Mean Field Intensity Research Articles

Trade-off between filtering and symmetry breaking mean-field coupling in inducing macroscopic dynamical states

We study the manifestation of the competing interaction between the mean-field intensity and the symmetry breaking coupling on the phenomenon of aging transition in an ensemble of limit-cycle oscillators comprising of active and inactive oscillators. Further, we also introduce filtering in both the intrinsic and extrinsic variables of the mean-field diffusive coupling to investigate the counter-intuitive effect of both filterings. We find that large values of the mean-field intensity near unity favor the oscillatory nature of the ensemble, whereas low values favor the onset of the aging transition and heterogeneous dynamical states such as cluster oscillation death and chimera death states even at low values of the symmetry breaking coupling strength. Heterogeneous dynamical states predominates at large values of the coupling strength in all available parameter spaces. We also uncover that even a weak intrinsic filtering favors the aging transition and heterogeneous dynamical states, while a feeble extrinsic filtering favors the oscillatory state. Chimera death state is observed among the active oscillators for the first time in the aging literature. Our results can lead to engineering the dynamical states as desired by an appropriate choice of the control parameters. Further, the transition from the oscillatory to the aging state occurs via an inverse Hopf bifurcation, while the transition from the aging state to the cluster oscillation death states emerges through a supercritical pitch-fork bifurcation. The deduced analytical bifurcation curves are in good agreement with the numerical boundaries of the observed dynamical states.

Abstract 5497: Transducer array layouts for treating head and neck cancer with TTFields

Abstract Tumor Treating Fields (TTFields) are a novel antimitotic treatment for solid tumors. TTFields utilize low frequency (1-4 V/cm) electric fields in the intermediate frequency range (100-300 kHz), and are currently FDA approved for the treatment of glioblastoma multiforme (GBM) using the Optune device. TTFields are also approved for multi pleural mesothelioma (MPM). The fields are delivered using two pairs of transducer arrays placed on different places on the patient's skin. In order for the treatment to be efficacious, placement should be performed in a manner such that the tumor receives significant dose of TTFields. An effective dose is considered to be at least 1 V/cm in the region of interest. Nevertheless, preclinical studies has shown that higher field values result in greater tumor growth inhibition. When TTFields are delivered, the field distribution is determined by a series of non-intuitive factors, such as the different electric conductivity of the different organs, making intuitive placement inaccurate. Therefore, different parts of the body require specific array layout design. Such case occurs with head and neck cancer. In this work we examined our ability to deliver TTFields to the larynx and its surroundings. Methods We used computer simulations to estimate the field distribution different layouts would provide. The simulations used a computational phantom representing a 34 years old male (DUKE 3.1, ITI'S foundation, Zurich). We placed virtual transducer arrays comprising either 13 or 9 ceramic disks were placed on the model's skin and delivery of TTFields to the model was simulated Sim4Life v4.4 (by ZMT, Zurich). 6 different array layouts were tested. In layouts 1-3, one array comprising 13-disks was placed on the model's scalp while the other 13-disks array was placed on its chest. Forcase 4 a pair of 9-disks arrays was used, one array was placed on the forehead of the model and the other on it'supper chest. In cases 5-6, we placed 9-disks arrays around the patient's neck. We then analyzed the field intensity within a region of interest (ROI) including the larynx and surrounding tissues. Results In cases 1-2 and 4, mean field intensities within the ROI were 3.29 V/cm, 3.46 V/cm and 2.6 V/cm, respectively, well above the clinical threshold of 1 V/cm. Cases 3, 5 and 6 showed to have median field of 1.41, 1.37 and 1.27 V/cm. Though still above the clinical threshold, these field intensities are significantly lower than in the other cases. This, apparently, is due to current flow through the neck muscles behind the ROI. Conclusions This study shows that it is possible to deliver TTFields at therapeutic intensities to the larynx and the surrounding tissues. Thus, TTFields may be a therapeutic option for treating head and neck tumors located in the larynx and the surrounding tissues. Citation Format: Ze'ev Bomzon, Ariel Naveh, Yissachar Abraham. Transducer array layouts for treating head and neck cancer with TTFields [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 5497.

