Préface à l'édition française

Application of finite mixture models for vehicle crash data analysis

Developing sound or reliable statistical models for analyzing motor vehicle crashes is very important in highway safety studies. However, a significant difficulty associated with the model development is related to the fact that crash data often exhibit over-dispersion. Sources of dispersion can be varied and are usually unknown to the transportation analysts. These sources could potentially affect the development of negative binomial (NB) regression models, which are often the model of choice in highway safety. To help in this endeavor, this paper documents an alternative formulation that could be used for capturing heterogeneity in crash count models through the use of finite mixture regression models. The finite mixtures of Poisson or NB regression models are especially useful where count data were drawn from heterogeneous populations. These models can help determine sub-populations or groups in the data among others. To evaluate these models, Poisson and NB mixture models were estimated using data collected in Toronto, Ontario. These models were compared to standard NB regression model estimated using the same data. The results of this study show that the dataset seemed to be generated from two distinct sub-populations, each having different regression coefficients and degrees of over-dispersion. Although over-dispersion in crash data can be dealt with in a variety of ways, the mixture model can help provide the nature of the over-dispersion in the data. It is therefore recommended that transportation safety analysts use this type of model before the traditional NB model, especially when the data are suspected to belong to different groups.

Inversion of noisy Radon transform by SVD based needlets

A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in Lp (1⩽p⩽∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed

