Analysis on the resistive force in penetration of a rigid projectile

According to the dimensionless formulae of DOP (depth of penetration) of a rigid projectile into different targets, the resistive force which a target exerts on the projectile during the penetration of rigid projectile is theoretically analyzed. In particular, the threshold V_c of impact velocity applicable for the assumption of constant resistive force is formulated through impulse analysis. The various values of V_c corresponding to different pairs of projectile-target are calculated, and the consistency of the relative test data and numerical results is observed.     

Estimation of the kinetic parameters for thermal decomposition of HNIW and its adiabatic time-to-explosion by Kooij formula

A differential/integral method to estimate the kinetic parameters (apparent activation energy E_a and pre-exponential factor A) for thermal decomposition reaction of energetic materials based on Kooij formula are applied to study the nonisothermal decomposition reaction kinetics of hexanitrohexaazaisowurtzitane (HNIW) by analyzing nonisothermal DSC curve data. The apparent activation energy (E_a) obtained by the integral isoconversional non-isothermal method based on Kooij formula is used to check the constancy and validity of apparent activation energy by the differential/integral method based on Kooij formula. The most probable mechanism function of thermal decomposition reaction of HNIW is determined by a logical choice method. The equations for calculating the critical temperatures of thermal explosion (T_b) and adiabatic time-to-explosion (t_TIad) based on Kooij formula are used to calculate the values of T_b and t_TIad to evaluate the thermal safety and heat-resistant ability of HNIW. All the original data needed for analyzing the kinetic parameters are from nonisothermal DSC curves. The results show that the kinetic model function in differential form and the values of E_a and A of decomposition reaction of HNIW are 3(1 − α)[−ln(1 − α)]^2/3, 152.73 kJ mol⁻¹ and 10^11.97 s⁻¹, respectively, and the values of self-accelerating decomposition temperature (T_SADT), T_b and t_TIad are 486.55 K, 493.11 K and 52.01 s, respectively.     

Effect of energy content of the nitraminic plastic bonded explosives on their performance and sensitivity characteristics

Information about the forty nine nitraminic plastic bonded explosives (PBXs) and different nitramines were collected. Fillers of these PBXs are nitramines 1,3,5-trinitro-1,3,5-triazinane (RDX) and β-1,3,5,7-tetranitro-1,3,5-tetrazocane (β-HMX), cis-1,3,4,6-tetranitro-octahydroimidazo-[4,5-d]imidazole (bicyclo-HMX, BCHMX) and ε-2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (ε-HNIW, CL-20) which are bonded by polyfluoro-elastomers, polydimethyl-siloxane, poly-glycidyl azide, polyisobutylene, polystyrene-butadiene, poly-acrylonitrile-butadiene and hydroxyl-terminated polybutadiene in addition to a melt cast compositions based on 2,4,6-trinitrotoluene. For thirty two of these PBXs the relationships are specified and analyzed between heats of their combustion and relative explosive strengths; by means of these relationships it might be possible to estimate, which groupings in the macromolecule of binder could be liable to their primary fission in the PBXs initiation. Similarly, for forty two of these explosives, the relationships are described and analyzed between their enthalpies of formation and impact sensitivities; here is especially attention paid to PBXs filled by BCHMX. Specific rate constants from Vacuum Stability Test (VST) of four nitramines and twenty PBXs are introduced into relationships with their enthalpies of formation. Regarding to all the mentioned cases, increasing of energy content of the studied explosives leads to increase of the relative explosive strength or initiation reactivity, respectively. Exception with the opposite trend, the outputs of VST are for BCHMX, where in PBXs are matrices with the esteric plasticizers or the energetic poly-glycidyl azide. Admixture of RDX or HMX, respectively, into the BCHX PBXs gives ternary PBXs whose thermal stability, in the sense of applied VST, is higher comparing to the original binary explosives.     