P11.21 Treating numerous secondary tumors in the brain with tumor treating fields: Simulation study to identify optimal transducer array layout

Abstract BACKGROUND Tumor Treating Fields (TTFields) use alternating electric fields for the treatment of solid tumors. The therapy is approved for glioblastoma multiforme (GBM), and a phase III trial in 1–10 brain metastases from non-small cell lung cancer (METIS) is currently enrolling patients. In GBM, the layout of the transducer arrays delivering the TTFields to the tumor is optimized for high field intensity in the tumor, while the dose in other regions is decreased. In the setting of secondary brain tumors, as they manifest as brain metastases in 10–30 % of adult cancer patients - especially in melanoma, lung, breast, colon, and kidney cancer - a high TTFields dose in the entire brain would be beneficial. Thus, numerous tumors instead of only one lesion should receive therapeutic TTFields doses. In this study, transducer array layouts aiming for a homogeneous TTFields distribution in the whole brain were investigated. MATERIAL AND METHODS We used computer simulations in a realistic computational head model of a 40+ years old man, constructed in-house from a T1 MRI series, to compute the field distributions obtained with various transducer array layouts. The distribution of TTFields delivered by pairs of transducer arrays at different positions on the head and neck was simulated using Sim4Life v3.0 (ZMT Zürich). For each layout, we determined and compared the mean and median field intensities in five pre-determined sections of the brain: (1) the cerebellum and brain stem together with other infra-tentorial anatomical regions; and (2–5) the four cerebral quadrants. RESULTS One array layout could be identified yielding median intensities between 1.5 V/cm to 1.7 V/cm in all areas and a homogeneous distribution within the brain. This layout is composed of one pair of arrays positioned on the right temple and left scapula, and the other pair positioned on the left temple and right scapula. CONCLUSION This study was able to determine a novel TTFields transducer array layout that might be used for treatment of the entire brain with therapeutic intensities, as would be beneficial in patients with brain metastases.

P11.18 Tumor treating fields (TTFields) treatment of spinal cord metastases

Abstract BACKGROUND Tumor Treating Fields (TTFields) is an anti-mitotic cancer treatment approved for the treatment of Glioblastoma multiforme (GBM) and is currently also investigated in a phase III trial in 1–10 brain metastases from non-small cell lung cancer (METIS). Apart from spread to the brain, some cancer types, such as breast cancer, lung cancer, and melanoma, may lead to metastatic spread to the spinal cord. Previous studies have shown that reported transducer array layouts for the treatment of abdominal/pelvic tumors (e.g. pancreatic cancer), with one pair of arrays positioned on the anterior and posterior of the patient, and the second pair of arrays placed on each side of the thorax, yield therapeutically insufficient field intensities of <1 V/cm in the spinal cord. This finding probably results from the anatomical structure of the spine, consisting of the cerebrospinal fluid as a highly conductive layer, encased by a resistive bone structure that shunts the current delivered across the body by the arrays away from the spine. This simulation-based study aimed at resolving this challenge by identifying novel array layouts on the body that effectively deliver TTFields to the spine. MATERIAL AND METHODS For the simulations of the TTFields delivery to the spine, a human male 34 years old realistic computational model (DUKE v3.1 by ITI’S, Zurich) and the ZMT’s Sim4Life v4.0 electro-quasi-static solver was utilized. TTFields were simulated by imposing an alternating current with a current density of 200 mA/disk and a frequency of 150 kHz on the outer surfaces of the disks of each pair of arrays. RESULTS For one of the tested array layouts, a high electric field was shown to be induced within the spinal cord and surrounding CSF: Our calculations of mean field intensity within the spine and nerves from vertebrae T8-T9 at the top to L3-L4 at the bottom added up to 1.77 V/cm. This layout consisted of the placement of a pair of arrays on the back of the patient, with one array positioned above the section in the spine to which treatment would be delivered, and the other array positioned below the target section. Notably, the resulting electric field is directed along the spine in this setting (ie, vertically). CONCLUSION Our results demonstrate that treatment of the whole spinal cord and nerves in a single direction can be achieved by placing a pair of transducer arrays on the patient’s back: one array on the neck, and one at the bottom of the spine. For the development of an active treatment in the perpendicular direction, further studies need to be conducted.