Energy barriers and hysteresis in martensitic phase transformations

We report results from a systematic program of alloy development in the system TiNiX, X = Cu, Pt, Pd, Au, to pursue certain special lattice parameters that have been identified previously with low hysteresis. We achieve λ 2 = 1 , where λ 2 is the middle eigenvalue of the transformation stretch matrix, for alloys with X = Pt, Pd, Au. In all cases there is a sharp drop in the graph of hysteresis vs. composition at the composition where λ 2 = 1 . When the size of the hysteresis is replotted vs. λ 2 we obtain a universal graph for these alloys. Motivated by these experimental results, we present a new theory for the size of the hysteresis based on the growth from a small scale of fully developed austenite martensite needles. The energy of the transition layer plays a critical role in this theory. Overall, the results point to a simple systematic method of achieving low hysteresis and a high degree of reversibility in transforming materials. Keywords Martensitic phase transformation Hysteresis Nucleation and growth Nickel–titanium alloys Continuum mechanics 1 Introduction This paper concerns the hysteresis that accompanies martensitic phase transformations. We focus mainly on thermal hysteresis. The work reported here follows up a conjecture of James and Zhang [21] that asserts a relation between the conditions of compatibility between two phases and the hysteresis seen during cyclic transformation. The conjecture was formulated by looking at the literature (references in Ref. [21] ) and trying to understand what is common among alloys with particularly low hysteresis. A special focus of this literature search was on data from repeated experiments on the same specimen, restored to its original shape after each test by heating, in a material with minor training effects, so as to factor out as much as possible processing conditions. Three conditions of compatibility were conjectured to be relevant to the minimization of hysteresis and the reversibility of transformation: (1) det U = 1 , where the symmetric positive-definite matrix U is the transformation stretch matrix [6,13] ; (2) λ 2 = 1 , where λ 1 ⩽ λ 2 ⩽ λ 3 are the ordered eigenvalues of U ; and (3) the conditions λ 2 = 1 , a ˆ · U 1 cof ( U 1 2 - I ) n = 0 and a certain inequality, together called the cofactor conditions . In the latter, the vectors a ˆ and n are certain vectors that describe the twin system, as explained below (see Eq. (4) ). In geometric terms, det U = 1 represents the condition of no volume change, λ 2 = 1 represents the presence of an invariant plane between austenite and martensite, and the cofactor conditions imply the existence of an infinite number of compatible interfaces between austenite and finely twinned martensite, rather than the usual four per twin system as predicted by the crystallographic theory. The first of these conditions summarizes a well-accepted idea in the community. Cui et al. [10] noticed that the system Ti 50 Ni 50 - x Cu x for small values of x nearly satisfies the first two of these conditions, and they measured both the eigenvalues of U and the hysteresis over a wide composition range, using combinatorial synthesis methods. Their results showed a strong correlation between the second of these conditions ( λ 2 = 1 ) and the size of the hysteresis. Surprisingly, the measurements showed only a weak correlation between the size of the hysteresis and the volume change, even though det U varied widely from about 0.96 to 1.07, with quite a few alloys near the extremes of this range. More surprisingly, the alloys with det U very near 1 included some alloys with the largest, and others with the smallest, hysteresis among all the alloys measured. Possible reasons for this are discussed in Section 7 . All this is surprising because, since the earliest days of the study of martensite, the condition det U ∼ 1 has been widely considered important for reversibility of the transformation, and elementary elasticity calculations of the stress field and energy surrounding an island of martensite growing in a hole of austenite of a different volume suggests the presence of a rather large energy barrier associated with det U ≠ 1 . The main purpose of this paper is twofold: to describe the results of a program of alloy development in which the composition of alloys was systematically tuned to pursue the relation λ 2 = 1 , and to give a new theory for the prediction of hysteresis. Other measurements and approaches to the prediction of hysteresis [5,7,10,16,22,26–28,30–32,35,38–40,43–45,48,49,51,53] are reviewed and compared to the present theory. We are able to achieve λ 2 = 1 in the systems TiNiPd, TiNiPt and TiNiAu, and we exhibit alloys in each of these systems with λ 2 1 . There is a sharp drop in the hysteresis for alloys with λ 2 = 1 , the most dramatic example being Ti 50 Ni 37 Au 13 , which shows a decrease in the size of the hysteresis of about a factor of 10. When the size of the hysteresis is plotted as a function of composition, it has no particularly distinguishing features, but, when it is replotted as a function of λ 2 , there is a collapse of the data onto an approximately universal curve. The combinatorial data of Cui et al. [10] also fall near this curve. This graph has some interesting features, including an apparent singularity at λ 2 = 1 . This also is quite surprising, as hysteresis could well be expected to be sensitive to many other physical parameters besides λ 2 , as well as processing conditions. To understand this dominance of λ 2 , we are led to propose a new theory of hysteresis. The condition λ 2 = 1 is the condition that there is an exact interface between austenite and martensite, and that such an interface does not contribute the usual bulk energy of its transition layer, nor its interfacial energy on twin bands. The theory of hysteresis we propose is based on the hypothesis that the main energy barrier leading to hysteresis arises from these contributions. Thus, we propose that the main energy barrier leading to hysteresis is the growth of fully developed austenite/martensite interfaces. We implement this idea via a nucleation calculation. Ours is not the first nucleation calculation that has been done for martensite, but, as far as we can determine, previous calculations have not allowed such fully developed interfaces. Recently, the interfaces between austenite and martensite in one of the alloys with λ 2 = 1 in the system TiNiPd has been observed using high-resolution electron microscopy by Delville et al. [12] . These observations confirm the presence of untwinned, atomically sharp interfaces. The microstructures observed are unusual as compared with normal ( λ 2 ≠ 1 ) martensites. This theory predicts a dramatic sensitivity of the size of the hysteresis to λ 2 . In particular, the predicted graph of hysteresis vs. λ 2 has a singularity at λ 2 = 1 , like the measured data. The theory predicts that this graph depends on other physical parameters including the critical nucleus size, the other eigenvalues λ 1 , λ 3 , the interfacial energy constant, the elastic moduli, the transformation temperature and the latent heat. However, for the alloys studied, the dependence on these other parameters, to the extent we can estimate them, is weak, consistent with the universality of the measured graphs. The graph of hysteresis vs. λ 2 is not predicted to be universal among all other alloys of other symmetries and properties. Our prediction is not completely quantitative because of lack of knowledge of the interfacial energy constant, the critical nucleus size and the fact that our model of the transition layer is not optimal. Because of recent and ongoing work [17,20,25,36,41,42,46,47,50] on various new methods of measuring interfacial energy, progress is expected on the former. Regarding the optimality of the transition layer, we present a new approach to the calculation of the optimal layer. We want to do this in order to lay the groundwork for a quantitative calculation of the hysteresis, but also for another reason suggested by this paper. That is, when we use a naive but reasonable calculation of the energy of the layer, we find a dramatic dependence of the energy of layer on the twin system that participates in the austenite/martensite interface ( Table 4 ). For the lattice parameters of Ti 50 Ni 50 - x Pd x , x ∼ 11 , this energy varies by almost two orders of magnitude, depending on the twin system, even within a given twin type. This is quantified by a certain geometric factor. If this property extends to the optimal layer, then it could explain why certain twin systems are preferred in martensitic phase transformations. Normally, the energy of the transition layer is thought to depend on the nonlinear elastic properties of the material. However, the elastic energy minimization problem for determining the structure of the layer contains a small parameter for these alloys, namely | λ 2 - 1 | . This opens the way for the use of Γ -convergence arguments (see Refs. [1,9] and Section 3 ) to derive a limiting variational principle for determination of the elastic energy of the layer for alloys with λ 2 near 1 (Section 8 ). As is typical in such arguments, the limiting variational principle has a universal status. That is, the input for the calculation of the limiting energy involves only the lattice parameters of austenite and martensite, together with the linear elastic moduli. In our derivation we consider only minimization of the elastic energy of the martensite. Future work should also consider relaxation of the austenite, as well as the possibility of branching of the twins in the martensite [23–25] . We believe that our derivation lays the groundwork for these further calculations, which can lead to accurate evaluation of the energy in the transition layer. A side benefit of such a derivation is that it provides a way to measure interfacial energy constant, by balancing bulk and interfacial energy in the usual way by studying alloys with λ 2 near 1 and using the measured fineness of the twins of these alloys. The full statement of the Γ -limiting problem is the problem of minimizing the following elastic energy, (1) ∫ Ω ℓ 1 2 v , 1 ⊗ A - T m + a + 1 ζ v , 2 ⊗ A - T n · C v , 1 ⊗ A - T m + a + 1 ζ v , 2 ⊗ A - T n ζ dt 1 dt 2 , over functions v and parameters η ˆ subject to the boundary conditions, (2) v ( t 1 , 0 ) ∥ a , v ( t 1 , 1 ) ∥ a , ( v ( t 1 , 0 ) - v ( t 1 , 1 ) ) · a ⩾ 0 , - ℓ ⩽ t 1 ⩽ 0 , v ( 0 , t 2 ) = 0 , v ( - ℓ , t 2 ) = ζ ( 1 - t 2 + η ˆ ) a , 0 ⩽ t 2 ⩽ 1 . The notation is as follows. Ω ℓ is a rectangular domain of length ℓ , m is the normal to the habit plane when the condition for exact compatibility ( λ 2 = 1 ) is satisfied, a is the amplitude of the twin and n is its normal at λ 2 = 1 , A = I + b ⊗ m is the deformation gradient of the martensite variant that is compatible with austenite at λ 2 = 1 , C is the elasticity tensor at A , i.e. of the martensite at the compatible variant, ζ is the periodicity (length scale) of the twin bands and η ˆ is a length that describes the offset of the vanishingly small twin band; essentially, it describes asymptotic bending of this band. It is believed that, without the rigorous Γ -convergence argument presented here, it would not be possible to guess the detailed form of this linear elasticity problem for the transition layer. Reversibility, measured, for example, by fatigue life under cyclic transformation, is as important as low hysteresis for actuator applications. The connection between the size of the initial or stabilized hysteresis loop and