I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Prevalence and magnitude of body weight and image dissatisfaction among women in dietetics majors

[EN] Some authors have suggested that body weight dissatisfaction may be high in students majoring in dietetics. Therefore, this study was conducted to examine the extent of body weight and image dissatisfaction in a sample of women in dietetics major. Additionally, predictors of magnitude of body weight dissatisfaction were analyzed. Participants were 62 volunteers with normalweight whose mean age was 21.87±1.89 years old (nonrandom sample). The assessment instruments included anthropometric measurements, a somatomorphic matrix test and an eating disorders inventory (EDI-2). Data were analyzed using SPSS vs. 15.0. A larger proportion of students chose an ideal body weight lower than actual weight (67.7%) and body image with less body fat and more muscle mass than actual values (56.4%). The magnitude of body weight dissatisfaction was associated with muscle mass and body fat dissatisfaction, and with the subscale of EDI-2 “body dissatisfaction”. So, from a public health standpoint, we consider important to continue working in this line of research with the aim of better understanding the extent of body weight dissatisfaction in women dietitians, and how this dissatisfaction could interfere with their professional practice.

Body image and body composition: comparisons of young male elite soccer players and controls

[EN] The purpose of this study was to evaluate body composition and body image (perception and satisfaction) in a group of young elite soccer players and to compare the data with those of a control group (age and BMI matched). Participants were 56 volunteer males whose mean age and BMI were 19.6 (SD 1.3) years and 23.3 (SD 1.1) kg/m2, respectively. Results showed that soccer players have a higher lean mass and lower fat mass than controls. Moreover, body perception (difference between current and actual image) was more accurate in controls than in soccer players, and the results suggest a tendency for soccer players to aspire to have more muscle mass and body fat. Soccer players perceived an ideal image with significantly higher body-fat percentage than their current and actual images. There were no body-dissatisfaction differences between groups, however. Although the results are necessarily limited by the small sample size, the findings should be of interest to coaches of young elite soccer teams.

On the methods of determining size/weight characteristics of food organisms of fish. (Determination of the length of Copepoda in larval stages by egg-laying females of the free living freshwater Copepoda). [Translation from: Voprosy Ikhtiologii 14, 182-194, 1960. ]

As is known, copepods play an important role in the nutrition of fish. Therefore with a view to facilitating research on the study of the quantitative side of feeding, there have recently appeared a considerable number of papers devoted to the development of methods for determining the wet. weight of these crustaceans. For the further facilitating of research in the nutrition of fish it would be of great interest to clarify the problem, is there not some kind of rule in the growth of the crustaceans during metamorphosis, and if there is such a rule is it not possible, to determine the length of the larvae at each stage, not by measuring them, but by using the formulae derived on the basis of these rules. This article examines the growth curves of different species of freshwater Copepoda, obtained on the basis of experimental observations in cultures or by way of measurement of mass material at all stages of development in samples from water-bodies. The authors study in particular the ratio of the mean diameter of the eggs to the mean length of the egg-bearing females.

Extension theorems for functions of vanishing mean oscillation

A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in R^d converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO function.

We consider the similar extension problem pertaining to BMO(ρ) functions; that is, those VMO functions whose mean oscillation over any cube is O(ρ(l(Q))) where l(Q) is the length of Q and ρ is a positive, non-decreasing function with ρ(0⁺) = 0.

We apply these results to obtain sufficient conditions for a Blaschke sequence to be the zeros of an analytic BMO(ρ) function on the unit disc.

Ecologia térmica e comportamento de construção de abrigos de Liolaemus lutzae (Lacertilia, Liolaemidae) em três áreas de restinga no estado do Rio de Janeiro, sudeste do Brasil: os efeitos de fatores extrínsecos e intrínsecos