Delivering Uniform TTFields Distribution to the Brain

Tumor Treating Fields (TTFields) are alternating electric fields in the intermediate frequency known to inhibit tumor growth. TTFields are approved for the treatment of Glioblastoma Multiforme, and a study investigating the efficacy of TTFields for treating brain metastases is underway [NCT02831959]. TTFields are delivered in two almost orthogonal directions using two pairs of transducer arrays placed on the scalp. When treating glioblastoma, treatment planning is performed in order to place the arrays on the scalp in a manner thought to optimize the field power delivered to the tumor bed. The increased delivery of power to the tumor often leads to reduced field power in other regions of the brain. In particular, when optimizing to treat tumors in the supratentorium, lower intensities are observed in the infratentorial brain. However, in some clinical cases, such as multiple metastases spread throughout both the infratentorial and supratentorial brain, it might be desirable to deliver TTFields at therapeutic levels to the entire brain. Here, we present some novel transducer array layouts designed for delivering a uniform distribution of TTFields to the entire brain. Numerical simulations were utilized to identify layouts that yielded uniform field distributions throughout the entire brain. The simulations utilized a realistic computerized head model of a 40+ years old human male prepared from a T1 MRI series. The Sim4Life v3.0 (ZMT Zürich) low frequency electromagnetic solver was used to simulate the delivery of TTFields using pairs of virtual array layouts placed at different locations on the head and neck of the model. To quantify field uniformity in the brain, we divided the brain into five compartments: 1) the cerebellum, brain stem and other infra-tentorial anatomical regions; 2-5) four quadrant of the cerebrum. Mean and median field intensities generated by each layout in those five regions were calculated and compared. A layout in which one pair of arrays is placed on the right temple and left scapula, and the second pair placed on the left temple and right scapula delivered a highly uniform field distribution. With this layout, median field intensities between 1.5 and 1.7 V/cm were calculated in all 5 compartments. We have presented a novel TTFields transducer array layout that delivers uniform field distributions throughout the brain. This layout could be used for treating clinical scenarios such as multiple metastases spread throughout the entire brain.

Abstract 692: Treating spinal cord metastases with tumor treating fields

Abstract Introduction: Tumor Treating Fields (TTFields) is an anti-mitotic technology utilizing low-intensity (1-3 V/cm) electric fields within the medium frequency range (100-300 kHz) to treat solid tumors. TTFields are currently approved for the treatment of Glioblastoma (GBM). Some cancer types, such as breast cancer, lung cancer, and melanoma, frequently result in metastases to the spinal cord. Transducer array positioning used to treat abdominopelvic diseases (e.g. pancreatic cancer), in which one pair of arrays are placed on the anterior and posterior of the patient, and another pair of arrays placed on the lateral aspects of the patient have been shown to be inefficient for treating the spinal cord because the clinical threshold for field intensity of 1V/cm is not reached in the spine when these layouts. The structure of the spine, in which a relatively resistive bone structure encapsulates a highly conductive layer of fluid (cerebrospinal fluid), shunts the current delivered across the body by the arrays away from the spine, reducing the field within the spine to below the therapeutic threshold. To overcome this limitation, a new approach of array placement on the body is needed. Here we present a simulation-based study designed to identify array layouts that effectively deliver TTFields to the spine. Methods: To simulate delivery of TTFields to the spine, we used a human male 34 years old realistic computerized model (DUKE v3.1 by ITI’S, Zurich). In order to generate TTFields, an alternating current with current density of 200mA/disk with a frequency of 150 kHz was imposed on the outer surfaces of the disks of each pair of arrays. The simulations were performed using ZMT's Sim4Life v4.0 electro-quasi-static solver. Results: One of the array layouts tested was placement of a pair of arrays on the back of the patient. One array is placed above the target region in the spine to which treatment would be delivered, and the other array is placed below the region. With this configuration, a high electric field is induced within the spinal cord and surrounding CSF. Mean field intensity within the spine and nerves in between vertebrae T8-T9 at the top, and L3-L4 at the bottom were calculated at a value of 1.77 V/cm. It is important to note that the electric field is oriented along the spine in this instance (a vertical field). In general, the whole spine could be treated by placing one array on the neck, and one at the bottom of the spine. Conclusions: Placing two transducer arrays on the patient’s back allows single-direction treatment of the spinal cord and nerves. Further work should be conducted to find an effective treatment in the perpendicular direction. Citation Format: Ofir Yesharim, Ariel Naveh, Ze'ev Bomzon. Treating spinal cord metastases with tumor treating fields [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 692.

