具有特殊非齐次项波动方程的处理方法

针对一维非齐次波动方程,介绍了当其自由项具有几种特殊形式时的特殊解法,并举例说明.     

Functional magnetic resonance imaging reference phantom

Functional magnetic resonance imaging (fMRI) is widely used to pinpoint active brain areas. Changes in neuronal activity modulate the local blood oxygenation level, and the associated modulation of the magnetic field homogeneity can be detected with magnetic resonance imaging. Thus, the blood oxygenation level-dependent (BOLD) fMRI indirectly measures neuronal activity. Similar modulation of magnetic field homogeneity was here elicited by other means to generate a BOLD-like change in a new phantom constructed to provide reference activations during fMRI. Magnetic inhomogeneities were produced by applying current to coils located near the phantom containing 1.5 ml of Gd-doped water. The signal-to-noise ratio of the images, produced by gradient-recalled echo-planar imaging, varied between 104 and 107 at a selected voxel when the field was and was not inhomogenized, respectively. The contrast of signals between homogeneous and inhomogeneous conditions was generally stable, except in 3% of time points. During the periods of greatest deviations an observable change would have been detected in a simultaneously measured BOLD signal. Such changes could result from the imaging method or occur through glitches in hardware or alterations in the measurement environment. With identical measurement setups, the phantom could allow comparing intersession or intersubject brain activations.     

Phase diagram and critical fields of organic quasi-1d superconductors in an applied magnetic field

No consensus has been reached about the symmetry of the Bechgaard salts superconducting phase. An RG analysis is in favor of interactions dominant in the singlet channel, but very close and sub-dominant in the triplet channel. We study the properties, in a magnetic field along the b′ direction, of a d-wave singlet phase, as well as of an f-wave triplet phase. Recent data about NMR Knight shift, as well as upper critical fields have brought strong indications about the possible symmetries. We have analyzed theoretically the consequences of these experimental data: our results are in favor of a singlet phase in low field, but of a triplet phase in large fields.     

一种用硬件实现的Bayer格式图像恢复算法

针对传统的双线性Bayer彩色图像恢复算法恢复效果不理想,边界部分不明显,局部图像有团块等问题,提出了一种基于硬件实现的Bayer图像快速插值算法。采用梯度算法对Bayer格式图像绿色通道进行恢复,根据像素点所属的颜色组对蓝色通道进行恢复。实验结果表明,本文算法比双线性法有更好的峰值信噪比(PSNR)值,RGB 3个通道的PSNR值均比双线性法高5 dB以上,而且算法消耗时间比双线性法少,恢复的图像视觉效果更好。实验处理一幅512×512的全彩图像仅需要9.3 ms,完全可以满足实时性的要求,因此,本文算法在对实时性要求高的场合有很好的应用前景。     

Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.     

Automatic Regularization by Quantization in Reducible Representations of CCR: Point-Form Quantum Optics with Classical Sources

Electromagnetic fields are quantized in a manifestly covariant way by means of a class of reducible “center-of-mass N-representations” of the algebra of canonical commutation relations (CCR). The four-potential A _a (x) transforms in these representations as a Hermitian four-vector field in Minkowski four-position space (without change of gauge), but in momentum space it splits into spin-1 massless photons and two massless scalars. What we call quantum optics is the spin-1 sector of the theory. The scalar fields have physical status similar to that of dark matter (spin-1 and spin-0 particle numbers are separately conserved). There are no negative-norm or zero-norm states. Unitary dynamics is given by the point-form interaction picture, with minimal-coupling Hamiltonian constructed from fields that are free on the null-cone boundary of the Milne universe. SL(2,C) transformations as well as the dynamics are represented unitarily in the Hilbert space corresponding to N four-dimensional oscillators. Vacuum is a Bose-Einstein condensate of the N-oscillator gas and is given by any N-oscillator product state annihilated by all annihilation operators. The form of A _a (x) is determined by an analogue of the twistor equation. The same equation guarantees that the set of vacuum states is Poincaré invariant. The formalism is tested on quantum fields produced by pointlike classical sources. Photon statistics is well defined even for pointlike charges, with ultraviolet and infrared regularizations occurring automatically as a consequence of the formalism. The probabilities are not Poissonian but of a Rényi type with α=1−1/N; the Shannon limit N→∞ is an ultraviolet/infrared-regularized Poisson distribution. The average number of photons occurring in Bremsstrahlung splits into two parts: The one due to acceleration, and the one that remains nonvanishing even for inertially moving charges. Classical Maxwell electrodynamics is reconstructed from coherent-state averaged solutions of Heisenberg equations. We show in particular that static pointlike charges polarize vacuum and produce effective charge densities and fields whose form is sensitive to both the choice of representation of CCR and the corresponding vacuum state.     

