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The purpose of this Comment is to highlight several inaccuracies in the recently published paper of Yankelevsky and Feldgun, which criticizes our work on concrete penetration. The main subject of their criticism concerns our treatment of the entrance phase in concrete penetration, and we show here that their claims are inaccurate and misleading. We do not engage in the existing debates concerning different approaches to the penetration mechanics of rigid projectiles.

The paper is concerned with the perforation process of aluminum plates by 7.62 mm APM2 projectiles. In particular, we compare experimental values of the ballistic limit velocities for various aluminum alloys with predictions from our numerically-based model, which has been published a few years ago. The data include different thicknesses of aluminum plates of several alloys, ranging in their dynamic compressive strengths between 0.2 and 0.65 GPa We introduce an empirical correction factor to account for the effect of the brass jacket around the hard steel cores of these projectiles. We also discuss the issues of layered targets and inclined impacts, which may complicate the analysis. The good agreements between our predictions and the data for the ballistic limit velocities enhance the validity of the model, and suggest that it could also apply for other armor piercing projectiles, as well as for other metallic plates.

Consolidating multiple high-energy femtosecond scale lasers is expected to enable implementation of cutting edge research areas varying from wakefield particle accelerators to ultra-high intensity laser pulses for basic fresearch. The ability to guide while augmenting a short-pulse laser is crucial in future laser based TeV particle accelerators where the laser energy depletion is the major setback. We propose, analyze and experimentally demonstrate consolidating multiple femtosecond pulse lasers in coupled curved capillaries. We demonstrate a proof of principle scheme of coupled curved capillaries where two femtosecond laser pulses are combined. We found that the details of the coupling region and injection scheme are crucial to the pulse consolidations. Furthermore, our simulations show that high-intensity short pulse laser can be guided in a small curvature radius capillary. Incorporating these finding in a curved capillary laser coupler will be a significant step towards realization of meters long TeV laser based particle accelerators., Comment: 5 pages, 7 figures