Abstract 4450: Novel transducer array layouts to optimize the treatment of multiple brain metastases with tumor treating fields

Abstract Introduction: Tumor Treating Fields (TTFields) is an antimitotic cancer treatment approved for the treatment of Glioblastoma Multiforme (GBM). TTFields are delivered using 2 pairs of transducer arrays positioned on the shaved scalp of the GBM patient to optimize the TTFields dose delivered to the tumor. This results in an increased dose of TTFields to the affected tumor region, whilst reducing the intensity of the fields to other regions. Brain metastases, or secondary brain tumors, occur in 10 to 30 percent of adults with cancer. Cancer types most likely to cause brain metastases are lung, breast, colon, kidney and melanoma. When using TTFields to treat brain metastases, it may be desirable to deliver TTFields at therapeutic intensities to the entire brain, in order to treat multiple rather than a single lesion. We investigated novel transducer array layouts designed to deliver a uniform distribution of TTFields to the entire brain. Methods Computer simulations were used to calculate the field distributions generated by different array layouts. The simulations utilized a realistic computerized head model of a 40+ years old human male prepared in-house from a T1 MRI series. Using Sim4Life v3.0 (ZMT Zürich), we simulated the delivery of TTFields using pairs of array layouts placed at different locations on the head and neck. To analyze the field distributions, the brain was divided into five regions: (1) the cerebellum, brain stem and other infra-tentorial anatomical regions; and (2-5) the four quadrants of the cerebrum. The mean and median field intensities in the five regions generated by each layout were calculated and compared. Results Median intensities between 1.5 V/cm to 1.7 V/cm within all regions were achieved using a layout in which one pair of arrays was placed on the right temple and left scapula, while the second pair was placed on the left temple and right scapula. This layout yielded a uniform intensity distribution within the brain. Conclusion We have identified a novel TTFields array layout that could potentially be used to treat the entire brain with sufficiently high intensity to treat for brain metastases. The ongoing Phase 3 METIS study [NCT02831959 is investigating radiosurgery with TTFields for 1-10 brain metastases from non-small cell lung cancer. Citation Format: Ofir Yesharim, Ariel Naveh, Ze'ev Bomzon. Novel transducer array layouts to optimize the treatment of multiple brain metastases with tumor treating fields [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 4450.