the fatigue life has been investigated by Gall and Maier [16] , and Kato et al. [22] , and recently by Moumni et al. [35] . All of these authors show a correlation between the hysteresis and the fatigue life. The latter authors conclude that “it is shown that the dissipated energy of the stabilized cycle is a relevant parameter for the estimation of lifetime”. There are many papers that discuss hysteresis in martensites. These include papers that propose constitutive equations for martensitic materials from which hysteresis loops are computed [48,28,7,49,30,53] ; those that discuss hysteresis in martensites in the presence of disorder [43,51] ; and papers that relate hysteresis to the attainment of a self-organized critical state [38] , to metastability induced by incompatibility [3] and to pinning of interfaces by defects [26,54] . Another line of work models hysteresis using the Preisach model and its generalizations [5] . Not all of these theories are in direct contradiction with the one proposed here. Some of these theories are “micromechanical” and contain the parameter λ 2 , which plays such an important role in this paper, and thus these theories can be implemented with λ 2 near 1 so as to examine their consistency with the measured hysteresis given here. The notation is similar to that in the book by Bhattacharya [6] . In particular, a ⊗ n is the 3 × 3 matrix with rectangular Cartesian components a i n j , defined from two vectors a , n ∈ R 3 . SO ( 3 ) = { R ∈ R 3 × 3 : R T R = I ,det R = 1 } denotes the set of 3 × 3 rotation matrices. The superscripted T denotes the transpose. Additional background for the Γ -convergence argument is given in Sections 3 and 8.4.1 (see also Refs. [1,9] ), and general references for the description of deformation, strain and elasticity are given in Refs. [6,13] . 2 Experimental methods The main experimental results reported in this paper are measurements of hysteresis vs. lattice parameters in a family of TiNiX alloys, X = Cu, Pd, Pt, Au, in which the composition was systematically tuned to make the middle eigenvalue of the transformation stretch matrix equal to 1. For the interpretation of these results in terms of energy barriers, measurements of transformation temperature, latent heat and density are needed, and these are also reported. The experimental results are presented in Section 4 . In this section we briefly summarize the experimental methods that were used. More detailed information, particularly concerning uncertainty and the repeatability of the measurements, can be found in the thesis of Zhang [55] . Alloys of TiNiX, X = Cu, Pd, Pt, Au, were arc-melted on a water-cooled copper hearth from high-purity elemental materials under argon protection, after purging the chamber several times under vacuum. Ti was used as a hydrogen-getter. The resulting buttons were sliced using an electrical discharge machine and then heat treated under vacuum in quartz ampoules, followed by quenching in water. For the various compositions the annealing temperature was 700–850 °C and the quenching water temperature was 0–40 °C. A careful electrolytic polishing gave samples for both the X-ray measurements and differential scanning calorimetric (DSC) measurements. The electrolyte was 85–90% glacial acetic acid ( CH 3 COOH ) and 10–15% perchloric acid ( HCLO 4 ) by volume, the cathode was stainless steel, the anode was stainless steel or Ti, the voltage was 35–40 V and the temperature of the bath was 0 °C. Lattice parameters of the alloys were measured on a Scintag X-ray diffractometer outfitted with a temperature controlled stage. Special attention was paid to alignment by using an internal standard (NIST standard reference 640c) and periodically doing in situ alignment at different temperatures. The eigenvalues λ 1 , λ 2 , λ 3 were calculated directly from the lattice parameters and formulas given below. The density of the alloys was calculated from atomic composition of the starting materials and measured unit cell volume. The DSC measurements were conducted on the TA Instruments Q1000 according to the ASTM standard F2004-03. The DSC samples were thinned to 100 μ m and electrolytically polished by the method described for the X-ray specimens. Both the X-ray diffraction and calorimetry methods were used to determine the transformation temperatures. Austenite is stable at high temperature and martensite is stable at low temperature. At some temperature θ c in between, the two phases have the same bulk free energy. Because of the presence of hysteresis, θ c is difficult to measure directly. When austenite is cooled down to a certain temperature, it begins to transform to martensite. This temperature is the martensite start temperature M s . With further cooling, the transformation is completed at the martensite finish temperature M f . When martensite is heated, it transforms back to austenite. The austenite start temperature and austenite finish temperature are denoted by A s and A f , respectively. To get these four temperatures from the DSC measurements we used the standard procedure of constructing intersections of approximate asymptotic lines. Operationally, we defined θ c as the average of the four characteristic temperatures, i.e. ( A s + A f + M s + M f ) / 4 . In the X-ray measurements, the transformation temperature θ c was defined as the intensity of austenite peak at half of its maximum value. The hysteresis was defined as ( A s + A f ) - ( M s + M f ) . In the X-ray method we determined the temperatures M s , M f , A s ,and A f using the following procedure. The 2 θ angle was first confined to the interval 39–46° because the (1 1 0) peak of B2 phase, the (1 1 1) peak of B19 phase and the ( 1 ¯ 1 1 ), (1 1 1) peaks of the B 19 ′ phase of the TiNiX alloys, which are the strongest among all peaks of the corresponding phases, are within this range. We then scanned the sample at high temperature to obtain a pure austenite pattern. Using the same method, we scanned the sample at low temperature to get a pure martensite pattern. Then we gradually decreased the scan interval of temperature. Because X-ray patterns are sensitive to a change of lattice structures, they can detect a tiny phase change which would be difficult to quantify by other methods. To have a definite criterion for “start” and “finish” we established a convention. We let the pure austenite pattern at high temperature and the pure martensite pattern at low temperature be standards. Then the temperatures at which the corresponding major peaks decreased 2% from those of the standard patterns were taken to be A s or M s , respectively. A f and M f were defined by a similar criterion using 98% of the standard peaks. The latent heat L was defined as the area within the triangle with base ( A f - A s ) / 2 and height equal to the maximum height of the DSC peak, divided by heating/cooling speed, which was typically 10 ° C s - 1 . These were measured on the heating part of the cycle because the cooling part exhibited a longer tail, which made the definition of M f somewhat difficult. 3 Theoretical methods The variable λ 2 will denote the middle eigenvalue of the transformation stretch matrix. For example, in the case of a cubic to orthorhombic phase transformation, the six linear transformations that map the cubic structure to the six orthorhombic variants of martensite are given by Eq. (16) in the cubic basis. Their eigenvalues are assumed to be ordered, λ 1 ⩽ λ 2 ⩽ λ 3 . The alloys of interest in this paper have λ 2 near 1. The theoretical part of this paper relies on a technique called Γ -convergence, due in its abstract form to De Giorgi [11] (expository treatments are given in Refs. [1,9] ). This method allows one to pass from a variational principle depending on a small parameter to a limiting variational principle. In the present case, the small parameter is 1 Or, equivalently, the small parameter can be chosen as λ , the volume fraction appearing in the crystallographic theory of martensite, this being related to λ 2 - 1 by (35) . 1 | λ 2 - 1 | , and the variational principle is the minimization of the free energy stored near the austenite/martensite interface. Typically, the limiting variational principle is not obtained by putting λ 2 = 1 (or expanding the energy density in a Taylor series about λ 2 = 1 ). While one could imagine finding the minimizers of the original variational principle, calculating their asymptotic form as λ 2 approaches 1 and then seeking a variational principle for these asymptotic limits, the method of Γ -convergence gives the limit directly, without the intermediate step of calculating the minimizers of the original variational principle. The method involves the careful calculation of upper and lower bounds on low energy deformations as λ 2 tends to 1. It follows from the method that the limit, in a well-defined sense, of a sequence of minimizers (parameterized by λ 2 ) of the original variational principle is a minimizer of the limit energy, and their energies also converge to the minimum of the limiting energy. As is typical with Γ -convergence, the limiting variational principle is simpler than the original one and has a universal status. In the present case this is realized by the fact that the limiting energy depends only on knowledge of the linearized elastic moduli of austenite and martensite, whereas the original principle depends on their nonlinear elastic properties. Once these moduli are measured for λ 2 ∼ 1 alloys and the interfacial energy on the twins are measured, the kinds of scaling laws discussed by Schryvers [42] can be investigated on a quantitative basis. Recent advances on the measurement of interfacial energies [17,41,50] make this a realistic possibility. 4 Measurements of hysteresis, transformation temperature and latent heat in alloys whose lattice parameters have been tuned to make λ 2 = 1 For this study we began with the Ti 50 Ni 50 - x Cu x system, relying on a paper by Moberly and Melton [34] that showed the presence of twin-free habit planes in this alloy at x = 10 . A closer examination of the original thesis of Moberly [33] revealed that these twin-free interfaces were rather rare: the photographs in the original thesis mainly showed twinned interfaces in the same alloy. In hindsight, we believe that the pictures chosen for publication were found are places in the specimen where, due to the presence of stress, the lattice parameters were perturbed from the stress-free, equilibrium values. (In our subsequent X-ray measurements this could be understood as arising from lattice parameters corresponding to points near the tails of the X-ray peaks in this system.) As is known, at about x = 10 at . % Cu this alloy loses the monoclinic martensite in favor of an orthorhombic martensite. We prepared a matrix of alloys of Ti = 48, 49, 50, 51, 52 at.%, Cu = 0, 5, 10, 15, 20, 25, 35 at.% with Ni = 100 − Ti − Cu and measured the lattice parameters. The variation of λ 2 vs. composition for these alloys is shown in Fig. 1 . For the case Ti = 50 at.