Background Notch signaling plays a key role in tumorigenesis. AL101 is a γ-secretase inhibitor that potently inhibits signaling through Notch receptors 1-4. AL101 has robust antitumor activity in ACC patient-derived xenograft models with Notchact mut (AACR ‘19, Abstr 4885). In P1 testing, AL101 was well tolerated, with manageable AEs and a recommended P2 dose of 4 mg IV QW (ASCO ‘18, Abstr 2515). One of the 4 responders in P1 had ACC with Notchact mut. ACC is a rare chemotherapy-refractory cancer of the secretory glands. Notchact mut are found in ∼20% of ACC pts, characterized by a particularly aggressive disease and poor prognosis. There is no proven active treatment for R/M ACC. Methods ACCURACY (NCT03691207) is an open-label, single-arm, multicenter study of AL101 (4 mg IV QW) in R/M ACC pts (bone-exclusive disease allowed) with known Notch1-4act mut (ASCO ‘19, Abstr TPS6098). Pts with disease progression ≤6 months of enrollment or newly diagnosed metastatic disease are allowed. Primary endpoint: ORR by RECIST v1.1 (or modified MD Anderson bone criteria), by independent review committee (IRC). Secondary endpoints: ORR by investigator review (IR), duration of response by IRC and IR, PFS by IRC, OS, and safety. Per Simon optimal design, 12 pts are enrolled in stage 1; if ≥ 2 pts respond, 24 additional pts are enrolled in stage 2. If ≥ 6 pts of 36 respond, the trial is deemed positive. This design yields 5% type I error rate and 80% power, if ORR is 25%. Results In stage 1, 12 pts are being treated (median of 1.5 cycles, as of May ‘19). Most pts are males, with ECOG PS of 0, and with Notch mutations in the PEST domain (Table). Table: 1148P . Disposition and Baseline characteristics of patients treated with the investigational new drug AL101 Screened/Enrolled (signed consent), n 18 Screen failures, n 6 Treated, n 12 Median number of cycles, n 1.5 Gender, n Male Female 8 4 Median age, years 56.5 Race, n White Black Asian Other Not Reported N/A 6 1 0 1 2 2 ECOG performance status, n 0 1 N/A 6 4 2 Disease status, n With nodal or visceral metastases With bone-exclusive metastases 10 2 Type of mutations, n In the NRR region In the PEST domain In the NRR and PEST regions 3 6 3 N/A=not available Conclusions In the stage 1 of the ACCURACY trial, 12 pts with Notch1-4act mut are being treated with the pan-Notch inhibitor AL101. The trial will advance to stage 2 if ≥ 2 pts respond. Efficacy/safety data on these first 12 pts will be presented at the meeting. Accrual to stage 2 is ongoing. Clinical trial identification NCT03691207. Editorial acknowledgement Francesca Balordi, PhD, of The Lockwood Group (Stamford, CT, USA), in accordance with Good Publication Practice (GPP3) guidelines, funded by Ayala Pharmaceuticals, Inc. Legal entity responsible for the study Ayala Pharmaceuticals, Inc. Funding Ayala Pharmaceuticals, Inc. Disclosure R. Ferrarotto: Honoraria (self), Advisory / Consultancy: Ayala Pharmaceuticals; Honoraria (self): Regeneron. A. Ho: Honoraria (self), Advisory / Consultancy, Research grant / Funding (self), Travel / Accommodation / Expenses: Ayala Pharmaceuticals; Honoraria (self), Advisory / Consultancy, Research grant / Funding (self), Travel / Accommodation / Expenses: Merck; Honoraria (self), Advisory / Consultancy, Research grant / Funding (self): Novartis; Honoraria (self), Advisory / Consultancy, Research grant / Funding (self): Eisai; Honoraria (self), Advisory / Consultancy, Research grant / Funding (self): Bristol-Myers Squibb; Honoraria (self), Advisory / Consultancy, Research grant / Funding (self): AstraZeneca; Advisory / Consultancy, Research grant / Funding (self): Genentech/Roche; Research grant / Funding (self): Celldex Therapeutics; Research grant / Funding (self): Bayer; Research grant / Funding (self): Eli Lilly and Company; Research grant / Funding (self): Astellas Pharma; Research grant / Funding (self): Daiichi Sankyo; Research grant / Funding (self): Allos Therapeutics; Research grant / Funding (self): Pfizer; Honoraria (self), Advisory / Consultancy: Sanofi Genzyme; Honoraria (self), Advisory / Consultancy: Sun Pharma; Honoraria (self), Advisory / Consultancy: Regeneron; Honoraria (self), Advisory / Consultancy: TRM Oncology; Research grant / Funding (self), Travel / Accommodation / Expenses: Kura Oncology; Travel / Accommodation / Expenses: Ignyta. L.J. Wirth: Honoraria (self), Advisory / Consultancy: Ayala Pharmaceuticals; Honoraria (self), Advisory / Consultancy: Eisai. C. Rodriguez: Honoraria (self), Advisory / Consultancy: Cue Biopharma; Research grant / Funding (institution): AstraZeneca; Research grant / Funding (institution): Bristol-Myers Squibb; Research grant / Funding (institution): Merck. E. Dekel: Shareholder / Stockholder / Stock options, Full / Part-time employment: Ayala Pharmaceuticals. R.M. Walker: Shareholder / Stockholder / Stock options, Full / Part-time employment: Ayala Pharmaceuticals. C. Nadri-Shay: Shareholder / Stockholder / Stock options, Full / Part-time employment: Ayala Pharmaceuticals. A. Vergara-Silva: Shareholder / Stockholder / Stock options, Full / Part-time employment: Ayala Pharmaceuticals. All other authors have declared no conflicts of interest.

The relevance of the cavity expansion analyses to the penetration mechanics of rigid projectiles, impacting metallic and concrete targets, is discussed. In the past six years we offered an alternative approach to that reviewed by Sobeski and Urgessa (2015), and we briefly discuss that work in this comment. To our best understanding, the cavity expansion analyses are irrelevant to the penetration mechanics of rigid projectiles impacting metallic or concrete targets.

This comment addresses several issues in the recent paper by Warren [1], who advocates the inclusion of target inertia in the resisting stress on rigid projectiles penetrating metallic targets. Our main argument is that this approach, which is based on the dynamic cavity expansion analysis, is incorrect and we outline its deficiencies. We briefly review our penetration model, in which the target exerts a constant force on the rigid projectile. This approach is more physically-based, and it accounts for the data presented in Warren [1] in a better way.

The process of ductile plate perforation by sharp-nosed rigid projectiles is further examined in this work through 2D numerical simulations. We highlight various features concerning the effective resisting stress ( σ r ) which a finite thickness plate, with a flow stress of Y t , exerts on the projectile during perforation. In particular, we show that the normalized resisting stress ( σ r / Y t ) can be represented as a unique function of the normalized thickness of the plate ( H / D , where H is plate thickness and D is projectile diameter), for a large range of normalized thicknesses. Our simulations for very thin target plates show that the penetration process is achieved through the well-known dishing mechanism, where the target material is pushed forward by the projectile’s nose. An important observation, which emerges from our simulations, is that the transition between the dishing and the hole enlargement mechanisms takes place at a normalized thickness of about H / D = 1/3. We also find that the normalized resistive stress for intermediate plate thicknesses, 1/3 H / D σ r / Y t = 2.0. This range of thicknesses conforms to a state of quasi plane stress in the plates. For thicker plates ( H / D > 1) the σ r / Y t ratio increases monotonically to values which represent the resistance to penetration of semi-infinite targets, where the stress state is characterized by plane strain conditions. Using a simple model, which is based on energy conservation, we can predict the values of the ballistic limit velocities for many projectile/target combinations, provided the perforation is done through the ductile hole enlargement mechanism. Good agreement is demonstrated between predictions from our model and experimental data from different sources, strongly enhancing the confidence in both the validity and usefulness of our model.