Optimization of tumor treating fields using singular value decomposition and minimization of field anisotropy

Tumor treating fields (TTFields) are increasingly used to treat newly diagnosed and recurrent glioblastoma (GBM). Recently, the authors proposed a new and comprehensive method for efficacy estimation based on singular value decomposition of the sequential field distributions. The method accounts for all efficacy parameters known to affect anti-cancer efficacy of TTFields, i.e. intensity, exposure time, and spatial field correlation. In this paper, we describe a further development, which enables individual optimization of the TTFields activation cycle. The method calculates the optimal device settings to obtain a desired average field intensity in the tumor, while minimizing unwanted field correlation.Finite element (FE) methods were used to estimate the electrical field distribution in the head. The computational head model was based on MRI data from a GBM patient. Sequential field vectors were post-processed using singular value decomposition. A linear transformation was applied to the resulting field matrix to reduce fractional anisotropy (FA) of the principal field components in the tumor.Results were computed for four realistic transducer array layouts. The optimization method significantly reduced FA and maintained the average field intensity in the tumor. The algorithm produced linear gain factors to be applied to the transducer array pairs producing the sequential fields. FA minimization was associated with an increase in total current delivered through the head during a activation cycle. Minimized FA can be obtained for an unchanged total current level, albeit with a reduction in average field intensity.We present an algorithm for optimization of the TTFields activation cycle settings. The method can be used to minimize the spatial correlation between sequential TTFields, while adjusting the total current level and mean field intensity to a desired level. Future studies are needed to validate clinical impact and assess sensitivity towards model parameters.

NIMG-72. A NOVEL ARRAY LAYOUT FOR DELIVERING TTFIELDS TO THE WHOLE BRAIN

INTRODUCTION: Tumor Treating Fields (TTFields) is an antimitotic cancer treatment approved for the treatment of Glioblastoma Multiforme. TTFields are delivered using 2 pairs of transducer arrays. When treating Glioblastoma, the array positioning on the head is planned to maximize TTFields dose delivered to the tumor. This results in an increased dose of TTFields at the tumor, whilst reducing the intensity of the field in other regions. In some clinical scenarios, such as treatment of multiple brain metastases, it might be desirable to deliver TTFields at therapeutic intensities to the entire brain, thereby ensuring that even microscopic lesions receive a therapeutic dose of TTFields. Here we present novel transducer array layouts designed to deliver a uniform distribution of TTFields to the entire brain. Methods Computer simulations were used to calculate the field distributions generated by different array layouts. The simulations utilized a realistic computerized head model of a 40+ years old human mal. Delivery of TTFields using pairs of array layouts placed at different locations on the head and neck was simulated using Sim4Life V3.0 (ZMT Zurich). To analyze the field distributions, the brain was divided into five regions: 1) the cerebellum, brain stem and other infra-tentorial anatomical regions; 2–5) four quadrant of the cerebrum. The mean and median field intensities in the five regions generated by each layout were calculated and compared. Results A layout in which one pair of arrays is placed on the right temple, and left scapula and the second pair placed on the left temple and right scapula yielded a uniform intensity distribution within the brain. (median intensities between 1.5 V/cm to 1.7 V/cm within all regions). Conclusion We have identified a novel TTFields array layout that will be beneficial in clinical scenarios where treatment of the entire brain with TTFields is desired.

Numerical simulation of electric field enhancement at the contact of positive and negative streamers in relation to the problem of runaway electron generation in lightning and in long laboratory sparks

The hypothetical mechanism of electric field amplification at contact of positive and negative streamers in a streamer corona up to magnitudes required for the generation of runaway electrons and secondary Bremsstrahlung in the x-ray range, observed in long spark discharges in the open atmosphere, is analyzed. The development of two streamers, moving towards each other in interelectrode gaps of the centimetre range, is numerically simulated at applied voltages from 73 to 250 kV. It is shown that the size of the domain with strong electric field, with intensity sufficient for the thermal electron runaway, is of 1–2 mm. The mean field intensity in this domain increases up to magnitudes of ≈250–280 kV cm−1. The maximum energy, to which electrons are capable of energizing in such field, is in the range of 20–70 keV. However, the electron energy is limited by an extremely small life-time of the strong field domain (less than 20 ps).

