Aharon Blank

Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components)

We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show that the details specifying and enforcing the smallest size of the components are crucial as well as the rules for creating new components. In particular, a growing system with a fixed number of components and a fixed smallest component size does not converge to a power law. We present a new model with variable number of components that converges to a power law for a very wide range of parameters. In a very large subset of this range, one obtains for the exponent α the special value 1 specific for the city populations distribution. We discuss the conditions in which α can take different values. In the case of the stock market, the distribution of the investors’ wealth is related to the ratio between the new capital invested in stock and the rate of increase of the stock index.

High resolution electron spin resonance microscopy

NMR microscopy is routinely employed in fields of science such as biology, botany, and materials science to observe magnetic parameters and transport phenomena in small scale structures. Despite extensive efforts, the resolution of this method is limited (>10 microm for short acquisition times), and thus cannot answer many key questions in these fields. We show, through theoretical prediction and initial experiments, that ESR microscopy, although much less developed, can improve upon the resolution limits of NMR, and successfully undertake the 1 mum resolution challenge. Our theoretical predictions demonstrate that existing ESR technology, along with advanced imaging probe design (resonator and gradient coils), using solutions of narrow linewidth radicals (the trityl family), should yield 64 x 64 pixels 2D images (with z slice selection) with a resolution of 1 x 1 x 10 microm at approximately 60 GHz in less than 1h of acquisition. Our initial imaging results, conducted by CW ESR at X-band, support these theoretical predictions and already improve upon the previously reported state-of-the-art for 2D ESR image resolution achieving approximately 10 x 10 mum, in just several minutes of acquisition time. We analyze how future progress, which includes improved resonators, increased frequency of measurement, and advanced pulsed techniques, should achieve the goal of micron resolution.

Transparent miniature dielectric resonator for electron paramagnetic resonance experiments

A novel miniature (∼2×2×1 mm) dielectric resonator for X-band electron paramagnetic resonance experiments is presented. The resonator is based on a single crystal of KTaO3, which is excited to its TE01δ resonance mode by means of a simple iris-screw coupling. Several configurations of resonators are considered and discussed with respect to their filling factor, power conversion ratio, and optical excitation efficiency. Our findings are presented in terms of both experimental and theoretical studies. For small samples, the high filling factor of this resonator results in a signal increase by a factor of 140–800 (assuming nonsaturating conditions) as compared to a rectangular X-band cavity. The high power conversion factor (∼40 G/W), should enable one to perform pulse experiments employing power amplifiers, with ∼100-fold less peak power used for rectangular cavities. With an antireflective layer, the crystal’s transparency enables efficient laser illumination of the sample in light-induced experiments.

High-sensitivity Q-band electron spin resonance imaging system with submicron resolution.

A pulsed electron spin resonance (ESR) microimaging system operating at the Q-band frequency range is presented. The system includes a pulsed ESR spectrometer, gradient drivers, and a unique high-sensitivity imaging probe. The pulsed gradient drivers are capable of producing peak currents ranging from ∼9 A for short 150 ns pulses up to more than 94 A for long 1400 ns gradient pulses. Under optimal conditions, the imaging probe provides spin sensitivity of ∼1.6 × 10(8) spins∕√Hz or ∼2.7 × 10(6) spins for 1 h of acquisition. This combination of high gradients and high spin sensitivity enables the acquisition of ESR images with a resolution down to ∼440 nm for a high spin concentration solid sample (∼10(8) spins∕μm(3)) and ∼6.7 μm for a low spin concentration liquid sample (∼6 × 10(5) spins/μm(3)). Potential applications of this system range from the imaging of point defects in crystals and semiconductors to measurements of oxygen concentration in biological samples.

Miniature self-contained intravascular magnetic resonance (IVMI) probe for clinical applications

A miniature (1.73 mm in diameter) NMR probe, which contains a magnet and a radiofrequency (RF) coil, is presented. This probe is integrated at the tip of a standard catheter and can be inserted into the human coronary arteries, creating local magnetic fields needed to obtain the NMR signal from the blood vessel walls, without the need for external magnet or RF coils. The basic theory governing the probe performance in terms of signal‐to‐noise‐ratio and contrast parameters is presented, along with measured results from test samples. The NMR signal can be analyzed to obtain tissue contrast parameters such as T1, T2 and the diffusion coefficient, which may be used to detect lipid‐rich vulnerable plaques in the coronary arteries. Magn Reson Med 54:105–112, 2005.