The penetration of rigid long rods into semi-infinite concrete targets is revisited. In particular, we focus on the deceleration of these rods during their penetration, as inferred from the experimental data for penetration depths vs. impact velocities. We find that for a given concrete these decelerations are independent on impact velocity, which enables us to construct a simple relation between the penetration depth and impact velocity. Our model is different from the model which is based on the dynamic cavity expansion analysis to account for the resisting forces on the rod. The cavity expansion model has two terms for the resisting force, a strength term and an inertia term which depends on the velocity of the rod. In the present work we show that there is no physical basis for the inclusion of an inertia term and that the concrete's resisting force depends only on its strength, as with metallic targets. We demonstrate the validity of our approach by comparing its predictions with penetration depths from published data for different concrete and grout targets. We also find an empirical relation between the concrete's resisting stress and its unconfined compressive strength. Several important issues concerning target dimensions and the strength of the rod are discussed. These issues should be carefully considered as they influence the rigid nature of the rod and the semi-infinite condition of the target.

A series of 2D numerical simulations was performed in order to follow various features in the penetration mechanics of deforming long rods. In particular, we were interested in the threshold velocity which marks the transition from rigid to deforming rod and the resulting depths of penetration around this transition velocity. We simulated various cases in which we varied the yield strengths of the rod and the target, as well as their densities and the nose shape of the rod. With the results of these simulations we constructed a rather simple model which accounts for the threshold velocity from rigid to deforming rod behavior. This model’s predictions are in good agreement with both our simulations and with experimental data for various rods and targets.

The use of commercial manganin gauges is limited to shock pressures of about 20 GPa, at which they fail by a fast short-circuiting effect in the polymeric layers encapsulating these gauges. It is commonly agreed that this effect is the result of some high pressure chemical process in these polymers (e.g. epoxy, Kapton etc.), such as a phase transition or some bond rupture. The present paper explores this issue in order to better understand this short-circuiting phenomenon. In particular, we wanted to find out whether this effect is pressure or temperature dependent. We present the results of five high pressure experiments in which epoxy-encapsulated manganin gauges were loaded in a quasi-isentropic mode, in order to achieve much lower temperatures at high pressures. Under these conditions, the commercial gauges did not fail at pressures as high as 60 GPa. We shall show that gauge short-circuiting is closely related to the high pressure phase transition of epoxy. With the results of our stress measurements, together with temperature estimates from 1D simulations, we were able to construct the phase line of epoxy in the pressure–temperature plane.

We present results of a large number of 2D numerical simulations in which we investigated various aspects in the deep penetration of rigid short projectiles into semi-infinite targets, as well as their perforation through thin metallic plates. In particular, we analyze the effect of the entrance phase on the penetration characteristics of short ogive and spherical nosed projectiles. The second issue which we investigate here concerns the perforation of metallic plates by sharp nosed projectiles. Our simulation results show that a simple model, which is based on energy conservation, accounts for the residual velocities when the target is penetrated by the ductile hole enlargement process. In addition, we define a new concept, the effective resisting stress which the plate exerts on the projectile during perforation. We show that it has some valuable insights for the process of perforation and we perform a parametric study to understand its dependence on various parameters. This effective stress, which determines the ballistic limit velocity of the projectile, depends on the strength of the plate, as well as on its thickness, as we show here.

The penetration process of rigid long rods with different nose shapes (ogive, spherical, conical and flat) is analyzed through a series of 2D numerical simulations. Aluminum and steel targets with different strengths (and large dimensions) are used to follow the deceleration process of these rods from impact, at different velocities, to the final penetration point. We find that for low impact velocities the deceleration of these rods is practicably constant, depending only on the strength of the target and the nose shape of the rod. Above a threshold (critical) impact velocity rod deceleration becomes velocity dependent due to the inertial response of the target. These critical velocities depend on the strength of the target and the nose shape of the rod. These observations led us to propose a simple penetration formula which accounts very well for penetration depths data for rigid steel rods with different nose shapes, impacting various aluminum targets at velocities up to about 1.5 km/s. For higher impact velocities, where the dynamic (inertial) contribution to the target resistance is important, we find good agreement between our model predictions and the simulation results for final penetration depths.