Abstract 1569: Optimizing transducer array configuration for treatment of pancreatic cancer using Tumor Treating Fields (TTFields)

Abstract Introduction TTFields is an antimitotic cancer treatment that utilizes low intensity (1-3 V/cm) alternating electric fields in the intermediate frequency (100-300 kHz) that are delivered in two orthogonal directions using 2 pairs of transducer arrays. TTFields are currently approved for Glioblastoma Multiforme (GBM). A phase II clinical trial (EF-20) showed that TTFields in combination with gemcitabine was safe in patients with locally advanced pancreatic cancer. Preclinical studies show that the effect of TTFields is intensity-dependent with a therapeutic threshold of 1 V/cm. Simulation-based studies show that the field distribution changes with array placement. Treatment planning with arrays positioned on the scalp to maximize field intensity to the tumor is standard of practice when treating GBM. Studies to examine array layout on the abdomen to maximize the field distribution in this region have not been done. In the EF-20 study, a generic layout was used. We used computer simulations to test how altering the transducer array layout on the mid-body alters the field distribution within the abdomen and pancreas. Methods To simulate delivery of TTFields to the abdomen, we used a realistic computerized model of a human male (DUKE 3.0 from ZMT-Zurich). Eight different layouts utilizing combinations of arrays with either 13 or 20 disks placed at different locations on the abdomen were simulated. In order to generate TTFields, an alternating voltage difference with a peak to peak magnitude of 100V and a frequency of 150 KHz was imposed on the outer surfaces of the disks of each pair of arrays. The simulations were performed using ZMT's Sim4Life V3.0 electro-quasi-static solver. For each pair of transducer arrays, the mean field intensity in the abdomen and chest, and in the pancreas and liver, was calculated. Results All eight layouts delivered fields with mean intensities of about 2 V/cm to the abdomen. The average field intensity delivered to the pancreas and the liver exceeded the therapeutic threshold of 1 V/cm for all layouts. The highest intensities were delivered to the pancreas by layouts in which a 20-disk array was placed at the middle of the back, and either a 20 disk array placed at the middle of the abdomen or a 13 disk array placed on the front-left side of the abdomen over the pancreas. Generally, field intensities in the pancreas are lower than in the rest of the abdomen because of the high electric conductivity of this organ. Conclusion This work shows that TTFields can be delivered to the pancreas with intensities well above the therapeutic threshold of 1 V/cm, and that altering the location of the arrays on the abdomen can influence the field intensity and distribution within the body. This work forms the basis for developing optimal strategies for delivering TTFields to the pancreas. Citation Format: Ariel Naveh, Ze'ev Bomzon, Noa Urman, Ofir Yesharim, Eilon D. Kirson, Uri Weinberg. Optimizing transducer array configuration for treatment of pancreatic cancer using Tumor Treating Fields (TTFields) [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr 1569. doi:10.1158/1538-7445.AM2017-1569

Numerical simulation of temperature effect on particles behavior via electrostatic precipitators

A comprehensive numerical model is developed and applied to study the effect of temperature on the behavior of charged particles in a wire-plate electrostatic precipitator (ESP). In this model, the complex interactions in different temperature conditions between the electric field, fluid dynamics and the particulate flow are taken into account. The finite volume method is used to solve the electric field and Euler-Lagrange model is used to describe particle-laden flows. From the present simulation, the effect of temperature on electro-hydrodynamics (EHD) characteristics and particle charging and tracing are investigated. The numerical results show that high temperature thickens the boundary layer along the plate and strengthens turbulence. The corona onset electric field intensity and mean field intensity both decrease as temperature increases. Considering space charging and diffusion charging, high temperature weakens the particle charging. With the increase of temperature, the Coulomb, Saffman lift and Brownian forces go down while the drag force goes up. The Coulomb force and the drag force are the key forces acting on particles in the ESP for 10 μm particle. The variation of the two forces along with particles trajectories indicates that high temperature enhances the interaction between particles and fluid. Finally, it becomes more difficult to collect particles when temperature increases.

