The upper critical dimension of the Ising model is known to be dc=4,above which critical behavior is regarded to be trivial.We hereby argue from extensive simulations that,in the random-cluster representation,the Isin...The upper critical dimension of the Ising model is known to be dc=4,above which critical behavior is regarded to be trivial.We hereby argue from extensive simulations that,in the random-cluster representation,the Ising model simultaneously exhibits two upper critical dimensions at(d_(c)=4,d_(p)=6),and critical clusters for d≥d_(p),except the largest one,are governed by exponents from percolation universality.We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs.Our findings significantly advance the understanding of the Ising model,which is a fundamental system in many branches of physics.展开更多
An artificial neural network （ANN） model was developed for simulating and predicting critical dimension dc of glass forming alloys. A group of Zr-Al-Ni-Cu and Cu-Zr-Ti-Ni bulk metallic glasses were designed based on...An artificial neural network （ANN） model was developed for simulating and predicting critical dimension dc of glass forming alloys. A group of Zr-Al-Ni-Cu and Cu-Zr-Ti-Ni bulk metallic glasses were designed based on the dc and their de values were predicted by the ANN model. Zr-Al-Ni-Cu and Cu-Zr-Ti-Ni bulk metallic glasses were prepared by injecting into copper mold. The amorphous structures and the determination of the dc of as-cast alloys were ascertained using X-ray diffraction. The results show that the predicted de values of glass forming alloys are in agreement with the corresponding experimental values. Thus the developed ANN model is reliable and adequate for designing the composition and predicting the de of glass forming alloy.展开更多
Developing highly accurate critical dimension standards is a significant task for nanoscale metrology. In this paper, we put forward an alternative approach to fabricate amorphous Si critical dimension structures with...Developing highly accurate critical dimension standards is a significant task for nanoscale metrology. In this paper, we put forward an alternative approach to fabricate amorphous Si critical dimension structures with direct Si lattice calibration in the same frame scanning transmission electron microscopy image. Based on the traceable measurement analysis, the optimized method can provide the same calibration accuracy and increase the fabrication throughput and lower the cost simultaneously, which benefits the application needs in atomic force microscopy(AFM) tip geometry characterization,benchmarking measurement tools, and conducting comparison measurements between different approaches.展开更多
The dynamical behaviors of logistic map（May＇s model） and duffing equation are studied through fractal dimension of time series at different parameters. It is shown that the parameters of dynamical behaviors can be ...The dynamical behaviors of logistic map（May＇s model） and duffing equation are studied through fractal dimension of time series at different parameters. It is shown that the parameters of dynamical behaviors can be identified effectively by the curve of fractal dimension with parameter increments. For further verification, the relation between the fractional dimension of time series and rotational speed can be used to identify critical speed effectively by using this method to a plate Jeffoctt rotor system. The numerical and experimental result indicates that the identification of critical parameters is effective.展开更多
Considering the cosmological constantΛas a thermodynamic pressure and its conjugate quantity as a thermodynamic volume as proposed by Kubiznak and Mann[J.High Energy Phys.1207(2012)033],we discuss the critical behavi...Considering the cosmological constantΛas a thermodynamic pressure and its conjugate quantity as a thermodynamic volume as proposed by Kubiznak and Mann[J.High Energy Phys.1207(2012)033],we discuss the critical behavior of charged AdS black hole in arbitrary dimensions d.In particular,we present a comparative study in terms of the spacetime dimension d and the displacement of critical points controlling the transition between the small and the large black holes.Such behaviors vary nicely in terms of d.Our result shows that the equation of state for a charged Reissner–Nordstrom AdS black hole predicts an universal number given by(2d-5)/(4d-8).The three-dimensional solution is also discussed.展开更多