The dynamic spherical cavity expansion is treated through a complete analytical solution of the equations of motion for an elasto-plastic solid obeying von-Mises yield criterion. The solutions for various metals, with different elastic and plastic properties, are fitted with a third order polynomial which relates the normalized pressure inside the cavity with the normalized velocity of the cavity wall. An extensive search for material similarities is conducted in order to highlight the roles of the elastic properties of the solid, as well as its strength and equation of state parameters. Using the simple terms we derive, for the coefficients in the third order polynomial, one can easily calculate the relation between pressures inside the cavity and their wall velocities for any solid to within 1%.

A series of plate impact experiments with soda-lime glass specimens was performed in order to further investigate the complex behavior of this material in the 0–8 GPa range of shock loading. Using commercial manganin gauges we followed the stress histories and their different shapes as the stresses increase from 3.5 to about 8.0 GPa. In particular, we find that there are meaningful differences between the shapes of these signals at pressures below about 4.0 GPa, in between 4.0 and 6.0 GPa and above 6.0 GPa. We also gather more data on the fractured glass behind the fracture wave front, from our measured stress histories, and offer a new way to determine the Hugoniot elastic limit of this material, as well as other brittle solids.

The important mechanisms for defeating armor piercing (AP) projectiles are reviewed in this paper. These mechanisms are based on the compressive strength of the target material (its inherent resistance to penetration) and on the asymmetrical forces which it exerts on the threat, through proper geometrical arrangements. We discuss the basic features of the resistance to penetration, starting with the classical analysis of the cavity expansion process in elasto-plastic solids. This property of the target is responsible for the deceleration of hard cored projectiles and for the erosion of long rods, under normal impact conditions. We then discuss the asymmetrical interaction of AP projectiles with inclined plates (metals and polymers) and with ceramic spheres. These asymmetric forces are responsible for their deflection and breakup. Our work combines experimental observations with numerical simulations and engineering models, which enhance the understanding of the various phenomena encountered in these complex situations. This understanding is necessary for optimizing the performance of any armor design against a given threat.

The paper describes a series of 2D numerical simulations which followed the cavity expansion process in an elasto- plastic solid. The results from these simulations, in terms of cavity wall motion as a function of the applied pressures inside the cavity, highlighted several issues concerning cavity expansion process and the terminal ballistics of both rigid and eroding long rods. These issues include the form of the relation between the dynamic radial stress on the cavity wall and its velocity, which can be written in a simple, normalized form, at least for the materials we simulated here. Also, the difference between target resistance to the penetration of rigid and eroding-rod penetration, was quantified with a series of simulations in which the pressures in the cavity were applied on an angular section, rather than on its whole surface. Finally, we explored the inherent differences between spherical and cylindrical cavity expansion processes, which can be helpful for analytical models of the penetration of rigid rods with different nose shapes.

The ricochet of eroding long rods, from inclined steel targets, is investigated by a series of three-dimensional (3D) numerical simulations. These are compared with the predictions of our, previously published, analytical model for ricochet. The agreement between simulation results and model predictions is excellent, strongly enhancing our simple ricochet model. We also highlight several aspects of our model which are derived from its simple closed form. One of these is the fact that ricochet of long rods can take place only at velocities and obliquities which are higher than certain threshold values. Otherwise, the process involves rod bending and sliding along the target impact face.

One of the most complex processes, in the field of terminal ballistics, is that of yawed impact of long rods. In spite of many experimental observations, and some analytical modeling, a clear picture of this issue is still lacking. In order to gain some insight into the operating mechanisms, we developed a simple engineering model which considers the yawed rod as a series of small disks. We then define the effective length and diameter of the rod by considering those disks which are going to hit the initial crater which is opened by the impact. We also performed a series of 3D numerical simulations with various L/D tungsten alloy rods impacting a steel target, at yaws in the full range of 0-90°. We analyzed the results of these simulations in terms of the normalized penetration (P/D), where D is the rod diameter, and looked for systematic trends in the results for the various rods. The agreement between our model predictions and both experimental data and simulation results is quite good. Based on this agreement we can highlight some new features of the penetration process of yawed rods.

When a rigid armor piercing (AP) projectile impacts an inclined plate it can be deflected by the asymmetric forces, which the target exerts on the projectile. This is a well-known phenomenon which has been investigated by several workers impacting various metallic targets with AP projectiles. These works have shown that if the incidence angle is small enough the projectile can ricochet from any metallic target, provided the target is thick enough. In the present study we investigated the deflection, and ricochet, of 0.3″ AP projectiles impacting inclined polymeric targets, which, to our best knowledge, were not investigated before. We concentrate our attention on Plexiglas targets, which turned out to exert the strongest asymmetric forces on the AP projectile. We present a thorough 3D numerical study following the important properties of the target, which control the ricochet and deflection processes. It turns out that these properties are the high compressive strength and the low tensile strength of the target. In other words, the high brittleness of Plexiglas is responsible for the large deflection which was observed in our experiments. Other polymers, less brittle, resulted in a much lower effect or no effect at all.

