Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressur...Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressure fluctuations obtained from a gas liquid solid three phase self aspirated reversed flow jet loop reactor,respectively.The results indicate that the local fractal dimensions and the local largest Lyapunov exponents in both the jet region and the tubular region inside the draft tube increase with the increase in the jet liquid flowrates and the solid loadings,the local fractal dimension profiles are similar to those of the largest Lyapunov exponent,the local largest lyapunov exponents are positive for all cases,and the flow behavior of such a reactor is chaotic.The local nonlinear characteristic parameters such as the local fractal dimension and the local largest Lyapunov exponent could be applied to further study the flow properties such as the flow regime transitions and flow structures of this three phase jet loop reactor.展开更多
Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relat...Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relationship between torus bifurcation and some complex dynamics. Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system. Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence. It is also found that chaos has close relationship with various instability scenarios of power systems. Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.展开更多
Maceral composition and aromatic compounds were determined on columnsamples to study the peat-forming environments of Permian coal seam 2 and Carboniferouscoal seam 9^(-2) from the Xingtai coalfield,China.The macerals...Maceral composition and aromatic compounds were determined on columnsamples to study the peat-forming environments of Permian coal seam 2 and Carboniferouscoal seam 9^(-2) from the Xingtai coalfield,China.The macerals were dominated by inertinitein seam 2 and by vitrinite in seam 9^(-2).Three maceral groups were selected as indicatorsof peat-forming environments.Two triangle diagrams were drawn based on the indicatorsto explicate the peat-forming environments of permian seam 2 and Carboniferousseam 9^(-2).The results indicate that the peat of carboniferous seam 9^(-2) formed dominantlyin wet swamps,whereas the peat of Permian seam 2 formed dominantly in dry swampsand open moor environments.展开更多
An essential annulus A properly imbedded in a 3-manifold M is said to be spanning with respect to a Hereaard splitting VUFW of M if the two components of A are lying in A and separately and A intersects the Heegaard s...An essential annulus A properly imbedded in a 3-manifold M is said to be spanning with respect to a Hereaard splitting VUFW of M if the two components of A are lying in A and separately and A intersects the Heegaard surface F in one circle. In this paper,a sufficient and necessary condition that there is a spanning annulus A in a 3-manifold M with respect to the Heegaard splitting VUFW is given.展开更多
Thermophoresis is an important mechanism of micro-particle transport due to temperature gradients in the surrounding medium.It has numerous applications,especially in the field of aerosol technology.This study has num...Thermophoresis is an important mechanism of micro-particle transport due to temperature gradients in the surrounding medium.It has numerous applications,especially in the field of aerosol technology.This study has numerically investigated the thermophoretic deposition efficiency of particles in a laminar gas flow in a concentric annulus using the critical trajectory method.The governing equations are the momentum and energy equations for the gas and the particle equations of motion.The effects of the annulus size,particle diameter,the ratio of inner to outer radius of tube and wall temperature on the deposition efficiency were studied for both developing and fully-developed flows.Simulation results suggest that thermophoretic deposition increases by increasing thermal gradient,deposition distance,and the ratio of inner to outer radius,but decreases with increasing particle size.It has been found that by taking into account the effect of developing flow at the entrance region,higher deposition efficiency was obtained,than fully developed flow.展开更多
In considering next-nearest neighbor (NNN) coupling, we numerically investigate the magnetoelastic instability in ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. Th...In considering next-nearest neighbor (NNN) coupling, we numerically investigate the magnetoelastic instability in ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. The results indicate that, for antiferromagnetic NNN coupling J2, there may be a critical value J2^c, at which the ground state is dimerized for arbitrary lattice spring constant and beyond and below which the magnetoelastic instability behavior is different from each other. The values of J2^c are irrelevant to the system size. For ferromagnetic NNN coupling, only continuous transition is present from dimerized phase to uniform phase as lattice spring constant is increased.展开更多