Fatores extrínsecos afetam a ecologia térmica e o comportamento de lagartos no habitat, com as características ambientais locais podendo ocasionar alterações na temperatura corpórea (Tc) e no comportamento destes animais. Entretanto, fatores intrínsecos também representam uma importante influência para sua biologia, assim como fatores filogenéticos (históricos). Liolaemus lutzae (Liolaemidae) é uma espécie de lagarto com ocorrência restrita a restingas do estado do Rio de Janeiro (entre a Restinga da Marambaia no município do Rio de Janeiro e a restinga da Praia do Peró no município de Cabo Frio), vivendo exclusivamente na zona de vegetação halófila-psamófila-reptante a chamada área-de-praia da restinga (sujeita a altas temperaturas ambientais e ventos intensos constantes). Nessa área, onde vivem restritos a uma faixa de poucos metros de restinga, os indivíduos se abrigam escavando abrigos no substrato arenoso. Avaliei a importância de fontes ambientais de calor, da intensidade dos ventos, do sexo, da ontogenia, do comprimento rostro-cloacal (CRC) e da massa corpórea para a Tc e a taxa de atividade de lagartos L. lutzae (observando a ocorrência de variações sazonais), em estudos conduzidos no município de Arraial do Cabo, estado do Rio de Janeiro, sudeste do Brasil. Além disso, eu analisei se o comportamento de L. lutzae, direcionando as aberturas de seus abrigos foi afetado por fatores ambientais nas restingas da Reserva Ecológica Estadual de Jacarepiá e do Parque Natural Municipal de Grumari, ambas no estado do Rio de Janeiro. A atividade dos lagartos se estendeu durante o dia (0600h às 1800h), com máximo entre 1100h e 1300h (com variações sazonais). A Tc dos indivíduos foi 31,7  3,4 C, e variou ao longo do dia e sazonalmente. Em ambas as estações a Tc dos lagartos relacionaram-se às temperaturas do microhabitat (substrato e ar). A intensidade do vento influenciou a Tc dos lagartos (causando seu decréscimo), e a intensidade média do vento afetou o número de lagartos ativos (causando redução da atividade). Houve diferenças intersexuais no CRC, com os machos maiores do que as fêmeas, embora as fêmeas tenham tido maior massa corpórea relativa ao CRC correspondente, comparado aos machos. A Tc também diferiu inter-sexualmente (com machos mais quentes do que fêmeas) e ontogeneticamente (com jovens mais quentes do que adultos depois de removido o efeito do tamanho corpóreo). Houve relações entre a Tc e o CRC e entre a Tc e a massa corpórea, com lagartos maiores tendo Tc mais elevada (causada pela inércia térmica dos corpos). A variabilidade na Tc dos lagartos parece refletir a interação entre características ambientais locais, fatores intrínsecos e a filogenia da espécie. As aberturas dos abrigos foram localizadas principalmente próximas à linha de praia (possivelmente devido ao substrato menos compacto), predominantemente em terrenos inclinados e tiveram uma tendência de orientação influenciada pela inclinação do terreno. O comportamento de L. lutzae de orientar a entrada de seus abrigos para a direção descendente das inclinações pode ser vantajoso para torná-los menos vulneráveis a potenciais ameaças e distúrbios vindos da superfície.

Ecologia de Tropidurus torquatus (Wied, 1820) (Squamata, Tropiduridae) no Costão de Itacoatiara, Parque Estadual da Serra da Tiririca, municípios de Niterói e Maricá, RJ