The terminal ballistics of long-rod penetrators is a very complex field of research involving high pressure physics, continuum mechanics, material science and high strain rate phenomena. The research in this field is advanced through experimental data collection, engineering models, and numerical simulations. In the present paper, we summarize some of our recent work which is focused on determining the important material parameters in the interaction of long rods with various targets (both stationary and moving). Our basic goal is to be able to account for various phenomena encountered in the experiments, rather than reproduce the data very accurately. We achieve this goal by using the minimal set of material parameters which is needed in order to highlight the basic features in the interaction. We also show how 3D numerical simulations help to establish a simple model for the complex interaction between a tungsten alloy rod and a moving steel plate.

The behavior of rigid long rods, during deep penetration into thick metallic targets, is quite different from that of eroding rods. These differences are discussed in the present paper, through a series of 2D numerical simulations, compared with experimental data, on steel rods impacting aluminum targets. Special emphasis is placed on the threshold impact velocity, where the rods are starting to deform. At these velocities, penetration depths of the rods decrease substantially, and we were trying to account for these reductions in our simulations. We also study the effect of rod aspect ratio (L/D) on its penetration efficiency (P/L), as well as the role of rod and target strengths and their density ratio (ρ P/ ρ t ) on this efficiency.

We study optically single self-assembled quantum dots embedded within the wide quantum well of a mixed type quantum structure. We compare the steady state and pulsed photoluminescence spectra of these dots to those of previously studied "regular" dots. We unambiguously identify experimentally emission from various discrete charge state of the dots. We provide means for optically tune the charge state of the dot, both negatively and positively. Our observations are used to accurately determine the asymmetry between the quantum dots' confined electron and hole envelope wavefunctions.

The secondary penetration of long rods, impacting semi-infinite metallic targets, has been investigated since the early 60's, both experimentally and analytically. Several models have been proposed for the extra penetration which is achieved by these rods at the later stages of the process. However, the models are of limited applicability since they cover only limited regimes of the relevant parameters. In order to further understand the phenomenon of secondary penetration, we performed a large number of numerical simulations using the PISCES 2 DELK code. These simulations dealt with the relevant parameters in large ranges of variability, such as: the rod impact velocity, its aspect ratio (L/D), as well as the densities and strengths of rod and target material. We show that the semi-empirical formulations do not account for the whole range of these parameters. Our simulations show that the strength of the rod has a major influence on the values of the secondary penetrations. In addition, these values are strongly dependent on L/D and target strength.

The process of long-rod penetration into thick metallic targets is examined through a series of two-dimensional simulations. The aim of the research presented here is to uncover the inherent material similarities in this process. In particular, the search is for non-dimensional parameters which account for the depth of penetration, such as the density ratio, and the relative strengths of penetrator and target. The simulation results are in accord with existing empirical data, shedding more light on the penetration process and emphasizing the difficulties in achieving an overall normalization procedure for this process.

We resolve spatially, spectroscopically and temporally the photoluminescence emission from single self-assembled In(Ga)As/GaAs quantum dots, The temporal evolution of the emission spectrum after pulsed excitation is measured for various excitation intensities at various ambient temperatures. The evolution of the spectrum with the increase in both steady state and pulse excitation intensities is measured as well. A multi-exciton model is used for calculating the temporal and excitation intensity dependence of the measured spectra. The quantitative agreement between the measured and calculated spectra provides an unambiguous determination of the radiative lifetime of a single quantum dot exciton. This lifetime is 4-6 ns long and is temperature independent. The reduced spatial coherence between the confined exciton and the radiation electromagnetic field quantitatively explains this long radiative time.

Using time correlated single photon counting combined with temperature dependent diffraction limited confocal photoluminescence spectroscopy we accurately determine, for the first time, the intrinsic radiative lifetime of single excitons confined within semiconductor quantum dots. Their lifetime is one (two) orders of magnitude longer than the intrinsic radiative lifetime of single excitons confined in semiconductor quantum wires (wells) of comparable confining dimensions. We quantitatively explain this long radiative time in terms of the reduced spatial coherence between the confined exciton dipole moment and the radiation electromagnetic field., Comment: 4 pages, 3 figures

We resolve spatially, spectroscopically, and temporally the photoluminescence emission from single self-assembled InAs/GaAs quantum dots. The rich photoluminescence spectrum and its evolution with time after pulse excitation and with the density of excitation is experimentally measured and analyzed using a theoretical multiexciton model. The model accounts quantitatively for the dynamics of a small number of interacting electrons and holes confined in optically excited semiconductor quantum dots.

The work presented here examines the possibility of achieving an overall non-dimensional expression for the penetration depth of long rod penetrators into semi-infinite metallic targets. The work is based on 2D numerical simulations, using the PISCES 2DELK code, varying all the relevant material parameters in a wide range. These include rod and target densities and strengths, penetrator aspect ratio and impact velocity. It is found that a single normalized expression for the penetration depth vs. impact velocity is very difficult, if not impossible, to achieve over the whole range of parameters. However, for limited ranges one can obtain such representations in a non-dimensional presentation.