Weighted vertex packing problem for specially structured geometric graphs

Consider a set of vertices V = {1, 2,…, n} placed on a two-dimensional Euclidean plane R² with each vertex attached a nonnegative weight w: V → R. For a given constant d>0, the geometric graph G = (V, E) is defined to have edge set E = {(i, j): d_ij ⩽ d} with d_ij being the Euclidean distance between vertices i and j. The geometric vertex packing (GVP) problem, which is often called the independent set problem, is defined as selecting the set of pairwise nonadjacent vertices with maximum total weight. We limit our attention to the special case that no vertex is within a distance βd of any other vertices where 0 ⩽ β < 1. A special value of β (= 1/2) is referred to frequently because of its correspondence to a manufacturing problem in circuit board testing. In this article we show that the weighted vertex packing problem for the specially structured geometric graph (SGVP) defined with the above restriction is NP-complete even for the case that all vertex weights are unity and for any β. Polynomial procedures have been designed for generating cuts to obtain tight LP upper bounds for the SGVP. Two heuristics with bounded worst-case performance are applied to the LP solution to produce a feasible solution and a lower bound. We then use a branch-and-bound procedure to solve the problem to optimality. Computational results on large-scale SGVP problems will be discussed. © 1995 John Wiley & Sons, Inc.     

Some properties and computational results for a general repair process

We consider a general repair process where the virtual age V_i after the ith repair is given by V_i = ϕ(V_i−1 + X_i), ϕ(·) is a specified repair functional, and X_i is the time between the (i − 1)th and ith repair. Some monotonicity and dominance properties are derived, and an equilibrium process is considered. A computational method for evaluating the expected number/density of repairs is described together with an approximation method for obtaining some parameters of the equilibrium process. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 391–405, 1998     

Ballistic response of armour plates using Generative Adversarial Networks

It is important to understand how ballistic materials respond to impact from projectiles such that informed decisions can be made in the design process of protective armour systems. Ballistic testing is a standards-based process where materials are tested to determine whether they meet protection, safety and performance criteria. For the V₅₀ ballistic test, projectiles are fired at different velocities to determine a key design parameter known as the ballistic limit velocity (BLV), the velocity above which projectiles perforate the target. These tests, however, are destructive by nature and as such there can be considerable associated costs, especially when studying complex armour materials and systems. This study proposes a unique solution to the problem using a recent class of machine learning system known as the Generative Adversarial Network (GAN). The GAN can be used to generate new ballistic samples as opposed to performing additional destructive experiments. A GAN network architecture is tested and trained on three different ballistic data sets, and their performance is compared. The trained networks were able to successfully produce ballistic curves with an overall RMSE of between 10 and 20 % and predicted the V₅₀ BLV in each case with an error of less than 5 %. The results demonstrate that it is possible to train generative networks on a limited number of ballistic samples and use the trained network to generate many new samples representative of the data that it was trained on. The paper spotlights the benefits that generative networks can bring to ballistic applications and provides an alternative to expensive testing during the early stages of the design process.     

The non-isothermal gravimetric method for study the thermal decomposition kinetic of HNBB and HNS explosives

The hexanitrostilben (HNS) is a thermally stable explosive that can be prepared from hexanitrobibenzyl (HNBB). Therefore, the investigation of thermal stability of HNBB can be important in the yield of preparation of HNS. The decomposition kinetic of HNBB and HNS are studied by non-isothermal gravimetric method. The TG/DTG curves in non-isothermal method are obtained in range of 25°C–400 °C at heating rates of 3 °C/min, 5 °C/min, 8 °C/min, 10 °C/min and 12 °C/min. The data of weight-temperature are used for calculation of activation energy (E_a) of thermal decomposition reactions by methods of Ozawa, Kissinger, Ozawa-Flynn-Wall (OFW) and Kissinger-Akahira-Sunose (KAS) as model-free methods and Strink's equation as model-fitting method. The compensation effect is used for prediction of mechanism and determination of pre-exponential factor (lnA) of the decomposition reaction. A reduction 60 kj/mol for the average of activation energy of thermal decomposition reaction of HNBB is obtained versus HNS. This result shows the lower thermal stability of HNBB in comparison to HNS. The Avrami equation (A_3/2) with function f(α) = 3/2(1-α)[-ln(1-α)]^1/3 indicates the predicted mechanism for thermal decomposition reaction both explosives.     