Studies of critical concentration distribution features of polluted elements of Cd and As in main soil types of China, such as laterite, crimson soil, purplish soil, yellow brown soil, brunisolic soil, black soil, cin...Studies of critical concentration distribution features of polluted elements of Cd and As in main soil types of China, such as laterite, crimson soil, purplish soil, yellow brown soil, brunisolic soil, black soil, cinnamon soil and sierozem revealed that soil types vary in different zones, so do their critical concentrations.The critical concentration has a zonal differentiation with the distribution of soil types from south to north, and from east to west. The critical concentration of Cd increases from south to north (yellow brown soil,brunisolic soil and cinnamon soil),and from east to west (black soil and sierozem). This coincides With changes of climate zones and soil zones. On the contrary, the critical concentration of Asdecreases from south to north and from east to west.展开更多
In this work, a 90-nm critical dimension （CD） technological process in an ArF laser lithography system is simulated, and the swing curves of the CD linewidth changing with photoresist thickness are obtained in the a...In this work, a 90-nm critical dimension （CD） technological process in an ArF laser lithography system is simulated, and the swing curves of the CD linewidth changing with photoresist thickness are obtained in the absence and presence of bottom antireflection coating （BARC）. By analysing the simulation result, it can be found that in the absence of BARC the CD swing curve effect is much bigger than that in the presence of BARC. So, the BARC should be needed for the 90-nm CD manufacture. The optimum resist thickness for 90-nm CD in the presence of BARC is obtained, and the optimizing process in this work can be used for reference in practice.展开更多
We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical ex...We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.展开更多
We study the self-gravitating stars with a linear equation of state, P = aρ, in AdS space, where a is a constant parameter. There exists a critical dimension, beyond which the stars are always stable with any central...We study the self-gravitating stars with a linear equation of state, P = aρ, in AdS space, where a is a constant parameter. There exists a critical dimension, beyond which the stars are always stable with any central energy density; below which there exists a maximal mass configuration for a certain central energy density and when the central energy density continues to increase, the configuration becomes unstable. We find that the critical dimension depends on the parameter a, it runs from d = 11.1429 to 10.1291 as a varies from a = 0 to 1. The lowest integer dimension for a dynamically stable self-gravitating configuration should be d = 12 for any a E [0, 1] rather than d = 11, the latter is the case of self-gravitating radiation configurations in AdS space.展开更多
文摘The upper critical dimension of the Ising model is known to be dc=4,above which critical behavior is regarded to be trivial.We hereby argue from extensive simulations that,in the random-cluster representation,the Ising model simultaneously exhibits two upper critical dimensions at(d_(c)=4,d_(p)=6),and critical clusters for d≥d_(p),except the largest one,are governed by exponents from percolation universality.We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs.Our findings significantly advance the understanding of the Ising model,which is a fundamental system in many branches of physics.
基金Project(50874045)supported by the National Natural Science Foundation of China
文摘An artificial neural network （ANN） model was developed for simulating and predicting critical dimension dc of glass forming alloys. A group of Zr-Al-Ni-Cu and Cu-Zr-Ti-Ni bulk metallic glasses were designed based on the dc and their de values were predicted by the ANN model. Zr-Al-Ni-Cu and Cu-Zr-Ti-Ni bulk metallic glasses were prepared by injecting into copper mold. The amorphous structures and the determination of the dc of as-cast alloys were ascertained using X-ray diffraction. The results show that the predicted de values of glass forming alloys are in agreement with the corresponding experimental values. Thus the developed ANN model is reliable and adequate for designing the composition and predicting the de of glass forming alloy.
基金supported by the National Key Scientific Instrument and Equipment Development Projects of China(Grant No.2014YQ090709)the National Key Research and Development Program of China(Grant No.2016YFA0200902)Major Projects of Science and Technology Commission of Shanghai,China(Grant No.17JC1400800)
文摘Developing highly accurate critical dimension standards is a significant task for nanoscale metrology. In this paper, we put forward an alternative approach to fabricate amorphous Si critical dimension structures with direct Si lattice calibration in the same frame scanning transmission electron microscopy image. Based on the traceable measurement analysis, the optimized method can provide the same calibration accuracy and increase the fabrication throughput and lower the cost simultaneously, which benefits the application needs in atomic force microscopy(AFM) tip geometry characterization,benchmarking measurement tools, and conducting comparison measurements between different approaches.