Based on the fractal theory, the spatial structure of China's vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1) The relationships between size and frequency o...Based on the fractal theory, the spatial structure of China's vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1) The relationships between size and frequency of patch area and patch shape index exist objectively for China's vegetation. 2) The relationships between perimeter and area exist objectively for China's vegetation. 3) The fractal dimension of evergreen needleleaf forests on mountains in subtropical and tropical zones is the largest, while the smallest for deciduous broadleafand evergreen needleleaf mixed forests in temperate zone, reflecting the most complex spatial structure for evergreen needleleaf forests on mountains in subtropical and tropical zones and the simplest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone. 4) The fractal dimensions of China's vegetation types tend to decrease from thc subtropics to both sides. 5) The stability of spatial structure of deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone is the largest, while the smallest for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards, reflecting the steadiest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone and the most unstable for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards in spatial structure. 6) The stability of spatial structure of China's vegetation tends to decrease from the temperate zone to both sides, it is significantly pertinent to understand the formation, evolution, dynamics and complexity rule of ecosystem of vegetation.展开更多
Each nationality has formed unique ethnic culture in the long history. Ethnic culture is spatially reflected byethnic distribution. The distribution of nationalities is influenced by ethnic history, culture, society a...Each nationality has formed unique ethnic culture in the long history. Ethnic culture is spatially reflected byethnic distribution. The distribution of nationalities is influenced by ethnic history, culture, society and religion, alsoaffected by regional physical setting. This paper analyzes the relationship between ethnic distribution pattern and naturalsetting with contrast analytical method. The digital elevation model (DEM) is established on basis of contour map on ascale of 1:250,000 in the Nujiang River basin, Yunnan Province by ArcGIS, a Geographic Information System (GIS)software. Based on DEM, the spatial analysis and statistical function of GIS, the landscape patterns of populationdistribution of the selected minorities is described, and 4 sub-regions are divided in the Nujiang River basin of YunnanProvince while the features and disparity of landscape pattern and its forming mechanism are discussed, along withhistorical and archaeological data. The conclusions are as follow: (1) The ethnic distribution is mosaic in the matrix ofother racial distribution, and have a distinct spatial correlation. (2) For the difference in cultivation between differentnationalities, certain nationality lived in the area suitable for production mode of its own and coincident with appropriategeographical setting. (3) The spatial distribution of settlement spots of the minorities is controlled by the convenience ofwater supply. The landscape pattern of ethnic distribution is closely relative to natural environment.展开更多
By employing dynamic Monte Carlo simulations, we investigate a coil-to-toroid transition of self-attractive semiflexible polymers and the spatial distributions of nanoparticles in self- attractive semiflexible polymer...By employing dynamic Monte Carlo simulations, we investigate a coil-to-toroid transition of self-attractive semiflexible polymers and the spatial distributions of nanoparticles in self- attractive semiflexible polymer/nanoparticle composites. The conformation of self-attractive semiflexible polymers depends on bending energy and self-attractive interactions between monomers in polymer chains. A three-stage process of toroid formation for self-attractive semiflexible chains is shown: several isolated toroids, a loose toroid structure, and a compact toroid structure. Utilizing the compact toroid conformations of self-attractive semiflexible chains, we can control effectively the spatial distributions of nanoparticles in self-attractive semiflexible polymer nanocomposites, and an unconventional toroid structure of nanoparti- cles is observed.展开更多
With the ability of representing the association and inner-feedback between plant morphological structure and physiological functions, functional-structural plant modeling (FSPM) approach has been used in many works...With the ability of representing the association and inner-feedback between plant morphological structure and physiological functions, functional-structural plant modeling (FSPM) approach has been used in many works, trying to better understand the mechanisms of integrating plant functions and its structure, and their communication with environmental factors. To do so, an FSPM of rice seedling was developed in this study, including structural morphogenetic model, photosynthetic model and biomass partitioning module. It can thus describe the developmental course of the rice structure dynamically based on the processes of biomass producing and partitioning. Furthermore, the processes of nitrogen metabolism, which influence the N content and growth dynamics of the virtual rice, were also considered. The model was developed with L-system on a platform established with Java programming language, which took over the parsing and visualization of the L-system strings to 3D objects using Java 3D extended library. The physiological processes in the model can be modified and further improved to gradually meet the needs for modeling the whole life cycle of rice, e.g., considering the respiration, and interaction with other environmental factors like CO2, temperature, etc.. The model was developed to provide a platform to systematically study and understand how plant systems like rice seedling work. The model and the virtualization platform can be expanded to provide decision support on N fertilizer application for the rice seedling and the other crops.展开更多
