A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution ...A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution of the corresponding homogeneous equation that does not change the Lagrange equations. When dynamics is described by momenta and coordinates, this transformation is not the vector potential modification, which does not change expressions for other physical quantities, but a canonical transformation of momentum, which changes expressions for all fimctions of momentum, not changing the Poisson brackets, and, hence, the integrals of motion. The generating function of this transformation must reverse sign under the time-charge reversal. In quantum mechanics the unitary transformation corresponds to this canonical transformation. It also does not change the commutation relations. The phase of this unitary operator also must reverse sign under the time-charge reversal. Examples of necessary vector potentials for some magnetic fields are presented.展开更多
Gradient coil is an essential component of a magnetic resonance imaging(MRI)scanner.To achieve high spatial resolution and imaging speed,a high-efficiency gradient coil with high slew rate is required.In consideration...Gradient coil is an essential component of a magnetic resonance imaging(MRI)scanner.To achieve high spatial resolution and imaging speed,a high-efficiency gradient coil with high slew rate is required.In consideration of the safety and comfort of the patient,the mechanical stability,acoustic noise and peripheral nerve stimulation(PNS)are also need to be concerned for practical use.In our previous work,a high-efficiency whole-body gradient coil set with a hybrid cylindrical-planar structure has been presented,which offers significantly improved coil performances.In this work,we propose to design this transverse gradient coil system with transformed magnetic gradient fields.By shifting up the zero point of gradient fields,the designed new Y-gradient coil could provide enhanced electromagnetic performances.With more uniform coil winding arrangement,the net torque of the new coil is significantly reduced and the generated sound pressure level(SPL)is lower at most tested frequency bands.On the other hand,the new transverse gradient coil designed with rotated magnetic gradient fields produces considerably reduced electric field in the human body,which is important for the use of rapid MR sequences.It's demonstrated that a safer and patient-friendly design could be obtained by using transformed magnetic gradient fields,which is critical for practical use.展开更多
Gradient nanostructured(GNS)metallic materials are commonly achieved by gradient severe plastic de-formation with a gradient of nano-to micro-sized structural units from the surface/boundaries to the center.Certainly,...Gradient nanostructured(GNS)metallic materials are commonly achieved by gradient severe plastic de-formation with a gradient of nano-to micro-sized structural units from the surface/boundaries to the center.Certainly,such GNS can be inversely positioned,which however has not yet been reported.The present work reports a facile method in deformation gradient control to attain inverse gradient nanostructured(iGNS),i.e.,tailoring the cross-section shape,successfully demonstrated in Ti-50.3Ni shape memory alloy(SMA)wire through cold rolling.The microstructure of the rolled wire is characterized by a macroscopic inverse gradient from boundaries to the center—the average sizes of grain and martensite domain evolve from micrometer to nanometer scale.The iGNS leads to a gradient martensitic transforma-tion upon stress,which has been proved to be effectively reversible via in-situ bending scanning electron microscopy(SEM)observations.The iGNS Ti-50.3Ni SMA exhibits quasi-linear superelasticity(SE)in a wide temperature range from 173 to 423 K.Compared to uniform cold rolling,the gradient cold rolling with less overall plasticity further improves SE strain(up to 4.8%)and SE efficiency.In-situ tensiling synchrotron X-ray diffraction(SXRD)analysis reveals the underlying mechanisms of the unique SE in the iGNS SMAs.It provides a new design strategy to realize excellent SE in SMAs and sheds light on the advanced GNS metallic materials.展开更多
The transient mass transter processes in the natural drying of wood particle materials were experimental;y studied A new theory tio determme the mass transfer parameters in the Materials was developed in terms of grad...The transient mass transter processes in the natural drying of wood particle materials were experimental;y studied A new theory tio determme the mass transfer parameters in the Materials was developed in terms of gradient transformation method(GTM).By making use of GTM.Thewater vapour diffusion coefficient and the surtaee emission coefficent of wood chip were expermentally determined both in air phase and in solid phase.It Was found that the internal resistance to water vapour diffusion in the air phase of wood partiele aggregates is around ten to the third power as large as that in common air The drag coefficient was given to quantify the effect The phenomenon of undersurface diffusion in wood partiele bed was quantitatively modelled.The dimensionless Fourier snumber and the Biot's number for mass transfer were theoretically derived.The study showed that Biot's number for the problem investigated was the ratio of the characteristie length of wood partiele bed to the penetrating depth of the undersurface.An analytical solution of the nonlinear goveming equation for water transport process in the aggregates of wood chip was obtained by introducing the variable coefficients measured in the study into the governing equation.The comparison between the analytical solution and the observed moisture content of wood chip showed that the deviation was less than ±7%.The thermophysieal properties of wood particle materials are little known at present.The knowledge provided in the paper will be and in the handling.researeh or engineering application of wood chip.wood shavingsete.展开更多
文摘A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution of the corresponding homogeneous equation that does not change the Lagrange equations. When dynamics is described by momenta and coordinates, this transformation is not the vector potential modification, which does not change expressions for other physical quantities, but a canonical transformation of momentum, which changes expressions for all fimctions of momentum, not changing the Poisson brackets, and, hence, the integrals of motion. The generating function of this transformation must reverse sign under the time-charge reversal. In quantum mechanics the unitary transformation corresponds to this canonical transformation. It also does not change the commutation relations. The phase of this unitary operator also must reverse sign under the time-charge reversal. Examples of necessary vector potentials for some magnetic fields are presented.