% we also prepared alloys with Cu = 25, 30, 35, but these contained excessive TiCu precipitates and so are not discussed here. This data motivated the wider combinatorial study [10] of this system. Taken together, and accounting for the slightly decreased accuracy of the combinatorial measurements, we did not find convincing evidence that λ 2 = 1 was achieved at any composition of the TiNiCu system, although, as seen in Fig. 1 , Ti 49 Ni 31 Cu 20 comes quite close. Thus, we shifted further study to other alloys. The Hume–Rothery rules for atomic size and valence indicated that Rh, Ir, Pd, Pt, Ag and Au, all substituting for Ni, would be good candidates for stabilization of the orthorhombic phase. Extensive work on the alloys Ti 50 Ni 50 - x Ag x revealed a maximum solubility of x = 2 at. % Ag, which we were not able to overcome by heat treatment, and therefore did not yield any useful alloys. We note that λ 2 1 was critical for an interpolation scheme. We noticed from work by Donkersloot and van Vucht [14] that measured lattice parameters at the martensitic transformation in TiPd have λ 2 > 1 , and our subsequent measurement of lattice parameters in Ti 50 Ni 34 Pd 16 showed λ 2 > 1 . With regard to the basic hypothesis of a connection between hysteresis and λ 2 = 1 , we were also motivated by the data collected in US Patent 5,951,793, which did not report lattice parameters but indicated a sharp drop in hysteresis for Ti 49.5 Ni 40.5 Pd 10 . The review article of Miyazaki and Ishida [32] also indicated a sharp drop in the hysteresis near 10 at.% Pd in the data they report on films, although the interpretation suggested by the authors was of a continuous decrease in hysteresis with increasing Pd. Referring to their data, Miyazaki and Ishida state that this is a surprising result. Having found that Ti 50 Ni 34 Pd 16 has λ 2 = 1.005 > 1 , we did a straightforward interpolation. A similar procedure was followed with Ti 50 Ni 50 - x X x , X = Pt, Au: first locate an alloy with λ 2 > 1 , then interpolate backward. The data for hysteresis vs. composition for X = Pd, Pt, Au are shown in Fig. 2 . Note the drop in hysteresis of a factor between 5 and 10. Although the minimum hysteresis in all cases occurs at different values of x , in each case the minimum occurs very near the composition where λ 2 = 1 . At each data point of Fig. 2 we also measured lattice parameters of the two phases at the same temperature. From this we calculated λ 2 corresponding to each point in Fig. 2 . It becomes more interesting to eliminate x and plot hysteresis directly vs. λ 2 . This is done in Fig. 3 . The combinatorial data from Ref. [10] on TiNiCu is also included in this plot. One can see a remarkable collapse of the data onto two lines shaped like a V. This plot suggests a universal behavior. However, one should note that, while latent heats, elastic moduli and the other lattice parameters vary somewhat among these alloys, the crystallography in all cases (except the TiNiHf data; see below) is cubic to orthorhombic. Thus, one can conjecture that, within a certain crystallographic change, the main parameter that controls hysteresis is λ 2 and the behavior is universal. The theory presented later in this paper supports this viewpoint. We have also included in Fig. 3 data on the system TiNiHf, which undergoes a cubic to monoclinic (B2–B19′) crystallographic transformation, as in TiNi. The line was drawn using the data of Matveeva et al. [31] and Potapov et al. [39] , and was confirmed by our own measurements on this system. Alloys in the family TiNiHf, once considered promising candidates as high-temperature shape memory alloys, show excessive hysteresis at concentrations of Hf that raise the transformation temperature significantly. This can be understood from the following simple observation. Binary TiNi has λ 2 0 , n ⊥ · m = m ⊥ · n . (This normalization is not the standard one, but it is more convenient here.) We assume a basic framework for martensitic phase transformations. That is, we consider a free energy density φ ( F , θ ) as a function of deformation gradient and temperature defined on M 3 × 3 × R ⩾ (for background, see Refs. [6,13] ). We hold θ fixed, below transformation temperature, and drop it from the notation until later in this paper. At this temperature φ is assumed to have a local minimum at I and a lower global minimum on the martensite energy wells, SO ( 3 ) U 1 , … ,SO ( 3 ) U N . We assume the distinct matrices U 1 , … , U N are positive-definite, symmetric and symmetry related: there exists R ∼ 2 , … , R ∼ N ∈ SO ( 3 ) such that U i = R ∼ i U 1 R ∼ i T , i = 2 , … , N . We also assume that the wells SO ( 3 ) U 1 and SO ( 3 ) U 2 are rank-1 connected, i.e. there are a ˆ , n ∈ R 3 , | n | = 1 , and R ∈ SO ( 3 ) such that (4) RU 2 - U 1 = a ˆ ⊗ n . To do the asymptotic analysis we stay away from the singular situation λ 2 = 1 by assuming that det ( U 1 2 - I ) ≠ 0 . The matrices A = R ^ U 1 and B = R ^ RU 2 , R ^ ∈ SO ( 3 ) , are assumed to satisfy the equations of the crystallographic theory of martensite, (5) ( λ B + ( 1 - λ ) A ) - I = b ⊗ m , for suitable 0 0 , which is the height of the triangle as shown in Fig. 4 , as one can see by calculating - v · m . Now it can be seen that the following expression for C satisfies Eq. (12) : (14) C = I + f ⊗ m , f = b + ε α λ ( 1 - λ ) a . The matrix C is of course not on the energy wells. 6 Energy barrier of a fully developed austenite/martensite interface Consider the case of cooling from austenite to form martensite. We picture a lenticular nucleus, stabilized by a defect (e.g. precipitate, triple junction on a grain boundary), and we imagine that this nucleus is already present at temperatures above M s . Our main hypothesis is that this nucleus is already twinned, so its boundary consists of two fully developed, slightly bowed austenite/martensite interfaces. We ignore the ends of the nucleus and picture simply a twinned laminate of martensite of length ℓ (i.e. the half-width of the nucleus) meeting austenite. As sources of energy, we consider the interfacial energy on the twin boundaries modeled by a sharp interface theory, the bulk elastic energy stored near the austenite/martensite interface, and the bulk free energies of the two phases. We analyze the energy as a function of ℓ accounting for the possibility that the twin density and elastic transition layer may relax as ℓ is changed. In this section we consider a simple model for the transition layer that is improved later in this paper. We consider the case in which the middle eigenvalue λ 2 of the matrix U 1 is close to 1 and, for simplicity, we fix the other eigenvalues. 2 The other eigenvalues λ 1 , λ 3 could also be allowed to vary as long as they are bounded away from 1; this of course forbids the cubic to tetragonal case, since in that case λ 2 = 1 and λ 1 ⩽ λ 2 ⩽ λ 3 imply that λ 1 = 1 or λ 3 = 1 . 2 In a basis for which U 1 is diagonal, we then evaluate the formula (6) for δ : (15) δ = ( a 1 n 1 ) λ 1 λ 1 2 - 1 + ( a 2 n 2 ) λ 2 λ 2 2 - 1 + ( a 3 n 3 ) λ 3 λ 3 2 - 1 . This is dominated by the middle term and we note that, typically, as λ 2 approaches 1, the quantity a 2 n 2 does not tend to zero. 3 “Typically” here means that, if U 1 is changed to ρ U 1 for ρ near 1, the middle eigenvalue of ρ U 1 can be made to pass through 1 but a 2 n 2 is only changed to ρ a 2 n 2 . 3 In view of the first condition of (6) , we have the following: assuming that a 2 n 2 | λ 2 = 1 ≠ 0 then for a given twin system the crystallographic theory has solutions for at most one of the regions λ 2 ≳ 1 or λ 2 ≲ 1 . (See also Items 1 and 2 below.) We now give a more detailed study of this in the cubic to orthorhombic case, which applies to all the NiTiX alloys described above. In this case, the six transformation stretch matrices are: (16) U 1 = λ 2 + λ 3 2 λ 2 - λ 3 2 0 λ 2 - λ 3 2 λ 2 + λ 3 2 λ 1 , U 2 = λ 2 + λ 3 2 λ 3 - λ 2 2 0 λ 3 - λ 2 2 λ 2 + λ 3 2 λ 1 , U 3 = λ 2 + λ 3 2 0 λ 2 - λ 3 2 0 λ 1 0 λ 2 - λ 3 2 0 λ 2 + λ 3 2 , U 4 = λ 2 + λ 3 2 0 λ 3 - λ 2 2 0 λ 1 0 λ 3 - λ 2 2 0 λ 2 + λ 3 2 , U 5 = λ 1 λ 2 + λ 3 2 λ 2 - λ 3 2 0 λ 2 - λ 3 2 λ 2 + λ 3 2 , U 6 = λ 1 λ 2 + λ 3 2 λ 2 - λ 3 2 0 λ 2 - λ 3 2 λ 2 + λ 3 2 . Written this way, λ 1 , λ 2 , λ 3 are the eigenvalues of each of these matrices, and, for the application to the TiNiX alloys studied here, we can assume, without loss of generality, that these are ordered λ 1 ⩽ λ 2 ⩽ λ 3 . We consider twin systems that consist of variant 1 twinned with all other variants; it is sufficient to consider these by symmetry. Variant 1 is compound twinned with variant 2, but it forms Type I/Type II twins with the other four variants (thus, all pairs of variants are twinned). By direct calculation, in the notation of Eq. (15) , we have the expressions for a 2 n 2 listed in Table 2 at λ 2 = 1 . The numerators of the expressions in the last column of Table 2 , for eigenvalues near 1, are close to λ 3 2 - 1 + 2 ( λ 1 2 - 1 ) , which is typically negative for experimental cases and also for any case which is nearly volume preserving. Hence, under the typical situation that entries in the last column of Table 2 are negative, we reach the following conclusions: 1. λ 2 ≲ 1 . Only compound twins form austenite/martensite interfaces. Altogether, there are only six of these twin systems, two each for variants 1–2, 3–4, 5–6. 2. λ 2 ≳ 1 . All of the Type I and Type II twin systems can form austenite/martensite interfaces. This striking conclusion is consistent with results of Hane and Shield [18] . Experimental values of the dominant factor a 2 n 2 for alloys in which λ 2 = 1 are given in Table 3 . Within a given twin type, these numbers do not vary greatly across these various systems. One should remark that, even though the crystallographic theory forbids certain twins to participate in the austenite/martensite interface, all the types of twins listed above are possible in the martensite. For example, in cases where compound twins are forbidden by the crystallographic theory to be present in austenite/martensite interfaces, they could still be observed in the martensite, produced by stresses built up during transformation, especially in a polycrystal. Assume that we are in one of the regions where the crystallographic theory has a solution, that is, the second condition of (6) holds and either λ 2 ≳ 1 and a 2 n 2 0 . From Eq. (7) we then have that, in the regime of interest in this paper, λ ★ ∼ 1 . We confine attention to the solution λ = 1 - λ ★ . Thus, the volume fraction λ ∼ 0 , i.e. it is the volume fraction of the variant that is paired with variant 1 that is disappearing as λ 2 → 1 . Thus the martensite region contains a large volume fraction where the deformation gradient is A . Also, from Eqs. (5) and (14) we have (17) A → I + b ⊗ m , C → I + b ⊗ m as λ 2 → 1 with ε / α fixed. Since C is near A in this limit, it is natural to estimate the energy of C using a quadratic approximation of the free energy density φ near A . We would also like to optimize over the choice of α (see Fig. 4 ), but we keep ε fixed for now. Later, after we have introduced interfacial energy, we will optimize over the choice of the “fineness” ε . Note that C = I + f ⊗ m = I + b ⊗ m + ( ε / α ) λ ( 1 - λ ) a ⊗ m , and from (5) we have A = I + b ⊗ m - λ a ⊗ n . Thus, as must be true, rank ( C - A ) = 1 , i.e. (18) C = A + a ⊗ λ n + ε α λ ( 1 - λ ) m . For our simple estimate of the energy of C we let μ be a typical elastic shear modulus and note that the area of each triangle containing C is (19) ε α 2 m · n ⊥ . (Recall that, by definition, m · n ⊥ > 0 .) At this point it is convenient to fix one value of the free energy by putting φ ( A , θ ) = 0 , so the free energy of C will be positive. This of course implies that φ ( I , θ ) > 0 . Suppose the width (into the page) of the martensite plate is w . We can now estimate the energy of C by using a linear elasticity theory 4 Given that the crystallographic theory is geometrically exact, one could worry about the possible role of finite rotations in this calculation, and therefore be led to use nonlinear elasticity instead of linear elasticity to estimate the energy of C . The Γ -convergence argument given later in this paper justifies the use of linearized elasticity (linearized about A ) in this context for λ near 1. 