Solid concentration and particle velocity distributions in the transition section of a Ф 200 mm turbulent fluidized bed (TFB) and a q5200 mrn annulus turbulent fluidized bed (A-TFB) with a Ф 50 mm central standp...Solid concentration and particle velocity distributions in the transition section of a Ф 200 mm turbulent fluidized bed (TFB) and a q5200 mrn annulus turbulent fluidized bed (A-TFB) with a Ф 50 mm central standpipe were measured using a PVBD optical probe. It is concluded that in turbulent regime, the axial distribution of solid concentration in A-TFB was similar to that in TFB, but the former had a shorter transition section. The axial solid concentration distribution, probability density, and power spectral distributions revealed that the standpipe hin- dered the turbulence of gas-solid two-phase flow at a low superficial gas velocity. Consequently, the bottom flow of A-TFB approached the bubbling fluidization pattern. By contrast, the standpipe facilitated the turbulence at a high superficial gas velocity, thus making the bottom flow of A-TFB approach the fast fluidization pattern. Both the particle velocity and solid concentration distribution presented a unimodal distribution in A-TFB and TFB. However, the standpipe at a high gas velocity and in the transition or dilute phase section significantly affected the radial distribution of flow parameters, presenting a bimodal distribution with particle concentration higher near the internal and external walls and in downward flow. Conversely, particle concentration in the middle an- nulus area was lower, and particles flowed upward. This result indicated that the standpipe destroyed the coreannular structure of TFB in the transition and dilute phase sections at a high gas velocity and also improved the particle distribution of TFB. In conclusion, the standpipe improved the fluidization quality and flow homogeneity at high gas velocity and in the transition or dilute phase section, but caused opposite phenomena at low gas velocity and in the dense-phase section.展开更多
Ring polymer molecular dynamics(RPMD)calculations for the C(^(1)D)+H_(2)reaction are performed on the Zhang-Ma-Bian ab initio potential energy surfaces(PESs)recently constructed by our group,which are unique in very g...Ring polymer molecular dynamics(RPMD)calculations for the C(^(1)D)+H_(2)reaction are performed on the Zhang-Ma-Bian ab initio potential energy surfaces(PESs)recently constructed by our group,which are unique in very good descriptions of the regions around conical intersections and of van der Waals(vdW)interactions.The calculated reaction thermal rate coefficients are in very good agreement with the latest experimental results.The rate coefficients obtained from the ground˜a^(1)A′ZMB-a PES are much larger than those from the previous RKHS PES,which can be attributed to that the vdW saddles on our PESs have very different dynamical effects from the vdW wells on the previous PESs,indicating that the RPMD approach is able to include dynamical effects of the topological structures caused by vdW interactions.The importance of the excited˜b^(1)A′′ZMB-b PES and quantum effects in the title reaction is also underscored.展开更多
A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman tr...A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.展开更多
文摘Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressure fluctuations obtained from a gas liquid solid three phase self aspirated reversed flow jet loop reactor,respectively.The results indicate that the local fractal dimensions and the local largest Lyapunov exponents in both the jet region and the tubular region inside the draft tube increase with the increase in the jet liquid flowrates and the solid loadings,the local fractal dimension profiles are similar to those of the largest Lyapunov exponent,the local largest lyapunov exponents are positive for all cases,and the flow behavior of such a reactor is chaotic.The local nonlinear characteristic parameters such as the local fractal dimension and the local largest Lyapunov exponent could be applied to further study the flow properties such as the flow regime transitions and flow structures of this three phase jet loop reactor.
基金Supported by the Special Fund of the National Fundamental Research (No. 2004CB217904)National Natural Science Foundation of China (No. 50595413)Program for New Century Excellent Talents in Universities, Fok Ying Tung Education Foundation (No.104019 )Foundation for the Authors of National Excellent Doctoral Dissertation (No. 200439) ,Key Project of Chinese Ministry of Education (No. 10047).
文摘Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relationship between torus bifurcation and some complex dynamics. Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system. Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence. It is also found that chaos has close relationship with various instability scenarios of power systems. Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.
基金Supported by the National Natural Science Foundation of China(40773040)the National Basic Research Program of China (2003CB214607)
文摘Maceral composition and aromatic compounds were determined on columnsamples to study the peat-forming environments of Permian coal seam 2 and Carboniferouscoal seam 9^(-2) from the Xingtai coalfield,China.The macerals were dominated by inertinitein seam 2 and by vitrinite in seam 9^(-2).Three maceral groups were selected as indicatorsof peat-forming environments.Two triangle diagrams were drawn based on the indicatorsto explicate the peat-forming environments of permian seam 2 and Carboniferousseam 9^(-2).The results indicate that the peat of carboniferous seam 9^(-2) formed dominantlyin wet swamps,whereas the peat of Permian seam 2 formed dominantly in dry swampsand open moor environments.