O lagarto Tropidurus torquatus (Wied, 1820) possui ampla distribuição geográfica e é encontrado em abundância nas áreas onde ocorre, sendo considerada uma espécie apropriada para estudos ecológicos. No presente estudo nós analisamos o período de atividade, o uso do microhabitat, a intensidade de forrageamento, a dieta e a ecologia térmica de uma população de T. torquatus do Costão de Itacoatiara, no Parque Estadual da Serra da Tiririca, situado nos municípios de Niterói e Maricá, RJ. Os dados foram coletados em dois períodos: entre julho de 2004 e janeiro de 2008 para estudo do período de atividade, uso do microhabitat e intensidade de forrageamento, e entre julho e agosto de 2010 para estudo da ecologia térmica e dieta. Todos os indivíduos coletados eram adultos, com comprimento rostro-cloacal médio de 66,2 12,0mm para machos (n = 11) e 64,1 8,0mm para fêmeas (n = 03). O período de atividade de T. torquatus no Costão de Itacoatiara durou de 12 a 14 horas. Teve um padrão unimodal na estação seca, com pico de atividade entre 09:00h e 13:00h, durante as horas mais quentes do dia. Na estação chuvosa o padrão de atividade foi bimodal, com um pico entre 8:00h e 9:00h e outro entre 16:00h e 17:00h, ambos associados aos horários de temperaturas ambientais mais amenas. O período de atividade não diferiu entre as estações, o que pode ser explicado pelo extenso pico de atividade dos lagartos na estação seca. Os microhabitats mais utilizados foram o substrato rochoso do Costão e a bromélia, refletindo a disponibilidade destes na área. A intensidade de forrageamento não diferiu sazonalmente e o tempo médio que os lagartos ficaram parados foi maior do que o tempo médio em deslocamento. A dieta foi onívora e esteve composta por artrópodes, principalmente insetos, e material vegetal, principalmente frutos. Os principais insetos consumidos foram Formicidae, Coleoptera e Hymenoptera não-Formicidae como pequenas vespas e abelhas. Os frutos, as sementes e as flores consumidos pertenciam às cactáceas Rhipsalis cereoides e Coleocephalocereus fluminensis, para as quais T. torquatus pode ser um potencial agente dispersor de sementes na área. Lagartos maiores consumiram itens maiores, mas em menor número, indicando um balanço energético positivo. O consumo de material vegetal variou de acordo com o tamanho dos lagartos, aumentando sua proporção nos indivíduos mais velhos. A temperatura média em atividade de T. torquatus foi de 34,3 2,5C, estando na faixa de temperatura corpórea média encontrada para outras populações e para outros Tropidurus. O substrato foi a fonte de calor ambiental com maior importância relativa para a termorregulação dos lagartos durante a estação seca, explicando cerca de 48% da variação na temperatura corpórea da população. Os lagartos termorregularam de forma passiva, principalmente em relação à temperatura do substrato.

Estimates of body sizes at maturation and at sex change, and the spawning seasonality and sex ratio of the endemic Hawaiian grouper (Hyporthodus quernus, F. Epinephelidae)

A case study of the reproductive biology of the endemic Hawaiian grouper or hapu’upu’u (Hyporthodus quernus) is presented as a model for comprehensive future studies of economically important epinephelid groupers. Specimens were collected throughout multiple years (1978–81, 1992–93, and 2005–08) from most reefs and banks of the Northwestern Hawaiian Islands. The absence of small males, presence of atretic oocytes and brown bodies in testes of mature males, and both developed ovarian and testicular tissues in the gonads of five transitional fish provided evidence of protogynous hermaphroditism. No small mature males were collected, indicating that Hawaiian grouper are monandrous (all males are sex-changed females). Complementary microscopic criteria also were used to assign reproductive stage and estimate median body sizes (L50) at female sexual maturity and at adult sex change from female to male. The L50 at maturation and at sex change was 580 ±8 (95% confidence interval [CI]) mm total length (TL) and 895 ±20 mm TL, respectively. The adult sex ratio was strongly female biased (6:1). Spawning seasonality was described by using gonadosomatic indices. Females began ripening in the fall and remained ripe through April. A February–June main spawning period that followed peak ripening was deduced from the proportion of females whose ovaries contained hydrated oocytes, postovulatory follicles, or both. Testes weights were not affected by season; average testes weight was only about 0.2% of body weight—an order of magnitude smaller than that for ovaries that peaked at 1–3% of body weight. The species’ reproductive life history is discussed in relation to its management.

Ungewohnliche Gewichsabnahme von Dorsch im 2. Jahresquartal in Bornholm Becken (ICES-Gebeit 25) und der Arkonasee (ICES-Gebiet 24)

Cod captured by commercial fi shery in the Bornholm Basin in quarter 2 of 2001 were not suitable for the mechanical processing due to low condition and weight. The absolute mean weight of cod captured by the commercial fishery in the Arkona Sea and Bornholm Basin in the same quarter during the last fi ve years was studied to describe its development. The results of a GLM (Generalized Linear Model) analysis showed similar development of body weight in the Bornholm Basin and in the Arkona Sea between 2007 and 2011. The mean weight of cod in the Bornholm Basin increased from 2007 to 2008 in both areas followed by a relative stable weight until 2009 and a decrease until 2011. In the Arkona Sea the mean weight of cod 2009 has decreased in comparison to 2008, then have increased 2010 slightly and last have decreased in 2011. The analyses showed that the weight of cod is signifi cantly infl uenced by length, age and maturity of individuals.