4 obtained by linearizing about A . Using (19) and letting c λ = A - T n + ( ε / α ) ( 1 - λ ) A - T m (so that CA - 1 = I + λ a ⊗ c λ ), we have (20) energy of one triangle = ε α w 2 m · n ⊥ μ 2 1 2 [ ( CA - 1 - I ) + ( CA - 1 - I ) T ] 2 = ε α w 2 m · n ⊥ μ λ 2 8 | a ⊗ c λ + c λ ⊗ a | 2 = ε α w 2 m · n ⊥ μ λ 2 4 ( a · c λ ) 2 + | a | 2 | c λ | 2 . The triangle height α is contained in the prefactor as well as in the expression for c λ . Minimization of this energy over α > 0 gives (21) α min = ε ( 1 - λ ) ( a · A - T m ) 2 + | a | 2 | A - T m | 2 ( a · A - T n ) 2 + | a | 2 | A - T n | 2 . We insert this value of α from now on. Then, assuming the height of the martensite plate is h , giving h / ε triangles, we have (22) total energy of the triangles = ε wh μ λ 2 ( 1 - λ ) ξ , where the geometric factor ξ is given by (23) ξ = 1 4 m · n ⊥ ( a · A - T m ) 2 + | a | 2 | A - T m | 2 ( a · A - T n ) 2 + | a | 2 | A - T n | 2 + ( a · A - T m ) ( a · A - T n ) + | a | 2 ( A - T m · A - T n ) The geometric factor measures in a rough way, i.e. for a simple model of the transition layer, the effect that different twin systems have on the elastic energy stored in the austenite/martensite interface. It depends only on the data that goes into the crystallographic theory, that is, the energy wells and lattice parameters. It is interesting to look at values of the geometric factor for various twin systems. This is done in Table 4 for the alloy Ti 50 Ni 50 - x Pd x , x ∼ 11 . It can be seen that there is a very wide variation of almost two orders of magnitude of this number, and it also varies significantly within a given type of twin. This partly motivated the more careful treatment of the transition layer given later in this paper. It may possibly explain why certain twins predominate in certain alloys. It also suggests that, within a certain twin type, certain pairs of variants would tend to be strongly preferred. Now we repeat the classical calculation with this model of the transition layer, except we have the austenite and martensite wells at different heights. We introduce an interfacial energy per unit area κ on the twins and write the total energy as (24) total energy = 2 κ wh ℓ ε + ε wh μ λ 2 ( 1 - λ ) ξ + φ ( A , θ ) wh ℓ + φ ( I , θ ) wh ( L - ℓ ) , where L is the total length of the strip, including martensite and austenite ( L ≫ ℓ ) . We minimize this expression over ε > 0 and get (25) ε = 2 κ ℓ μ λ 2 ( 1 - λ ) ξ , giving an inverse relation between twin spacing ε and volume fraction λ in the limit as λ → 0 (i.e. as λ 2 → 1 ). This gives the total minimum energy: (26) 2 wh λ 2 κ μ ℓ ( 1 - λ ) ξ + wh ℓ ( φ ( A , θ ) - φ ( I , θ ) ) + const. This has the typical form of an energy with a single barrier that arises in a nucleation calculation. The ℓ term dominates for small ℓ and the linear term dominates for large ℓ . Recall that we have assumed that 0 = φ ( A , θ ) 1 , as indicated in Section 6 . The actual numbers of twin systems participating are six systems for λ 2 1 . There are four austenite/martensite interfaces per twin system, giving rise to 24 (respectively, 96) interfaces for λ 2 1 ) . Exactly at λ 2 = 1 , where the hysteresis is lowest, these degenerate to only 12 austenite/martensite interfaces. Thus, surprisingly, there appears to be no obvious connection of the numbers of strains or numbers of interfaces to the size of hysteresis. This indicates again that the main energy barrier is the growth of an austenite/martensite interface, and the numbers of such interfaces is of secondary importance for the size of the hysteresis. However, these numbers could well play an important role for other properties, for example the lifetime of the material under repeated transformation. Interesting unpublished data of Quandt [40] supports this view. The satisfaction of the cofactor conditions described above achieves both a dramatically larger set of strains and interfaces, as well as λ 2 = 1 . 8 Theory of the transition layer between austenite and martensite when λ 2 ∼ 1 We now develop ideas for a transition layer that can provide a more accurate evaluation of the bulk energy of the transition layer than the one given above by simply using the matrix C . For background on mechanics see Ref. [6,13] and on Γ -convergence see Ref. [1,9] . 8.1 Kinematic assumptions and boundary conditions We now formulate assumptions for a more general but still simplified transition layer. To begin, we look at common features of the deformation gradients that enter the boundary conditions for the transition layer. These are matrices A , B , I satisfying (37) B - A = a ⊗ n , ( λ B + ( 1 - λ ) A ) - I = b ⊗ m . Let e be a unit vector perpendicular to both m and n , and let p be a unit vector perpendicular to both a and b . From Eq. (37) (38) Ae = Be = Ie = e and A T p = B T p = I T p = p . Now we write the boundary conditions for a transition layer. On the left (see Fig. 6 ) we have a martensite laminate. Its deformation can be written with the aid of the following periodic function with period 1: (39) χ λ ( s ) = 1 - λ , 0 ⩽ s 0 . The latter means that | f ± ( s 2 ) - f ± ( s 1 ) | ⩽ c | s 2 - s 1 | for all - ℓ 0 , m λ ⊥ · m λ ⊥ = n λ ⊥ · n λ ⊥ = 1 and m λ ⊥ · n λ = m λ · n λ ⊥ of the crystallographic theory (5) with A λ → A 0 ∈ SO ( 3 ) U 1 | λ 2 = 1 ≠ I , n λ → n 0 , m λ → m 0 as λ → 0 , n 0 ∦ m 0 , and A λ - B λ = a λ ⊗ n λ , a 0 ≠ 0 , and | A λ - A 0 | ⩽ C λ for some C > 0 (generally, C below is a positive constant whose value can change from line to line). Summary of definitions and results used : (1) The notation dist ( F , S ) denotes the shortest Euclidean distance from the 3 × 3 matrix F to the (closed, bounded) set S . In the case of rotation matrices, S = SO ( 3 ) = { R : R T R = I ,det R = 1 } , and, assuming det F > 0 , an alternative expression is dist ( F ,SO(3) ) = | U - I | where U is the right stretch tensor of elasticity theory, i.e. F = R U is the polar decomposition of F . For 3 × 3 matrices the dot product between matrices A , B (such as used in Eq. (74) below) is defined by A · B = tr AB T , where tr is the trace. The notations L ∞ , L 2 , H 1 denote spaces of functions defined, respectively, as the set of functions for which the following norms are finite: for L ∞ ( Ω ) , ‖ f ‖ L ∞ ( Ω ) = ess sup Ω | f | ; for L 2 ( Ω ) , ‖ f ‖ L 2 ( Ω ) 2 = ∫ Ω | f | 2 d x ; for H 1 ( Ω ) , ‖ f ‖ H 1 ( Ω ) 2 = ∫ Ω | f | 2 d x + ∫ Ω | ∇ f | 2 d x . For a family of functions v λ ∈ L 2 ( Ω ) , λ > 0 , we say that v λ converges weakly to v in L 2 ( Ω ) , denoted v λ ⇀ v , if ‖ v λ ‖ L 2 ( Ω ) ⩽ C and averages of v λ converge to the average of v , i.e. ∫ D v λ d x → ∫ D vd x as λ → 0 , for every (measurable) subset D ⊂ Ω . Weak convergence v λ ⇀ v in H 1 ( Ω ) means that v λ ⇀ v in L 2 ( Ω ) and ∇ v λ ⇀ ∇ v in L 2 ( Ω ) . Bounded sequences in L 2 ( Ω ) or H 1 ( Ω ) necessarily have subsequences that converge weakly in their respective spaces. The interpolation inequality used below states that, for any Lipschitz function f , we have ‖ f ‖ L ∞ ( R ) ⩽ C ‖ f ‖ L 2 ( R ) 2 3 ‖ f ′ ‖ L ∞ ( R ) 1 3 . The following rigidity lemma [15] will also be used in the argument: for each given function y ∈ H 1 ( Ω ) there is a corresponding rotation matrix R ¯ ∈ SO ( 3 ) such that (67) ∫ Ω | ∇ y ( x ) - R ¯ | 2 d x ⩽ C ∫ Ω dist 2 ( ∇ y ( x ) ,SO(3) ) d x . Here C depends only on Ω ∈ R 3 , which is assumed to be a Lipschitz domain. This is a quantitative statement of the fact that, if a deformation gradient is near some rotation matrix at each x ∈ Ω , which a priori could vary from point to point in Ω , it is actually near a single rotation matrix on most of Ω . Below, the “original variables” refers to deformations expressed as a function of x 1 , x 2 , x 3 and satisfying boundary conditions (55) while “new variables” refers to functions u (see Eq. (58) ) expressed as a function of t 1 , t 2 , t 3 and satisfying the equivalent boundary conditions (62) . 8.4.2 Use of the rigidity lemma to restrict the form of a minimizer Suppose y λ , f λ ± have less energy than the naive test function (64) and satisfy the boundary conditions (55) . Then y λ , f λ ± satisfy (68) ∫ - ℓ 0 ∫ f λ + ζ + f λ - dist 2 ( ∇ y λ ,SO ( 3 ) A λ ) dx 2 dx 1 ⩽ ∫ - ℓ 0 ∫ f λ + ζ + f λ - φ ( ∇ y λ , θ ) dx 2 dx 1 ⩽ C λ 2 , the lower bound on the left being part of our hypotheses above. We first use of the rigidity lemma in the original variables to restrict the rotation. We note that the rigidity lemma (67) remains true also with R ¯ replaced by RA λ and SO(3) concurrently replaced by SO ( 3 ) A λ , by a linear change of variables. Applying this lemma, we therefore have the existence of R λ ∈ SO ( 3 ) such that (69) ∫ - ℓ 0 ∫ f λ + ζ + f λ - | ∇ y λ - R λ A λ | 2 dx 2 dx 1 ⩽ C λ 2 . By passing to a subsequence we can assume R λ → R 0 . In view of the uniform Lipschitz bound, f λ ± → f ± uniformly. Thus, we can assert (69) on a fixed domain, i.e. (70) ∫ - ℓ 0 ∫ f + + δ ζ + f - - δ | ∇ y λ - R λ A λ | 2 dx 2 dx 1 ⩽ C λ 2 . for δ > 0 . Then we use the trace theorem applied to the sub-boundary S = { ( x 1 , x 2 ) : x 1 = 0 , f + ( 0 ) + δ 0 for δ > 0 chosen small enough to respect the Lipschitz conditions. In particular, there are positive sequences λ k = λ δ k → 0 , δ k → 0 such that v λ k = λ k L λ k v ( δ k ) satisfies the Lipschitz conditions. By Taylor expansion, strong convergence and (104) , we have that (102) is satisfied for the sequence v λ k . 8.5 Summary of form of the limiting energy of the transition layer The lower bound found above in Section 8.4.4 shows that the limiting energy of a low energy sequence parameterized by λ is greater than or equal to (105) ∫ Ω ℓ 1 2 ∂ 2 φ ˜ ( I ) ∂ F 2 ( G , G ) ζ dt 1 dt 2 , with G replaced by v , 1 ⊗ A 0 - T m 0 + a 0 + 1 ζ v , 2 ⊗ A 0 - T n λ . We show in Section 8.4.5 that, given a function v ∈ H 1 ( Ω ℓ ) satisfying the limiting boundary conditions, its energy (105) can be approximated arbitrarily closely by the original expression for the energy evaluated on an appropriate sequence v λ satisfying the original boundary conditions. These two statements imply that the energy (105) is the Γ -limit of the original ( λ > 0 ) energy under its boundary conditions. In particular, it follows that the limit of the family of minimizers of the original energy, parameterized by λ , is a minimizer of (105) . Also, the energy of this family, rescaled by dividing by λ 2 , converges to the energy of the Γ -limit. The full statement of the Γ -limiting problem is: (106) min v ∈ A ∫ Ω ℓ 1 2 ∂ 2 φ ˜ ( I ) ∂ F 2 ( v , 1 ⊗ A 0 - T m 0 + a 0 + 1 ζ v , 2 ⊗ A 0 - T n λ , v , 1 ⊗ A 0 - T m 0 + a 0 + 1 ζ v , 2 ⊗ A 0 - T n λ ) ζ dt 1 dt 2 , where (107) A = { ( v , η ˆ ) ∈ H 1 ( Ω ℓ ) × R : v ( t 1 , 0 ) ‖ a 0 , v ( t 1 , 1 ) ‖ a 0 , ( v ( t 1 , 0 ) - v ( t 1 , 1 ) ) · a 0 ⩾ 0 , v ( 0 , t 2 ) = 0 , v ( - ℓ , t 2 ) = ζ ( 1 - t 2 + η ˆ ) a 0 } . Observe that η ˆ , which describes the asymptotic lowering of the thin twin band, takes part in the minimization. Acknowledgement We wish to acknowledge valuable discussions with John Ball, Rémi Delville, Eckhard Quandt, Nick Schryvers, Doron Shilo, Thomas Waitz, Barbara Zwicknagl, the comments of an anonymous reviewer and the assistance of Sakthivel Kasinathan. This work was supported by the ARO-MURI W911NF-07-1-0410, the MULTIMAT RTN network MRTN-CT-2004-505226, AFOSR (GameChanger, GRT00008581/ RF60012388) and DOE DE-FG02-05ER25706. 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Dot immunogold filtration assay (DIGFA) with multiple native antigens for rapid serodiagnosis of human cystic and alveolar echinococcosis

