energy efficiency evaluation model was developed,aimed at quantitatively ranking the energy performance status of each workshop.Using a real-world factory as a case study,applying our proposed evaluationmodel yielded detailed scores and rankings for each workshop.Furthermore,post hoc testing was performed using the Spearman correlation coefficient,revealing a statistic value of 10.209,which validates the effectiveness and reliability of the proposed evaluation model.This model not only assists in identifying underperforming workshops within the factory but also provides solid data support and a decision-making basis for future energy efficiency optimization strategies.展开更多
基金funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan,Program No.BR24992759。
文摘This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin models.DSR extends Einstein's special relativity by introducing an additional invariant scale—the Planck energy—leading to modified energy-momentum relations that encode potential quantum-gravitational effects at ultra-high energies.In this context,we derive the modified Dirac equations for both DSR scenarios and analytically determine the corresponding energy spectra.These spectra are subsequently used to compute the partition function and key thermodynamic quantities,including specific heat,by employing the Euler-Maclaurin formula to facilitate an efficient approximation of the partition function.The analysis is restricted to the positive-energy sector,enabled by the exact Foldy-Wouthuysen transformation,which effectively decouples positive and negative energy states.The findings reveal that Planck-scale deformation parameters induce significant modifications in the energy spectrum and thermodynamic behavior of the Dirac oscillator in each DSR framework,thereby offering valuable insights into possible observable imprints of quantum gravitational phenomena in relativistic quantum systems.
基金funded by the National Social Science Fund of China(Grant No.23BGL234).
文摘In the context of advancing towards dual carbon goals,numerous factories are actively engaging in energy efficiency upgrades and transformations.To accurately pinpoint energy efficiency bottlenecks within factories and prioritize renovation sequences,it is crucial to conduct comprehensive evaluations of the energy performance across various workshops.Therefore,this paper proposes an evaluation model for workshop energy efficiency based on the drive-state-response(DSR)framework combined with the fuzzy BORDA method.Firstly,an in-depth analysis of the relationships between different energy efficiency indicators was conducted.Based on the DSR model,evaluation criteria were selected from three dimensions-drive factors,state characteristics,and response measures-to establish a robust energy efficiency indicator system.Secondly,three distinct assessment techniques were selected:Grey Relational Analysis(GRA),Entropy Weight Method(EWM),and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)forming a diversified set of evaluation methods.Subsequently,by introducing the fuzzy BORDA method,a comprehensive energy efficiency evaluation model was developed,aimed at quantitatively ranking the energy performance status of each workshop.Using a real-world factory as a case study,applying our proposed evaluationmodel yielded detailed scores and rankings for each workshop.Furthermore,post hoc testing was performed using the Spearman correlation coefficient,revealing a statistic value of 10.209,which validates the effectiveness and reliability of the proposed evaluation model.This model not only assists in identifying underperforming workshops within the factory but also provides solid data support and a decision-making basis for future energy efficiency optimization strategies.