Precision estimates and suggested sample sizes for length-frequency data

For most fisheries applications, the shape of a length-frequency distribution is much more important than its mean length or variance. This makes it difficult to evaluate at which point a sample size is adequate. By estimating the coefficient of variation of the counts in each length class and taking a weighted mean of these, a measure of precision was obtained that takes the precision in all length classes into account. The precision estimates were closely associated with the ratio of the sample size to the number of size classes in each sample. As a rule-of-thumb, a minimum sample size of 10 times the number of length classes in the sample is suggested because the precision deteriorates rapidly for smaller sample sizes. In absence of such a rule-of-thumb, samplers have previously under-estimated the required sample size for samples with large fish, while over-sampling small fish of the same species.

Standard and routine metabolic rates of juvenile sandbar sharks (Carcharhinus plumbeus), including the effects of body mass and acute temperature change*

Standard and routine metabolic rates (SMRs and RMRs, respectively) of juvenile sandbar sharks (Carcharhinus plumbeus) were measured over a range of body sizes (n=34) and temperatures normally associated with western Atlantic coastal nursery areas. The mean SMR Q10 (increase in metabolic rate with temperature) was 2.9 ±0.2. Heart rate decreased with increasing body mass but increased with temperature at a Q10 of 1.8−2.2. Self-paired measures of SMR and RMR were obtained for 15 individuals. Routine metabolic rate averaged 1.8 ±0.1 times the SMR and was not correlated with body mass. Assuming the maximum metabolic rate of sandbar sharks is 1.8−2.75 times the SMR (as is observed in other elasmobranch species), sandbar sharks are using between 34% and 100% of their metabolic scope just to sustain their routine continuous activity. This limitation may help to explain their slow individual and population growth rates, as well as the slow recoveries from overfishing of many shark stocks worl

Length-weight relationship of fishes caught by trawl off Alexandria, Egypt

This paper presents the length-weight relationship parameters (a and b) for 29 fish species, belonging to 16 families, taken by otter trawl fishing from Egyptian Mediterranean waters. The b values obtained ranged from 2.50 to 3.44 (with a mean of 2.926).

Length-weight relationships of commercially important marine fishes and shellfishes of the southern coast of Karnataka, India

The parameters of the length-weight relationship of the form W = aLb are presented for 51 species of commercially important marine fishes and shellfishes caught along the southern coast of Karnataka, India. Samples from commercial (trawl, purse seines, gill nets) and artisanal gears were taken during August 1999 to May 2001. The ‘b’ value ranged between 1.942 and 3.616 with a mean of 2.80, standard deviation of 0.32, and mode of 3.

Length-weight relationship and relative condition of Heterobranchus longifilis (Valenciennes) from Idodo River, Nigeria

Length-weight relationship parameters of Heterobranchus longifilis males, females and combined sexes are given. The samples were collected from Idodo River, with size ranging from 123 mm total length, L, to 936 mm L. The values obtained for the mean L by sex show that males were significantly (p<0.05) larger than females. The results show that the slope (b) is significantly (p<0.05) below 3.0 for the male, female and pooled sample. The species exhibit a negative allometric growth pattern. The relative condition of fish shows seasonal variation, with females generally being in better condition than the males.

Length-weight relationship of fishes caught in the Itaipu Reservoir, Parana, Brazil

Parameters and related statistics of the length-weight relationship of the form W=aL super(b) are presented for 72 species of fish caught in the area of the Itaipu Reservoir in Parana, Brazil. The b values varied between 2.34 and 3.35, with the mean b=2.986 (s.d.=0.230) not significantly different from 3.0 (df=7, p=0.05).