A new 3-min rapid dot immunogold filtration assay (DIGFA) for serodiagnosis of human cystic and alveolar echinococcosis was developed using four native antigen preparations: crude and partially purified hydatid cyst fluid extracts from Echinococcus granulosus (EgCF and AgB), E. granulosus protoscolex extract (EgP) and Echinococcus multilocularis metacestode antigen (Em2). The overall sensitivity of DIGFA in a hospital diagnostic setting was 80.7% for human cystic echinococcosis (CE) (n=857) and 92.9% for human alveolar echinococcosis (AE) (n=42). Highest specificity was 93.4% with AgB extract for CE, and 90.3% with Em2 antigen for AE when CE versus AE cross-reactivity was excluded. Anti-AgB antibodies were present in 35.5% of AE cases and anti-Em2 in 7.4% of CE cases. In endemic communities in northwest China screened for echinococcosis, the sensitivity of DIGFA ranged from 71.8% to 90.7% in comparison to abdominal ultrasound; specificity for CE using AgB was 94.6% and for AE using Em2 was 97.1%. This simple eye-read rapid test can be used for both clinical diagnostic support, as well as in conjunction with ultrasound for mass screening in endemic CE and AE areas.

Expert consensus for the diagnosis and treatment of cystic and alveolar echinococcosis in humans