Enhanced field ionization of water adsorbed on a carbon monoxide-covered, platinum field emitter tip

The influence of carbon monoxide, adsorbed on a platinum field emitter tip, on field ionization of adsorbed water was examined. Ramped field desorption (RFD) measurements of water ionization were performed at 108 K for water layer thicknesses up to 80 ML on a clean or CO-saturated tip surface. In RFD the applied field is ramped linearly in time until water ionization is detected, giving the onset field of ionization. Water ionization yields hydrated hydroxide ions and protons; the hydroxide ions remain within the water layer on the tip, while the hydrated protons are emitted into vacuum. At a low water coverage of 1.5 ML, the CO adlayer substantially reduced the onset field of ionization (that is, facilitated ionization) of water by 40%, from a value of 0.43 V/Å for water on clean Pt to 0.26 V/Å for water on CO-covered Pt. The extent of the reduction gradually diminished with thicker coverages of water and was absent at coverages of 20 ML or greater. The characteristic decay length of the field enhancement was 4.7 ± 1 ML. The results were analyzed with the charge exchange model of ionization kinetics and changes in dipole moments of water adsorbed without and with CO. The analysis reveals that a change in water structure (dipole moment) caused by CO is an important contributor in field enhancement and that the dipole moment for hydrated hydroxide ion in an ice-like layer must be greater than that for bulk ice-like water. The significance of these results with respect to electrochemical oxidation of CO is discussed.     

Confinement of the field electron emission to atomic sites on ultra sharp tips

The spatially controlled field assisted etching method for sharpening metallic tips, in a field ion microscope (FIM), is used to study the evolution of the field emission when the tip apex radius is decreased below 1 nm. Unlike the conventional image formation in a field emission microscope (FEM), we demonstrate that at this scale the field emission is rather confined to atomic sites. A single atom apex fabricated at the end of such tips exhibits an outstanding brightness compared to other atomic tips. The measurements have been repeated for two double atom tips, with different atom-atom separations, and images of atomic field emission localization have also been obtained. We have found that the field emission intensity alternates between adjacent atoms when the applied voltage is gradually increased beyond a threshold value.     

Controlled Space Radiation concept for mesh-free semi-analytical technique to model wave fields in complex geometries

Numerical modelling of the ultrasonic wave propagation is important for Structural Heath Monitoring and System Prognosis problems. In order to develop intelligent and adaptive structures with embedded damage detector and classifier mechanisms, detailed understanding of scattered wave fields due to anomaly in the structure is inevitably required. A detailed understanding of the problem demands a good modelling of the wave propagation in the problem geometry in virtual form. Therefore, efficient analytical, semi-analytical or numerical modelling techniques are required. In recent years a semi-analytical mesh-free technique called Distributed Point Source Method (DPSM) is being used for modelling various ultrasonic, electrostatic and electromagnetic wave field problems. In the conventional DPSM approach point sources are placed along the transducer faces, problem boundaries and interfaces to model incident and scattered fields. Every point source emits energy in all directions uniformly. Source strengths of these 360° radiation sources are obtained by satisfying interface and boundary conditions of the problem. In conventional DPSM modelling approach it is assumed that the shadow zone does not require any special consideration. 360° Radiation point sources should be capable of properly modelling shadow zones because all boundary and interface conditions are satisfied. In this paper it is investigated how good this assumption is by introducing the ‘shadow zone’ concept at the point source level and comparing the results generated by the conventional DPSM and by this modified approach where the conventional 360° radiation point sources are replaced by the Controlled Space Radiation (CSR) sources.