Structure design and property adjustment of new cage rich-nitrogen pentazolyltetraazacubanes as potential high energy density compounds

In this study, based on two attractive energetic compounds pentazole (PZ) and tetraazacubane (TAC), a new family of high energy and high nitrogen compounds pentazolyltetraazacubanes were designed. Then, a different number of NH₂ or NO₂ groups were introduced into the system to further adjust the property. The structures, properties, and the structure-property relationship of designed molecules were investigated theoretically. The results showed that all nine designed compounds have extremely high heat of formation (HOF, 1226-2734 kJ/mol), good density (1.73–1.88 g/cm³), high detonation velocity (8.30–9.35 km/s), high detonation pressure (29.8–39.7 GPa) and acceptable sensitivity (ΔV: 41-87 ų). These properties could be effectively positive adjusted by replacing one or two PZ rings by NH₂ or/and NO₂ groups, especially for the energy and sensitivity performance, which were increased and decreased obviously, respectively. As a result, two designed pentazolyltetraazacubanes were predicted to have higher energy and lower sensitivity than the famous high energy compound in use 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane, while two others have better combination property than 1,3,5-Trinitro-1,3,5-triazacyclohexane. In all, four new pentazolyltetraazacubanes with good combination performance were successfully designed by combining PZ with TAC, and the further property adjustment strategy of introducing a suitable amount of NH₂/NO₂ groups into the system. This work may help develop new cage energetic compounds.     

A duel complicated by false targets and uncertainty as to opponent type

An attacker, being one of two types, initiates an attack at some time in the interval [-T, 0]. The a priori probabilities of each type are known. As time elapses the defender encounters false targets which occur according to a known Poisson process and which can be properly classified with known probability. The detection and classification probabilities for each type attacker are given. If the defender responds with a weapon at the time of attack, he survives with a probability which depends on the number of weapons in his possession and on attacker type. If he does not respond, his survival probability is smaller. These probabilities are known, as well as the current number of weapons in the defender's possession. They decrease as the number of weapons decreases. The payoff is the defender's survival probability. An iterative system of first-order differential equations is derived whose unique solution V₁(t),V₂(t),…,V_k(t) is shown to be the value of the game at time t, when the defender has 1, 2,…, k,… weapons, respectively. The optimal strategies are determined. Limiting results are obtained as t→-∞, while the ratio of the number of weapons to the expected number of false targets remaining is held constant.     

Bayes sequential strategies for crossing a field containing absorption points

A sequential decision problem is considered in which N particles have to cross a given field. Two alternative crossing paths are available. An unknown number of absorption points J₁ and J₂ are planted at each of the crossing paths. The bivariate prior distribution of (J₁,J₂) is given. If a particle passes close to an absorption point it may survive with probability s, 0 < s < 1. If a particle is absorbed, both the particle and the absorption point are ruined. There is no replacement of ruined absorption points. All absorption points act independently. The particles crciss the field in a consecutive order, and a crossing path can be chosen for each particle. The objective is to maximize the expected number of survivors. The Bayes sequential procedure is characterized. The csmditions under which the Bayes strategy is determined by the maximal posterior survival probabilities are specified.     

Investigating the surface integrity of aluminium based composites machined by EDM

In the present work, the surface characteristics of Electrical Discharge Machined (EDM) Al (6351)SiC and Al (6351)SiCB₄C composites are investigated. The composites are prepared by employing the conventional stir casting technique, as it can produce better particle dispersion in the matrix. The detailed experimental study is performed on the composites by varying current (I), duty factor (τ), pulse on time (T_on), and the gap voltage (V) in order to analyze the Heat Affected Zone (HAZ) formed in the sub surface and the average crater diameter formed on the machined surface of the composites as an output function. The formation of recast layers, presence of bubbles and the surface texture of the composites at various machining conditions are observed. The results show that the increased Metal Removal Rate (MRR) increases the depth of HAZ and the average crater diameter on the machined area. Further, the addition of B₄C particles to the composite produces more surface defect than the AlSiC composite.     