The earlier recommendations of the WHO-Informal Working Group on Echinococcosis (WHO-IWGE) for the treatment of human echinococcosis have had considerable impact in different settings worldwide, but the last major revision was published more than 10 years ago. Advances in classification and treatment of echinococcosis prompted experts from different continents to review the current literature, discuss recent achievements and provide a consensus on diagnosis, treatment and follow-up. Among the recognized species, two are of medical importance -Echinococcus granulosus and Echinococcus multilocularis - causing cystic echinococcosis (CE) and alveolar echinococcosis (AE), respectively. For CE, consensus has been obtained on an image-based, stage-specific approach, which is helpful for choosing one of the following options: (1) percutaneous treatment, (2) surgery, (3) anti-infective drug treatment or (4) watch and wait. Clinical decision-making depends also on setting-specific aspects. The usage of an imaging-based classification system is highly recommended. For AE, early diagnosis and radical (tumour-like) surgery followed by anti-infective prophylaxis with albendazole remains one of the key elements. However, most patients with AE are diagnosed at a later stage, when radical surgery (distance of larval to liver tissue of >2cm) cannot be achieved. The backbone of AE treatment remains the continuous medical treatment with albendazole, and if necessary, individualized interventional measures. With this approach, the prognosis can be improved for the majority of patients with AE. The consensus of experts under the aegis of the WHO-IWGE will help promote studies that provide missing evidence to be included in the next update.