We applied low-temperature diffraction-limited confocal optical microscopy to spatially resolve and spectroscopically study photoluminescence from single self-assembled semiconductor quantum dots. Using selective wavelength imaging we unambiguously demonstrated that a single photoexcited quantum dot emits light in a few very narrow spectral lines. The measured spectrum and its dependence on the power of either cw or pulsed excitation are explained by taking carrier correlations into account. We solve numerically a many-body Hamiltonian for a model quantum dot, and we show that the multiline emission spectrum is due to optical transitions between confined exciton multiplexes. We furthermore show that the electron-electron and hole-hole exchange interaction is responsible for the typical appearance of pairs in the photoluminescence spectra and for the appearance of redshifted new lines as the excitation power increases. The fact that only a few spectral lines appear in the emission spectrum strongly indicates fast thermalization. This means that a multiexciton relaxes to its ground state much faster than its radiative lifetime., The research was supported by the U.S.-Israel Binational Science Foundation (453/97) and the Technion Fund for the promotion of research.

2D numerical simulations were performed in order to further investigate the role of penetrator strength in the interaction of long rods and semi-infinite targets. These simulations are used to highlight the reasons for several discrepancies between existing data and the well-known 1D model for penetration. In particular, the nature of the secondary penetration of high-density rods, the hydrodynamic limits of high-strength rods, and the predicted maxima in their penetration curves are discussed. The causes for these discrepancies are established by additional numerical simulations which explore the validity of the penetrator strength parameter in the analytical model as a physical entity. It is shown that this is, indeed, the weakest part of the model since it is strongly dependent on both the impact velocity of the rod and its length-to-diameter ratio.

Summary The normal incidence of shaped charge jets on confined explosive sheets is investigated through a series of 2D numerical simulations with the Eulerian code PISCES 2DELK. The basic mechanisms of the interaction are explored using a relatively simple criterion for the sheet efficiency to disrupt the jet, which is based on the undisturbed length of the emerging jet. The simulations are compared with experimental results published several years ago and the agreement is good. Using these simulations we show how one can optimize the efficiency of this interaction by using non-symmetrical confinement plates and stronger explosive sheets.

The superiority of depleted uranium on tungsten-alloy penetrators has recently been assigned to the self-sharpening mechanism, at the tip of the DU rods, due to the adiabatic shear failure which this material experiences. The purpose of the work presented here was to further investigate the role of deformed nose profile on the deep penetrations of long rods into semi-infinite targets. This was achieved through a series of 2-D numerical simulations and several perforation experiments where we recovered and examined the residual penetrators. The simulations were performed for rigid tungsten-alloy rods having five different nose shapes with the density and elastic properties of tungsten alloys. For the normal impact experiments we chose three rod materials: a tungsten alloy, a copper and a titanium alloy. The residual rods (after perforation of finite thickness targets) were imaged by flash X-ray and softly recovered using sand boxes. As expected, the nose shapes of these rods were very different from each other.

Measurements of the dynamic spall strength in aluminum and copper shocked by a high power laser to pressures of hundreds of kbars show a rapid increase in the spall strength with the strain rate at values of about 107 s−1. We suggest that this behavior is a result of a change in the spall mechanism. At low strain rates the spall is caused by the motion and coalescence of material’s initial flaws. At high strain rates there is not enough time for the flaws to move and the spall is produced by the formation and coalescence of additional cavities where the interatomic forces become dominant. Material under tensile stress is in a metastable condition and cavities of a critical radius are formed in it due to thermal fluctuations. These cavities grow due to the tension. The total volume of the voids grow until the material disintegrates at the spall plane. Simplified calculations based on this model, describing the metal as a viscous liquid, give results in fairly good agreement with the experimental data and p...

The paper summarizes a series of two-dimensional numerical simulations which were performed to study the effects of material properties on the terminal ballistics of long-rod penetrators. Our focus was on the properties of the rod material, unlike recent works which concentrated on a target’s properties. We varied almost all the relevant parameters within a large range of values in order to study the separate effects of each one. These parameters included: compressive and tensile strengths, elastic moduli, melting temperatures and the maximum equivalent plastic strain (failure strain) of the rod material. Most of the simulations were performed for an actual experiment with 300 mm tungsten-alloy long-rod, impacting a semi-infinite steel target. The simulations show that the mechanical and thermal softening mechanisms are the most dominant, as far as the depth of penetration is concerned. In contrast, the elastic moduli and spall strength have a negligible effect as far as penetration depth is concerned.