Geomagnetic field intensity from Kilauea 1955 and 1960 lava flows: Towards a better understanding of paleointensity

The record of the Earth’s magnetic field intensity during the past (paleointensity) carries important information about the geodynamo and the state of the Earth’s interior that is not contained in the record of its paleodirection. To determine what the critical factors in obtaining reliable estimate of paleointensity are, we present new results of a paleointensity study of the 1955 and 1960 Kilauea volcano lava flows, from the Big Island of Hawaii. Rock magnetic measurements on representative hand samples from each flow in conjunction with reflected light microscopy observations show the primary carriers of remanence to be pseudo-single domain titanomagnetite with various titanium contents. Paleointensity samples (small fragments previously embedded into salt pellets) were subjected to the Thellier-Coe experimental procedure. Fourteen temperature steps were distributed over the entire temperature range used (ambient temperature to 570°C). Control heating steps (commonly referred to as partial thermo-remanent magnetization — pTRM checks) were also conducted each third double heating step. Mean field intensity value (36.6 ± 0.7 μT) retrieved from 3 reliable site mean determinations reproduces the expected value within 1.1%. With the knowledge of the rock magnetic characteristics of the samples and the strength of the geomagnetic field during cooling of the lava, our investigation suggests that the Hawaiian lavas can faithfully record the local geomagnetic field and confirms that the Thellier-Coe type techniques are suitable on historical lava flows to yield reliable absolute paleointensity determinations. The variations in direct field measurements and in lab paleofield determinations may reflect local heterogeneities of the lava or influence of very local field anomalies due to the volcanic underlying terrain. These results underscore the importance that a better understanding of intensity results of historical lava flows is still required if reliable paleointensity determinations of older periods, for which we do not know the answer, are sought.

Effective Maxwell equations for finite planar samples in QHE regime

Effective Maxwell equations for the mean quantum electromagnetic field in planar samples in QHE regime are investigated. Boundary conditions to be satisfied by the mean field intensities at the filamentary boundaries (edges) are determined. For ideal strictly 2D samples embedded in real 3D space, these constraints imply that the total filamentary charge at the boundaries (the free plus polarization terms) and current densities identically vanish at all times. In the static limit the exact quantization of the Hall resistance of samples of arbitrary form, directly follows from the boundary condition. The equations for the electromagnetic response in a neighborhood of the edge of a half-plane in QHE regime are solved. The system exhibits a weak diamagnetic response and inhomogeneous charge and current distributions develop in the sample.

Finite-amplitude standing acoustic waves in a cubically nonlinear medium

The acoustic field in a resonator filled with a cubically nonlinear medium is investigated. The field is represented as a linear superposition of two strongly distorted counterpropagating waves. Unlike the case of a quadratically nonlinear medium, the counterpropagating waves in a cubically nonlinear medium are coupled through their mean (over a period) intensities. Free and forced standing waves are considered. Profiles of discontinuous oscillations containing compression and expansion shock fronts are constructed. Resonance curves, which represent the dependences of the mean field intensity on the difference between the boundary oscillation frequency and the frequency of one of the resonator modes, are calculated. The structure of the profiles of strongly distorted “forced” waves is analyzed. It is shown that discontinuities are formed only when the difference between the mean intensity and the detuning takes certain negative values. The discontinuities correspond to the jumps between different solutions to a nonlinear integro-differential equation, which, in the case of small dissipation, degenerates into a third-degree algebraic equation with an undetermined coefficient. The dependence of the intensity of discontinuous standing waves on the frequency of oscillations of the resonator boundary is determined. A nonlinear saturation is revealed: at a very large amplitude of the resonator wall oscillations, the field intensity in the resonator ceases depending on the amplitude and cannot exceed a certain limiting value, which is determined by the nonlinear attenuation at the shock fronts. This intensity maximum is reached when the frequency smoothly increases above the linear resonance. A hysteresis arises, and a bistability takes place, as in the case of a concentrated system at a nonlinear resonance.