文摘An essential annulus A properly imbedded in a 3-manifold M is said to be spanning with respect to a Hereaard splitting VUFW of M if the two components of A are lying in A and separately and A intersects the Heegaard surface F in one circle. In this paper,a sufficient and necessary condition that there is a spanning annulus A in a 3-manifold M with respect to the Heegaard splitting VUFW is given.
文摘Thermophoresis is an important mechanism of micro-particle transport due to temperature gradients in the surrounding medium.It has numerous applications,especially in the field of aerosol technology.This study has numerically investigated the thermophoretic deposition efficiency of particles in a laminar gas flow in a concentric annulus using the critical trajectory method.The governing equations are the momentum and energy equations for the gas and the particle equations of motion.The effects of the annulus size,particle diameter,the ratio of inner to outer radius of tube and wall temperature on the deposition efficiency were studied for both developing and fully-developed flows.Simulation results suggest that thermophoretic deposition increases by increasing thermal gradient,deposition distance,and the ratio of inner to outer radius,but decreases with increasing particle size.It has been found that by taking into account the effect of developing flow at the entrance region,higher deposition efficiency was obtained,than fully developed flow.
文摘In considering next-nearest neighbor (NNN) coupling, we numerically investigate the magnetoelastic instability in ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. The results indicate that, for antiferromagnetic NNN coupling J2, there may be a critical value J2^c, at which the ground state is dimerized for arbitrary lattice spring constant and beyond and below which the magnetoelastic instability behavior is different from each other. The values of J2^c are irrelevant to the system size. For ferromagnetic NNN coupling, only continuous transition is present from dimerized phase to uniform phase as lattice spring constant is increased.
基金Under the auspices of the National Natural Science Foundation of China (No.40301002, No. 40335046)
文摘Based on the fractal theory, the spatial structure of China's vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1) The relationships between size and frequency of patch area and patch shape index exist objectively for China's vegetation. 2) The relationships between perimeter and area exist objectively for China's vegetation. 3) The fractal dimension of evergreen needleleaf forests on mountains in subtropical and tropical zones is the largest, while the smallest for deciduous broadleafand evergreen needleleaf mixed forests in temperate zone, reflecting the most complex spatial structure for evergreen needleleaf forests on mountains in subtropical and tropical zones and the simplest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone. 4) The fractal dimensions of China's vegetation types tend to decrease from thc subtropics to both sides. 5) The stability of spatial structure of deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone is the largest, while the smallest for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards, reflecting the steadiest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone and the most unstable for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards in spatial structure. 6) The stability of spatial structure of China's vegetation tends to decrease from the temperate zone to both sides, it is significantly pertinent to understand the formation, evolution, dynamics and complexity rule of ecosystem of vegetation.
文摘Each nationality has formed unique ethnic culture in the long history. Ethnic culture is spatially reflected byethnic distribution. The distribution of nationalities is influenced by ethnic history, culture, society and religion, alsoaffected by regional physical setting. This paper analyzes the relationship between ethnic distribution pattern and naturalsetting with contrast analytical method. The digital elevation model (DEM) is established on basis of contour map on ascale of 1:250,000 in the Nujiang River basin, Yunnan Province by ArcGIS, a Geographic Information System (GIS)software. Based on DEM, the spatial analysis and statistical function of GIS, the landscape patterns of populationdistribution of the selected minorities is described, and 4 sub-regions are divided in the Nujiang River basin of YunnanProvince while the features and disparity of landscape pattern and its forming mechanism are discussed, along withhistorical and archaeological data. The conclusions are as follow: (1) The ethnic distribution is mosaic in the matrix ofother racial distribution, and have a distinct spatial correlation. (2) For the difference in cultivation between differentnationalities, certain nationality lived in the area suitable for production mode of its own and coincident with appropriategeographical setting. (3) The spatial distribution of settlement spots of the minorities is controlled by the convenience ofwater supply. The landscape pattern of ethnic distribution is closely relative to natural environment.