Ibuprofen-loaded calcium phosphate granules: Combination of innovative characterization methods to relate mechanical strength to drug location

This paper studies the impact of the location of a drug substance on the physicochemical and mechanical properties of two types of calcium phosphate granules loaded with seven different contents of ibuprofen, ranging from 1.75% to 46%. These implantable agglomerates were produced by either low or high shear granulation. Unloaded Mi-Pro pellets presented higher sphericity and mechanical properties, but were slightly less porous than Kenwood granules (57.7% vs 61.2%). Nevertheless, the whole expected quantity of ibuprofen could be integrated into both types of granules. A combination of surface analysis, using near-infrared (NIR) spectroscopy coupling chemical imaging, and pellet porosity, by mercury intrusion measurements, allowed ibuprofen to be located. It was shown that, from 0% to 22% drug content, ibuprofen deposited simultaneously on the granule surface, as evidenced by the increase in surface NIR signal, and inside the pores, as highlighted by the decrease in pore volume. From 22%, porosity was almost filled, and additional drug substance coated the granule surfaces, leading to a large increase in the surface NIR signal. This coating was more regular for Mi-Pro pellets owing to their higher sphericity and greater surface deposition of drug substance. Unit crush tests using a microindenter revealed that ibuprofen loading enhanced the mechanical strength of granules, especially above 22% drug content, which was favorable to further application of the granules as a bone defect filler.

Universal reperfusion therapy can be implemented: Lessons from 20 years of management of patients admitted within 6 hours of symptom onset with ST-segment elevation acute myocardial infarction

To describe longitudinal trends in patients' characteristics, management and hospital outcomes over 20 years of therapy for ST-segment elevation myocardial infarction (STEMI).

Recurrent unexplained syncope may have a cerebral origin: Report of 10 cases of arrhythmogenic epilepsy

Despite thorough investigation, approximately 15-20% of syncope cases remain unexplained. An underrecognized cause of syncope may occur when partial epileptic discharges profoundly disrupt normal cardiac rhythm, including cardiac asystole, the so-called arrhythmogenic epilepsy (AE).

Incidence of atrial fibrillation during very long-term follow-up after radiofrequency ablation of typical atrial flutter

Radiofrequency ablation is an effective treatment for typical atrial flutter (AFL) but long-term results may be hampered by atrial fibrillation (AF).