基金supported by the Instrument Developing Project of Magnetic Resonance Union of Chinese Academy of Sciences,Grant No.2022GZL002.
文摘Gradient coil is an essential component of a magnetic resonance imaging(MRI)scanner.To achieve high spatial resolution and imaging speed,a high-efficiency gradient coil with high slew rate is required.In consideration of the safety and comfort of the patient,the mechanical stability,acoustic noise and peripheral nerve stimulation(PNS)are also need to be concerned for practical use.In our previous work,a high-efficiency whole-body gradient coil set with a hybrid cylindrical-planar structure has been presented,which offers significantly improved coil performances.In this work,we propose to design this transverse gradient coil system with transformed magnetic gradient fields.By shifting up the zero point of gradient fields,the designed new Y-gradient coil could provide enhanced electromagnetic performances.With more uniform coil winding arrangement,the net torque of the new coil is significantly reduced and the generated sound pressure level(SPL)is lower at most tested frequency bands.On the other hand,the new transverse gradient coil designed with rotated magnetic gradient fields produces considerably reduced electric field in the human body,which is important for the use of rapid MR sequences.It's demonstrated that a safer and patient-friendly design could be obtained by using transformed magnetic gradient fields,which is critical for practical use.
基金supported by the National Natural Science Foundation of China(Grant Nos.52171007,52101166,51931004)the 111 Projects 2.0(Grant No.BP0618008).
文摘Gradient nanostructured(GNS)metallic materials are commonly achieved by gradient severe plastic de-formation with a gradient of nano-to micro-sized structural units from the surface/boundaries to the center.Certainly,such GNS can be inversely positioned,which however has not yet been reported.The present work reports a facile method in deformation gradient control to attain inverse gradient nanostructured(iGNS),i.e.,tailoring the cross-section shape,successfully demonstrated in Ti-50.3Ni shape memory alloy(SMA)wire through cold rolling.The microstructure of the rolled wire is characterized by a macroscopic inverse gradient from boundaries to the center—the average sizes of grain and martensite domain evolve from micrometer to nanometer scale.The iGNS leads to a gradient martensitic transforma-tion upon stress,which has been proved to be effectively reversible via in-situ bending scanning electron microscopy(SEM)observations.The iGNS Ti-50.3Ni SMA exhibits quasi-linear superelasticity(SE)in a wide temperature range from 173 to 423 K.Compared to uniform cold rolling,the gradient cold rolling with less overall plasticity further improves SE strain(up to 4.8%)and SE efficiency.In-situ tensiling synchrotron X-ray diffraction(SXRD)analysis reveals the underlying mechanisms of the unique SE in the iGNS SMAs.It provides a new design strategy to realize excellent SE in SMAs and sheds light on the advanced GNS metallic materials.
文摘The transient mass transter processes in the natural drying of wood particle materials were experimental;y studied A new theory tio determme the mass transfer parameters in the Materials was developed in terms of gradient transformation method(GTM).By making use of GTM.Thewater vapour diffusion coefficient and the surtaee emission coefficent of wood chip were expermentally determined both in air phase and in solid phase.It Was found that the internal resistance to water vapour diffusion in the air phase of wood partiele aggregates is around ten to the third power as large as that in common air The drag coefficient was given to quantify the effect The phenomenon of undersurface diffusion in wood partiele bed was quantitatively modelled.The dimensionless Fourier snumber and the Biot's number for mass transfer were theoretically derived.The study showed that Biot's number for the problem investigated was the ratio of the characteristie length of wood partiele bed to the penetrating depth of the undersurface.An analytical solution of the nonlinear goveming equation for water transport process in the aggregates of wood chip was obtained by introducing the variable coefficients measured in the study into the governing equation.The comparison between the analytical solution and the observed moisture content of wood chip showed that the deviation was less than ±7%.The thermophysieal properties of wood particle materials are little known at present.The knowledge provided in the paper will be and in the handling.researeh or engineering application of wood chip.wood shavingsete.