A series of 2-D numerical simulations of the bulging of passive cassettes, penetrated by shaped charge jets, is described. The purpose of these simulations was to determine the factors affecting the speed of the bulging process in order to be able to design more efficient cassettes. Physical and geometrical parameters, of the different cassette constituents, were varied systematically. These included strengths, elastic moduli, thicknesses and densities of the materials involved.

The paper describes a set of experiments with copper and tungsten alloy long-rods, which were aimed at finding the sources of non-scaling effects recently discovered in terminal ballistics. Our basic assumption was that geometrical scaling should hold for ductile penetrators (like copper) and that any deviation from this scaling should be attributed to brittle failure mechanisms at the penetrator's head. Our experimental results support this assumption as far as the depth of penetration into steel of two penetrators, differing by a factor of 2, is considered. Thus, copper penetrators scaled well, within experimental error, while a difference of about 10% was found between the depth of penetration of 1:2 and 1:4 tungsten alloy penetrators. We also present two-dimensional simulations, which were performed with the PISCES 2DELK code, in order to determine lateral edge effects. These simulations enabled us to choose the right size for our “infinite” targets, avoiding any influence from their lateral-free surface.

A series of terminal ballistics experiments and 2-D simulations, with small scale tungsten alloy penetrators, was performed in order to quantify the ballistic efficiency of confined ceramic tiles. The data includes both depth of penetration (DOP), into thick steel backing and X-ray shadowgraphs during the penetration process. Impact velocities ranged between 1.25 to 3.0 km/s. The size of the tiles varied in order to check their performance as a function of thickness and lateral dimensions. We found that the differential ballistic efficiency of alumina tiles is practically independent on impact velocity and tile thickness, within the ranges of velocity and thicknesses, investigated here. A detailed simulation study, using the Eulerian processor of the PISCES 2-D ELK code, was performed in order to better understand the interaction between long-rods and ceramic tiles, and particularly, to adjust a proper failure criterion to the tiles. We found that a simple version of the Johnson-Holmquist model, with a single parameter, is fairly adequate to account for most of the data. These include: lateral confinement, tile thickness and impact velocity influence on the penetration depth. We used the code to further investigate the influence of lateral dimensions on tile performance.

A thought-provoking book by Boldrin and Levine (2009) argues that patents are always detrimental to competition and thereby to innovation. To provide support to their analysis these two authors built a growth model where innovation and growth can occur under perfect competition. The model is then used to argue that monopoly rents and therefore patents are not needed for innovation and growth: on the contrary, patents are detrimental to innovation because they reduce competition. That reducing competition can be detrimental to innovation, is a sound idea which could not be accounted for by the new growth models of Romer (1990) and Aghion and Howitt(1992). In these models, competition is detrimental for innovation and growth for exactly the same reason for why patent protection (IPRs) is good for innovation: namely because competition reduces (post innovation) rents whereas patent protection increases these rents. In this note we argue that this latter conclusion is not robust to considering more elaborated models of competition and innovation. In particular we show below that in a step-by-step innovation model, where a laggard firm needs to catch up with the current leader in its sector (and therefore go through a neck-and-neck stage) before it could later become a leader itself, not only can competition enhance innovation as in Boldrin and Levine’s model, but also and perhaps more importantly competition and IPRs become complementary policies. Why? Because the incentive to innovate depends on the gap between the post-innovation rent and the pre-innovation rent, call it the net innovation rent. And typically, what competition does is to lower pre-innovation rents, and also maybe post-innovation rents, although the difference between postand preinnovation rents may still increase with competition, and all the more so with stronger patents to protect post-innovation rents. In contrast, in our earlier Schumpeterian models where innovations are made by outsiders who then leapfrog incumbent firms, the pre-innovation rent is always equal to zero, thus all ∗Harvard University †Brown University ‡University of Cologne

Two-dimensional numerical simulations were used to explore the penetration capability of long-rods as a function of their strength. Tungsten alloy rods of varying strengths were ‘shot’ at semi-infinite armor steel targets in the velocity range of 1.4–2.2 km/s. It is found that penetration depths versus penetrator strength curves have a maximum which depends on the impact velocity. This effect which, to our best knowledge, has not been reported previously can be explained, at least qualitatively, by considering the deceleration of the rear part of the rod, as its strength increases. This deceleration can lead to a substantial decrease in the velocity of the rear part of the penetrator with the result that its penetration capability is reduced beyond that of a nondecelerating penetrator. The deceleration is a direct consequence of the elastic waves travelling along the back part of the rod with an amplitude which is equal to the strength of the penetrator material.