On convexity proofs in location theory

It is often assumed in the facility location literature that functions of the type ø_i(x_i, y) = β_i[(x_i-x)²+(y_i-y)²]^K/2 are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are given.     

Tuning the reactivity of Al–Ni by fine coating of halogen-containing energetic composites

In this paper, various core-shell structured Al–Ni@ECs composites have been prepared by a spray-drying technique. The involved ECs refer to the energetic composites (ECs) of ammonium perchlorate/nitrocellulose (AP/NC, NA) and polyvinylidene fluoride/hexanitrohexaazaisowurtzitane (PVDF/CL-20, PC). Two Al–Ni mixtures were prepared at atomic ratios of 1:1 and 1:3 and named as Al/Ni and Al/3Ni, respectively. The thermal reactivity and combustion behaviors of Al–Ni@ECs composites have been comprehensively investigated. Results showed that the reactivity and combustion performance of Al–Ni could be enhanced by introducing both NA and PC energetic composites. Among which the Al/Ni@NA composite exhibited higher reactivity and improved combustion performance. The measured flame propagation rate (v = 20.6 mm/s), average combustion wave temperature (T_max = 1567.0 °C) and maximum temperature rise rate (γ_t = 1633.6 °C/s) of Al/Ni@NA are higher than that of the Al/Ni (v = 15.8 mm/s, T_max = 858.0 °C, and γ_t = 143.5 °C/s). The enhancement in combustion properties could be due to presence of the acidic gaseous products from ECs, which could etch the Al₂O₃ shell on the surface of Al particles, and make the inner active Al to be easier transported, so that an intimate and faster intermetallic reaction between Al and Ni would be realized. Furthermore, the morphologies and chemical compositions of the condensed combustion products (CCPs) of Al–Ni@ECs composites were found to be different depending on the types of ECs. The compositions of CCPs are dominated with the Al–Ni intermetallics, combining with a trace amount of Al₅O₆N and Al₂O₃.     

A two-echelon multi-station inventory model for navy applications

The two inventory echelons under consideration are the depot, D, and k tender ships E₁, …, E_k. The tender ships supply the demand for certain parts of operational boats (the customers). The statistical model assumes that the total monthly demands at the k tenders are stationary independent Poisson random variables, with unknown means λ₁, …, λ_k. The stock levels on the tenders, at the heginning of each month, can be adjusted either by ordering more units from the depot, or by shipping bach to the depot an excess stock. There is no traffic of stock between tenders which is not via the depot. The lead time from the depot to the tenders is at most 1 month. The lead time for orders of the depot from the manufacturer is L months. The loss function due to erroneous decision js comprised of linear functions of the extra monthly stocks, and linear functions of shortages at the tenders and at the depot over the N months. A Bayes sequential decision process is set up for the optimal adjustment levels and orders of the two echelons. The Dynamic Programming recursive functions are given for a planning horizon of N months.     

A note on circular error probabilities

An approximation for P(X² + Y² ≤ K²σ²₁) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ²₁ and σ²₂ and σ₁ ≥ σ₂. Also, we provide asymptotic expressions for the probabilities for large values of β = K²(1 - c²)/4c² where c = σ₂/σ₁. These are illustrated by comparing with values tabulated by Harter [6]. Solution of K for specified P and c is also considered. The main point of this note is that simple and easily calculable approximations for P and K can be developed and there is no need for numerical evaluation of integrals.     

