A. Rabinovitch

Bacterial debris—an ecological mechanism for coexistence of bacteria and their viruses

A model of bacteria and phage survival is developed based on the idea of shielding by bacterial debris in the system. This model is mathematically formulated by a set of four nonlinear difference equations for susceptible bacteria, contaminated bacteria, bacterial debris and phages. Simulation results show the possibility of survival, and domains of existence of stable and unstable solutions

Fracture area calculation from electromagnetic radiation and its use in chalk failure analysis

Fracture area calculation from electromagnetic radiation and its use in chalk failure analysis A. Rabinovitch*, V. Frid, D. Bahat, J. Goldbaum The Deichmann Rock Mechanics Laboratory of the Negev, Israel Physics Department, Ben Gurion University of the Negev, PO Box 653, 84105, Beer-Sheva, Israel Department of Geological and Environmental Sciences, Ben Gurion University of the Negev, PO Box 653, 84105, Beer-Sheva, Israel

Parametrization of electromagnetic radiation pulses obtained by triaxial fracture of granite samples

We have accurately measured and parametrized individual pulses of electromagnetic radiation (EMR) obtained during a fracture experiment. Analysis of the parameters shows that they follow a log-normal distribution. Results indicate no dependence between fracture lengths and widths.

Experimental and theoretical investigations of electromagnetic radiation induced by rock fracture

Frid, V., Bahat, D., Goldbaum, J., Rabinovitch, A. 2000. Experimental and theoretical investigations of electromagnetic radiation induced by rock fracture. Isr. J. Earth Sci. 49: 9‐19. There is a general agreement in the literature that the technique of measuring electromagnetic radiation (EMR) emitted from cracked rock is a good candidate for forecasting of earthquakes. Our immediate objective in pursuing this goal is to correlate EMR with crack dimensions in micro-scales (mm–cm), coupling it with the understanding of atomic-scale phenomena for coherently understanding the EMR process. We review some of the results obtained in this laboratory. They include the isolation, both experimentally and theoretically, of an individual EMR pulse. Individual EMR pulse parameters are correlated with crack dimensions: the time from pulse origin up to its maximum is proportional to the crack length, and the frequency of the EMR pulse relates to the crack width. Individual EMR pulses are classified both according to their length and according to their location on the stress–strain curve. We find that the key elastic parameter for EMR characterization during triaxial compression is the Poisson ratio: the lower the Poisson ratio, the higher the EMR activity. Amplitudes of EMR and their changes with loading are shown to be independent of crack mode (tensile vs. shear), they are only dependent on the entire crack area. In order to experimentally overcome load limitations we introduce a new sample shape, the truncated cone, that fails more readily than standard cylindrical samples.

Finite element method for solving the two-dimensional schroedinger equation

Abstract A finite element package is presented that is able to treat two-dimensional Schroedinger equation problems over a finite region with an arbitrary potential and homogeneous boundary conditions. In order to present the applicability and accuracy of this approach, two cases for which the exact solution is known are solved: (i) a free particle in a spherical box, (ii) a hydrogen atom enclosed in a finite sphere. The results definitely indicate that the finite element method is both accurate and efficient and could serve as a useful tool in various single particle quantum mechanical problems.

Similarity and dissimilarity of electromagnetic radiation from carbonate rocks under compression, drilling and blasting