Electric field analysis on the improved skin concentration of benzoate by electroporation

The objective in the present study was to understand the relationship between the increased skin concentration of benzoate as a model drug after topical application of its sodium salt and the electric field intensity produced in the skin barrier, the stratum corneum, by electroporation. A piece of excised abdominal hairless rat skin was set in a Franz type diffusion cell, and 0.5% sodium benzoate and physiological saline were applied to the stratum corneum and dermis sides, respectively. Two needle electrodes made of Ag were connected to an electrical power source, which produced exponentially decaying pulses. The electrodes were placed on the skin surface with a distance of 0.5 cm between both electrodes. After the 4 h passive permeation experiment, an electrical pulse was applied to the rat skin at 300 V every minute for 10 min. The skin was then removed from the diffusion cell, and the amounts of benzoate in different positions of the skin specimen were measured. Field intensity generated in the stratum corneum by electroporation was determined by a finite element method using a computer program. The amounts of benzoate at different sites in the skin were almost proportional to the mean field intensity in the corresponding stratum corneum. These results suggested that the enhancing effect of electroporation can be evaluated by the field intensity more directly than the application voltage.

The gel edge electric field gradients in denaturing polyacrylamide gel electrophoresis.

It has previously been shown that zones of higher electric field form close to the loading end of the gel during denaturing polyacrylamide gel electrophoresis. Here we show that the field can reach up to three times its normal mean value a few cm in front of the loading wells when 44.5 mM Tris-44.5 mM boric acid-1 mM EDTA is used as the gel buffer. We also demonstrate that this electric field gradient is mostly due to the difference in ion transference numbers at the gel/buffer interface caused by the high viscosity of the urea solution contained in the gel. This field gradient leads to increased band widths and forces us to redefine both the electrophoretic mobility and the mean field intensity. We discuss some methods that can be used to minimize the effects of this gradient.

Effects of Electrofishing Fields on Captive Juveniles of Two Endangered Cyprinids

Abstract We conducted laboratory experiments to address concerns about potential harmful effects of electrofishing on juvenile humpback chubs Gila cypha. Four types of square-wave pulsed DC in homogeneous fields were tested: 30 Hz (12% duty cycle), 60 Hz (24% duty cycle), 80 Hz (40% duty cycle), and a complex pulse train of three 240-Hz, 2.6-ms pulses delivered at 15 Hz (12% duty cycle). We first determined peak-voltage gradients for each current sufficient to induce the electroshock responses of taxis, narcosis, or tetany in captive-reared early juvenile humpback chubs (49–96 mm total length) and bonytails G. elegans (46–79 mm). Bonytails were intended as surrogates for humpback chubs in most subsequent tests. However, mean voltage-gradient response thresholds were 8–43% lower for humpback chubs than for bonytails. We then exposed 30 humpback chubs for 10 s to the complex pulse current at mean tetanizing field intensity and 60 bonytails for 10 s to one of the four currents at mean field intensities requi...

The structure of the field of high-angle rays in a randomly inhomogeneous ionosphere at frequencies close to the maximum usable frequency

In this paper we investigate the structure of the field of high-angle rays in a randomly inhomogeneous ionosphere in the neighbourhood of the MUF. On the basis of an integral representation for the mean field intensity we have obtained an asymptotic formula governing the behaviour of the field in the neighbourhood of the MUF and with possible shadowing by the terrestrial surface taken into account. The paper presents the results of calculations obtained by using this formula and makes a comparison of them with experimental data for the Moscow Irkutsk path of 4100 km length.

Reflection from a One-Dimensional, Totally Refracting Random Multilayer II—Internal Field Statistics

The modeling of acoustic scattering by ocean sediments has led to the formulation of an idealized, one-dimensional problem involving the interplay of random scattering and total internal reflection. The behavior of the reflection coefficient in the lossless case was discussed in [W. E. Kohler, Reflection from a one-dimensional, totally refracting multilayer, SIAM J. Appl. Math., 46, 1986, pp. 464–482]. Using the ideas of invariant embedding, expressions for the mean field intensities and intensity fluctuations as functions of depth within the sediment layer are now derived.