基金This project is supported by Natural Science Foundation of Xi'an JiaotongUniversity, China, (No.2003025).
文摘The dynamical behaviors of logistic map（May＇s model） and duffing equation are studied through fractal dimension of time series at different parameters. It is shown that the parameters of dynamical behaviors can be identified effectively by the curve of fractal dimension with parameter increments. For further verification, the relation between the fractional dimension of time series and rotational speed can be used to identify critical speed effectively by using this method to a plate Jeffoctt rotor system. The numerical and experimental result indicates that the identification of critical parameters is effective.
文摘Considering the cosmological constantΛas a thermodynamic pressure and its conjugate quantity as a thermodynamic volume as proposed by Kubiznak and Mann[J.High Energy Phys.1207(2012)033],we discuss the critical behavior of charged AdS black hole in arbitrary dimensions d.In particular,we present a comparative study in terms of the spacetime dimension d and the displacement of critical points controlling the transition between the small and the large black holes.Such behaviors vary nicely in terms of d.Our result shows that the equation of state for a charged Reissner–Nordstrom AdS black hole predicts an universal number given by(2d-5)/(4d-8).The three-dimensional solution is also discussed.
文摘Studies of critical concentration distribution features of polluted elements of Cd and As in main soil types of China, such as laterite, crimson soil, purplish soil, yellow brown soil, brunisolic soil, black soil, cinnamon soil and sierozem revealed that soil types vary in different zones, so do their critical concentrations.The critical concentration has a zonal differentiation with the distribution of soil types from south to north, and from east to west. The critical concentration of Cd increases from south to north (yellow brown soil,brunisolic soil and cinnamon soil),and from east to west (black soil and sierozem). This coincides With changes of climate zones and soil zones. On the contrary, the critical concentration of Asdecreases from south to north and from east to west.
基金Project supported by the National Special Program of China (Grant No. 2009ZX02204-008)the National Basic Research Program of China (Grant No. 2007AA01Z333)
文摘In this work, a 90-nm critical dimension （CD） technological process in an ArF laser lithography system is simulated, and the swing curves of the CD linewidth changing with photoresist thickness are obtained in the absence and presence of bottom antireflection coating （BARC）. By analysing the simulation result, it can be found that in the absence of BARC the CD swing curve effect is much bigger than that in the presence of BARC. So, the BARC should be needed for the 90-nm CD manufacture. The optimum resist thickness for 90-nm CD in the presence of BARC is obtained, and the optimizing process in this work can be used for reference in practice.
基金Project supported by the National Natural Science Foundation of China (Grant No.10675021)the New Century Excellent Talents in University of China,the Natural Science Foundation of Anhui Province of China (Grant No.090416224)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20103402110053)
文摘We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.
基金Supported partially by National Natural Science Foundation of China under Grant Nos.10821504 and 10525060Chinese Academy of Sciences under Grant No.KJCX3-SYW-N2
文摘We study the self-gravitating stars with a linear equation of state, P = aρ, in AdS space, where a is a constant parameter. There exists a critical dimension, beyond which the stars are always stable with any central energy density; below which there exists a maximal mass configuration for a certain central energy density and when the central energy density continues to increase, the configuration becomes unstable. We find that the critical dimension depends on the parameter a, it runs from d = 11.1429 to 10.1291 as a varies from a = 0 to 1. The lowest integer dimension for a dynamically stable self-gravitating configuration should be d = 12 for any a E [0, 1] rather than d = 11, the latter is the case of self-gravitating radiation configurations in AdS space.