1. IntroductionNumerous investigations have examined differentaspectsofelectromagneticradiation(EMR)emittedbyfracture [1–6]. For example, it was noted that anincreaseofYoungmodulus,strength,andloadingrateenhancestheEMRamplitude[3,7–9].IndividualEMRpulseswerecarefullyinvestigatedunderuniaxialandtriaxialstiffcompression[8–11].AnexampleofanEMRpulsefromchalkcompressionisshowninFig.1.Itisknownnowthatapropagatingcrackconsistsofatomicbondseverage,whichexcitesatomic(orionic)oscilla-tions along the crack surfaces. These oscillations(Rayleigh-typewaves)induceelectromagneticradiation.Hence,eachcrackconstitutesasourceofanindividualEMRpulse.TheEMRamplitudeisafunctionofthecrackarea[12,13];thetimefromthepulseorigintothemaximumofitsenvelope,isproportionaltothecracklength;thefrequencyoftheEMRpulseisrelatedtothecrackwidth[12,13].AnanalysisoftheEMRpulsesemanating during uniaxial compression [14] showedthatindividualshortpulses(ofdurationof0.5–6ms,Table1)arecorrelatedwiththestageofindividualmicro-cracksformation;multi-pulsestringsarecorre-lated with the crack coalescence stage;andlengthypulses(ofdurationof30–400ms,Table1)arecorrelatedwithrockfailure.All these investigations were carried out in thelaboratory.Large-scaleEMRstudiespriortorockburstsinminesandtoearthquakes(EQ)arealsoregistered.Thus,Khatiashvilli[15]carriedoutaninvestigationofEMRintheTkibullideepshaft(Georgia)priortoanEQofa5.4magnitude.Theregistrationpoint(attheshaft position) was located 250km from the EQepicenter.PriortotheEQitself,anincreaseofintensityofthelowerpartofthespectrum(1–100kHz)andacorrespondingdecreaseofintensityofhigherfrequen-cies(100–1000kHz)wereobserved.NesbittandAustin[16]registeredEMRinagoldmine(2.5kmdepth).Frid[17,18]observedEMRanomaliesbeforerockburstsandgasoutbursts.Itisclaimed[19]thatanabnormallyhigh-EMRleveloccurshoursorevendaysbeforeanEQ,afterwhichEMRdecreases.Rikitake[20],analyzing60EQeventsmeasuredinJapan,alsoshowedthatEMRisa‘‘short-term’’precursor,withanestimatedmeantimepriortoan EQ of B6h. It was assumed [21–25] that theanomaliesofEMRpriortoanEQwereduetoadeformationoftheEarthsurface,whichresultedintheformation of micro-fractures and in friction of thenearbyrockblocks.Parrotetal.[26],afteradetailedconsiderationofalargenumberofEMR–EQinvestigations,remarkedthatalthoughtheexistenceofEMRinrelationtoseismicand/orvolcanicactivitieswereclear,EMRselectionoutofahostofartificialsignalsremainedasignificantproblem. Nevertheless, investigations of EMR as aprecursortolarge-scalefailurecontinue.In this work, we present the results of ourEMR investigations on carbonate rock fractureboth in the large scale (blasting in an openquarry) and in the micro-scale (drilling in the lab)and show the similarities and dissimilarities oftheseEMRresultstoourpreviousEMRlaboratorystudies during regular compression tests in thelaboratory.

Exploration via electromagnetic radiation and fractographic methods of fracture properties induced by compression in glass-ceramic

The fracture properties of glass ceramic induced by compression were investigated by combined electromagnetic radiation (EMR) and fractographic methods. The study of a transparent sample enabled us to elucidate the sequence of crack nucleation, growth and interaction, and the ultimate longitudinal splitting under incremental increase of uniaxial stress in five stages. The fracture process was accompanied by some 18 EMR pulses. The short EMR pulses (of a duration of 0. 8–1.5 μs) occur under low stresses (0.36–1.7 MPa) in association with microcracking at the sample outer surface. Medium pulses (durations of 15–25 μs) are associated with stresses of up to 65 MPa and are correlated with crack limited growth outside the specimen. A lengthy pulse (duration of more than 40 μs) occurs under greater stresses (112 MPa) and correlates with the longitudinal splitting at failure. A return to the 17–20 μs range occurs for the post-failure cracking during stress relaxation.

Comparison of electromagnetic radiation and acoustic emission in granite fracturing

The electromagnetic radiations and acoustic emision from two granite samples under compressive loading are studied in experiences. The two samples exhibit respectively plastic and brittle character. Differences in observed signals for these two samples are considered to be related to their different compositions.

Threshold, excitability and isochrones in the Bonhoeffer–van der Pol system

Some new insight is obtained for the structure of the Bonhoeffer-van der Pol system. The problems of excitability and threshold are discussed for all three types of the system classified according to the existing attractors: a focus only, a limit cycle only and a limit cycle together with a focus. These problems can be treated by the T-repellers and the T-attractors of the system which are mutually reciprocal under time inversion. The threshold depends on the structure of the T-repeller (unstable part of integral manifold). This structure is then used to understand the behavior and the properties of the two different types of isochrones: Winfree isochrones (W-isochrones) and regular isochrones. Winfrees description of a W-isochrone is extended to excitable systems. Both W-isochrones and regular isochrones are calculated for the Bonhoeffer-van der Pol system in its limit cycle and excitable regimes. The important role of the T-repeller as an asymptotic limit for both types of isochrones is manifested. (c) 1999 American Institute of Physics.

Tensile forces and shape entropy explain observed crista structure in mitochondria.

We present a model from which the observed morphology of the inner mitochondrial membrane can be inferred as minimizing the systems free energy. In addition to the usual energetic terms for bending, surface area, and pressure difference, our free energy includes terms for tension that we hypothesize to be exerted by proteins and for an entropic contribution due to many dimensions worth of shapes available at a given energy. We also present measurements of the structural features of mitochondria in HeLa cells and mouse embryonic fibroblasts using three-dimensional electron tomography. Such tomograms reveal that the inner membrane self-assembles into a complex structure that contains both tubular and flat lamellar crista components. This structure, which contains one matrix compartment, is believed to be essential to the proper functioning of mitochondria as the powerhouse of the cell. Interpreting the measurements in terms of the model, we find that tensile forces of ∼20 pN would stabilize a stress-induced coexistence of tubular and flat lamellar cristae phases. The model also predicts a pressure difference of -0.036 ± 0.004 atm (pressure higher in the matrix) and a surface tension equal to 0.09 ± 0.04 pN/nm.