Pulsed three-dimensional electron spin resonance microscopy

A three-dimensional (3D) electron spin resonance (ESR) microimaging system, operating in pulse mode at 9GHz is presented. This microscope enables the acquisition of spatially resolved magnetic resonance signals of free-radicals in solid or liquid samples with a resolution of up to ∼3.5×7×11.4μm in 20min of acquisition. The detection sensitivity at room temperature is ∼1.2×109spins∕√Hz, which enables the measurement of ∼2×107 spins in each voxel after 60min of acquisition. The resolution and detection sensitivity are the best obtained so far for ESR at ambient conditions of temperature and pressure. This ESR microscope can be employed in the investigation of a variety of samples in the fields of botany, life sciences, and materials science.

Molecular diffusion in porous media by PGSE ESR

Diffusion in porous media is a general subject that involves many fields of research, such as chemistry (e.g. porous catalytic pallets), biology (e.g. porous cellular organelles), and materials science (e.g. porous polymer matrixes for controlled-release and gas-storage materials). Pulsed-gradient spin-echo nuclear magnetic resonance (PGSE NMR) is a powerful technique that is often employed to characterize complex diffusion patterns inside porous media. Typically it measures the motion of at least approximately 10(15) molecules occurring in the milliseconds-to-seconds time scale, which can be used to characterize diffusion in porous media with features of approximately 2-3 mum and above (in common aqueous environments). Electron Spin Resonance (ESR), which operates in the nanoseconds-to-microseconds time scale with much better spin sensitivity, can in principle be employed to measure complex diffusion patterns in porous media with much finer features (down to approximately 10 nm). However, up to now, severe technical constraints precluded the adaptation of PGSE ESR to porous media research. In this work we demonstrate for the first time the use of PGSE ESR in the characterization of molecular restricted diffusion in common liquid solutions embedded in a model system for porous media made of sub-micron glass spheres. A unique ESR resonator, efficient gradient coils and fast gradient current drivers enable these measurements. This work can be further extended in the future to many applications that involve dynamical processes occurring in porous media with features in the deep sub-micron range down to true nanometric length scales.

A three-dimensional electron spin resonance microscope

An electron spin resonance (ESR) imaging system, capable of acquiring three-dimensional (3D) images with a resolution of ∼10×10×30 μm in a few minutes of acquisition, is presented. This ESR microscope employs a commercial continuous wave ESR spectrometer, working at 9.1 GHz, in conjunction with a miniature imaging probe (resonator+gradient coils), gradient current drivers, and control software. The system can acquire the image of a small (∼1.5×1.5×0.25 mm) sample either by the modulated field gradient method, the projection reconstruction method, or by a combination of the two. A short discussion regarding the resolution of the modulated field gradient method in two-dimensional (2D) and 3D imaging is given. Detailed descriptions of the various system components are provided, along with several examples of 2D and 3D images that demonstrate the capabilities of the system.

Ultra miniature resonators for electron spin resonance: Sensitivity analysis, design and construction methods, and potential applications

This paper describes a recently developed new family of miniature surface resonators, used for electron spin resonance spectroscopy and imaging. The first part of the paper provides a detailed description of the operational principles of the surface resonators. It also includes sensitivity analysis for a variety of configurations with inner dimensions ranging from 150 μm down to 2 μm, operating at the Ku, Q, and W frequency bands. Most of the data presented here is based on theoretical predictions; however, some of it is accompanied by experiential results for verification. The second part of the paper describes a new type of double-surface microresonator and its production method. This new configuration enables an efficient coupling of the microwave energy from millimetre-sized microstrip lines to micron structures even at relatively low frequencies. The resonator is analysed both theoretically and experimentally – exhibiting ultra-high spin sensitivity. The conclusion of the two parts of the paper is that micron-scale surface microresonators may achieve spin sensitivity of a few thousands of spins in one second of acquisition time for special samples, such as phosphorous-doped 28Si, at cryogenic temperatures. However, further miniaturization below 1–2 microns does not seem to be beneficial, sensitivity-wise. In addition to their high spin sensitivity, these resonators have a huge conversion factor, reaching in some cases to more than 500–1000 G of microwave magnetic field with input power of 1 W. Some possible applications of these unique capabilities are also described herein.

Induction-detection electron spin resonance with spin sensitivity of a few tens of spins

Electron spin resonance (ESR) is a spectroscopic method that addresses electrons in paramagnetic materials directly through their spin properties. ESR has many applications, ranging from semiconductor characterization to structural biology and even quantum computing. Although it is very powerful and informative, ESR traditionally suffers from low sensitivity, requiring many millions of spins to get a measureable signal with commercial systems using the Faraday induction-detection principle. In view of this disadvantage, significant efforts were made recently to develop alternative detection schemes based, for example, on force, optical, or electrical detection of spins, all of which can reach single electron spin sensitivity. This sensitivity, however, comes at the price of limited applicability and usefulness with regard to real scientific and technological issues facing modern ESR which are currently dealt with conventional induction-detection ESR on a daily basis. Here, we present the most sensitive ex...