文摘By employing dynamic Monte Carlo simulations, we investigate a coil-to-toroid transition of self-attractive semiflexible polymers and the spatial distributions of nanoparticles in self- attractive semiflexible polymer/nanoparticle composites. The conformation of self-attractive semiflexible polymers depends on bending energy and self-attractive interactions between monomers in polymer chains. A three-stage process of toroid formation for self-attractive semiflexible chains is shown: several isolated toroids, a loose toroid structure, and a compact toroid structure. Utilizing the compact toroid conformations of self-attractive semiflexible chains, we can control effectively the spatial distributions of nanoparticles in self-attractive semiflexible polymer nanocomposites, and an unconventional toroid structure of nanoparti- cles is observed.
文摘With the ability of representing the association and inner-feedback between plant morphological structure and physiological functions, functional-structural plant modeling (FSPM) approach has been used in many works, trying to better understand the mechanisms of integrating plant functions and its structure, and their communication with environmental factors. To do so, an FSPM of rice seedling was developed in this study, including structural morphogenetic model, photosynthetic model and biomass partitioning module. It can thus describe the developmental course of the rice structure dynamically based on the processes of biomass producing and partitioning. Furthermore, the processes of nitrogen metabolism, which influence the N content and growth dynamics of the virtual rice, were also considered. The model was developed with L-system on a platform established with Java programming language, which took over the parsing and visualization of the L-system strings to 3D objects using Java 3D extended library. The physiological processes in the model can be modified and further improved to gradually meet the needs for modeling the whole life cycle of rice, e.g., considering the respiration, and interaction with other environmental factors like CO2, temperature, etc.. The model was developed to provide a platform to systematically study and understand how plant systems like rice seedling work. The model and the virtualization platform can be expanded to provide decision support on N fertilizer application for the rice seedling and the other crops.
基金Supported by the National Natural Science Foundation of China(U1361112,U1162125)
文摘Solid concentration and particle velocity distributions in the transition section of a Ф 200 mm turbulent fluidized bed (TFB) and a q5200 mrn annulus turbulent fluidized bed (A-TFB) with a Ф 50 mm central standpipe were measured using a PVBD optical probe. It is concluded that in turbulent regime, the axial distribution of solid concentration in A-TFB was similar to that in TFB, but the former had a shorter transition section. The axial solid concentration distribution, probability density, and power spectral distributions revealed that the standpipe hin- dered the turbulence of gas-solid two-phase flow at a low superficial gas velocity. Consequently, the bottom flow of A-TFB approached the bubbling fluidization pattern. By contrast, the standpipe facilitated the turbulence at a high superficial gas velocity, thus making the bottom flow of A-TFB approach the fast fluidization pattern. Both the particle velocity and solid concentration distribution presented a unimodal distribution in A-TFB and TFB. However, the standpipe at a high gas velocity and in the transition or dilute phase section significantly affected the radial distribution of flow parameters, presenting a bimodal distribution with particle concentration higher near the internal and external walls and in downward flow. Conversely, particle concentration in the middle an- nulus area was lower, and particles flowed upward. This result indicated that the standpipe destroyed the coreannular structure of TFB in the transition and dilute phase sections at a high gas velocity and also improved the particle distribution of TFB. In conclusion, the standpipe improved the fluidization quality and flow homogeneity at high gas velocity and in the transition or dilute phase section, but caused opposite phenomena at low gas velocity and in the dense-phase section.
基金supported by the National Natural Science Foundation of China(No.21773251 and No.21973098)the Youth Innovation Promotion Association CAS(No.2018045)the Beijing National Laboratory for Molecular Sciences。
文摘Ring polymer molecular dynamics(RPMD)calculations for the C(^(1)D)+H_(2)reaction are performed on the Zhang-Ma-Bian ab initio potential energy surfaces(PESs)recently constructed by our group,which are unique in very good descriptions of the regions around conical intersections and of van der Waals(vdW)interactions.The calculated reaction thermal rate coefficients are in very good agreement with the latest experimental results.The rate coefficients obtained from the ground˜a^(1)A′ZMB-a PES are much larger than those from the previous RKHS PES,which can be attributed to that the vdW saddles on our PESs have very different dynamical effects from the vdW wells on the previous PESs,indicating that the RPMD approach is able to include dynamical effects of the topological structures caused by vdW interactions.The importance of the excited˜b^(1)A′′ZMB-b PES and quantum effects in the title reaction is also underscored.
文摘A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.