On the first time a separately maintained parallel system has been down for a fixed time

Consider a system consisting of n separately maintained independent components where the components alternate between intervals in which they are “up” and in which they are “down”. When the i^th component goes up [down] then, independent of the past, it remains up [down] for a random length of time, having distribution F_i[G_i], and then goes down [up]. We say that component i is failed at time t if it has been “down” at all time points s ?[t-A.t]: otherwise it is said to be working. Thus, a component is failed if it is down and has been down for the previous A time units. Assuming that all components initially start “up,” let T denote the first time they are all failed, at which point we say the system is failed. We obtain the moment-generating function of T when n = l, for general F and G, thus generalizing previous results which assumed that at least one of these distributions be exponential. In addition, we present a condition under which T is an NBU (new better than used) random variable. Finally we assume that all the up and down distributions F_i and G_i i = l,….n, are exponential, and we obtain an exact expression for E(T) for general n; in addition we obtain bounds for all higher moments of T by showing that T is NBU.     

Problem of the reference height of the projectile trajectory as a reduced meteo-ballistic weighting factor

This paper deals with the issue of preparation of the aiming angles with the use of tabular firing tables and needed determination of the ballistic elements μ_B (ballistic wind w_B, w_xB, w_ZB, ballistic (virtual) temperature τ_B, ballistic density ρ_B) from the standardized met messages. The weighting factors are used for the calculation of ballistic elements μ_B that are incorporated into the trajectory calculations characteristics of weapon and ammunition. Two different methodologies practically used in the praxis are analysed and compared. For the comparison of the two methodologies the reference height of trajectory determined from the weighting factor functions is employed. On the basis of the analyses conducted, the potential for further increase in accuracy of these aiming angles preparation methods is pointed out.     

二维 DFT 和 DCT 的 Systolic 阵列

超级计算中一个活跃的研究领域是将某些有限和,如离散富里叶变换(DFT)、离散余弦变换(DCT),映射到多处理机阵列上。本文首先通过二维DFT的行列分解算法流程图,给出了计算二维DFT的二种Systolic阵列:一种是由N_1个处理器组成的线性阵列,所花时间步为O(N_1N_2)(设二维DFT为N_1×N_2长的),与行列分解算法在单处理机上顺序执行所花时间相比,加速比为O(N)(设N_1=N_2=N)。这一结果无论是在时间消耗,还是在PE数量上都是目前最优的。另一种是由N_1×N_2个处理器组成的矩形阵列,所需时间为O(N_1+N_2),与行列算法在单处理机上顺序运行所花时间相比,加速比为O(N~2)(这里仍假定N_1=N_2=N)。本文还给出了二维DCT的与二维DFT相似的Systoilc阵列结构。不难将上述阵列推广到多维的情况。     

Theoretical study of an energetic material di-1H-1,3,4-triazole derivatives

Computations by density functional theory (DFT) method are performed on a series of di-1H-1,3,4-triazole derivatives with different substituents and linkages. The heat of formation (HOF) is predicted by the designed isodesmic reactions. The predicted results reveal that –N₃ and –NN– groups are effective structural units for increasing the HOF values of the di-1H-1,3,4-triazole derivatives. The HOMO–LUMO gap is affected by the substituents and linkage groups. Detonation performance is evaluated using the Kamlet–Jacobs approach based on the calculated density and HOF. The results indicate that –NO₂, –NF₂, –NH–, –NH–NH– and –NN– groups are helpful for enhancing the detonation properties of di-1H-1,3,4-triazole derivatives. The bond dissociation energy and bond order of the weakest bonds are analyzed to investigate their stability. It is observed that the –CH₂–, –CH₂–CH₂– and –CHCH– groups are effective structural units for improving the stabilities of these derivatives. Considering the detonation performance and the stability, five compounds are screened as the potential candidates for high energy density materials.     

On maximization of the integral of a bell-shaped function over a symmetric set

Given a target T in Euclidean n-space Rⁿ and a point bomb whose point of impact in Rⁿ is governed by a probability distribution about the aim point a, what choice of a maximizes the probability of a hit v_a(T)? Of course, only in special cases is an exact solution of this problem obtainable. This paper treats targets T which are symmetric about the origin o and demonstrates conditions on the extent of T and the impact density f, a density with respect to Lebesgue measure, sufficient for v_a(T) to be monotone in the distance from a to o and maximized at a = o. The results are applied to various tactical situations.