This paper investigates the interaction of long-rod penetrators with thick ceramic tiles, sandwiched between steel plates, through several model experiments and 2-D simulations. Experimental data from low velocity penetrations have been used to calibrate the relevant properties of the ceramic specimens. The influence of increasing impact velocity on tile performance was then investigated through data and simulations of shaped charge jets penetrating the ceramic. We found that the ballistic efficiency of the ceramic tile is lower against high velocity (5 km/s) long-rods, in contrast with the common thesis that their improved performance against shaped charge jets is the result of their enhanced strength. On the other hand, our simulations clearly show that, for high strength ceramics, there is a radial motion of metal and ceramic debris towards the penetration axis. This effect is, probably, the main reason for the considerable improvement in the performance of ceramic tiles against shaped charge jets.

The protective capability of a structure against a given threat can be evaluated by several measures. One of them is the ballistic limit velocity (Vbl) of the specific armor/threat combination. Obviously, the aim of the armor designer is to increase the value of Vbl without increasing the weight of the structure. The relevant measure of the armor weight is its areal density (AD), given in units of kg/m2, which is simply the density of the protective structure multiplied by its thickness. The ballistic efficiency of a given structure is defined by its areal density, as compared with that of a reference target, which is needed to defeat a given threat. Frank (1981) suggested several measures for the ballistic efficiency of improved structures, through their mass (Em) and space (Es) efficiency, according to: $$ {E_m} = \frac{{{{\left( {AD} \right)}_r}}}{{{{\left( {AD} \right)}_s}}} $$ $$ {E_s} = \frac{{{P_r}}}{{{P_s}}} $$ where the indices (r) and (s) denote the reference target and the improved structure, respectively, and P is the minimal thickness of the target which is needed to defeat the threat. It is clear that the ballistic efficiency should be higher than 1.0 and the task of the armor designer is to increase these efficiencies to higher values. As mentioned above, one of the more practical ways to defeat a given threat is by adding a relatively lightweight structure in front of the protected object, as shown in Fig. 6.1. This add-on armor structure can significantly reduce the penetration capability of a given threat through an effective defeat mechanism, as will be demonstrated in this part of the book.

Numerical simulations of high velocity impact events are performed with large computer codes called hydrocodes, because their early use was for high pressure problems in which materials were treated as fluids. These codes can handle impulsive loadings which include shock waves with extremely high pressures and short rise times, as well as high temperatures and large deformations. Several review articles about hydrocodes and their use have been published over the past 30 years. As far as terminal ballistics is concerned, the reviews by Anderson (1987) and by Zukas (1990) are the most comprehensive and informative. The present chapter highlights some of the important issues concerning these codes for terminal ballistics studies. We follow Anderson’s statement that “hydrocodes are the best instrumented experiment”, since they can (and should) be used for sensitivity studies in terminal ballistics. These studies highlight the role of each parameter in the investigated process, and the physics behind the process is unveiled. Through the different issues presented in this book we shall demonstrate the construction and validation of analytical models with such sensitivity studies. As an example, consider the difficulty to determine experimentally the dependence of a projectile’s penetration depth on the strength of the target. Any experimental attempt to vary only the strength of a target, within a large range of values, will result in some changes in its other properties as well. On the other hand, a series of simulations where only the strength of the target is varied systematically is easy to perform and it can offer the insight for this issue. Another important advantage of hydrocodes is that they can give information about events which are beyond any laboratory’s performance. For example, the impact of meteors at velocities of 20–40 km/s, cannot be studied in the laboratory but it can be easily investigated with these codes.

Summary The modified Bernoulli equation is examined through a series of two-dimensional simulations of long rods penetrating semi-infinite targets. These are copper, aluminium and tungsten alloy rods having zero strength with length-to-diameter ratios of 20. The targets are steel and tungsten alloy with yield strengths in the range of 0–2 GPa. Impact velocities were varied between 1 and 7 km/s. Each simulation results in a definite value for the steady-state penetration velocity, which is substituted in the modified Bernoulli equation to derive an effective resistance to penetration (Rt). The dependence of Rt on target yield strength, impact velocity and projectile and target characteristics is determined.

Summary Recent experimental studies, on the penetration of long rods into semi-infinite steel targets, reveal some features which cannot be predicted by the conventional 1-D penetration model of Alekseevskii and Tate. This paper presents experimental results together with 2-D simulations which were performed in order to investigate this discrepancy. Specifically we are interested in the question of whether the normalized penetration curve— P/L ( P is penetration depth, L is penetrator length)—is dependent on penetrator's length to diameter ratio in the range of L/D = 10–40. Both experimental and simulation results show a decrease of about 15% between P/L values for L/D = 10 and 20 rods as well as for L/D = 20 and 30. These, rather large, differences are discussed in terms of material parameters which are resonsible for the discrepancy between the 1-D model and both experiment and simulation. Moreover, we have simulated the penetration of long rods having zero yield strength. Our results show that for large aspect ratios ( L/D > 30) these weaker rods penetrate more than those with their full yield strength. This crossover phenomenon is both counterintuitive as well as opposed to the predictions of the 1-D model for this combination of rod-target materials.