Two-dimensional simulations of Rayleigh-Taylor instability in elastic-plastic media.

Two-dimensional numerical simulations for the Rayleigh-Taylor instability in an elastic-plastic medium are presented. Recent predictions of the theory regarding the asymmetric growth of peaks and valleys during the linear phase of the instability evolution are confirmed. Extension to the nonlinear regime reveals singular features, such as the long delay in achieving the nonlinear saturation and an intermediate phase with growth rate larger than the classical one.

Formation of spikes and bubbles in the linear phase of Rayleigh-Taylor instability in elastic-plastic media.

The generation of spikes and bubbles, a typical characteristic of the nonlinear regime in the Rayleigh-Taylor instability, is found to occur as well during the linear regime in an elastic-plastic solid medium caused, however, by a very different mechanism. This singular feature originates in the differential loads at different locations of the interface, which makes that the transition from the elastic to the plastic regime takes place at different times, thus producing an asymmetric growth of peaks and valleys that rapidly evolves in exponentially growing spikes, while bubbles can also grow exponentially at a lower rate.

Cylindrical convergence effects on the Rayleigh-Taylor instability in elastic and viscous media.

Convergence effects on the perturbation growth of an imploding surface separating two nonideal material media (elastic and viscous media) are analyzed in the case of a cylindrical implosion in both the Rayleigh-Taylor stable and unstable configurations. In the stable configuration, the perturbation damping effect due to angular momentum conservation becomes destroyed for sufficiently high values of the elastic modulus or of the viscosity of the media. For the unstable configuration, Rayleigh-Taylor instability can be suppressed by the elasticity or mitigated by the viscosity, but without practically affecting the perturbation growth due to the geometrical convergence. However, the convergence effects manifest themselves in a manner somewhat different from the classical Bell-Plesset effect by making the process more sensitive to the media compressibility than in the case involving ideal media.

Cost-effectiveness of Denosumab for the Treatment of Postmenopausal Osteoporosis in Malaysia.

From the perspective of Malaysian health care providers, denosumab was cost-effective in the treatment of postmenopausal osteoporosis, with an optimal outcome starting at age 60 years. Our results provide important insights into the value for money of anti-osteoporotic agents that can serve as a reference for other countries with comparable epidemiological data. INTRODUCTION: The study aimed to compare the cost-effectiveness of denosumab with alendronate and no treatment in the management of postmenopausal osteoporosis among the Malaysian population. METHODS: A well-validated Markov model was used to estimate the cost-effectiveness of denosumab in a hypothetical cohort of postmenopausal osteoporotic women between 50 and 80 years old who had no history of fractures. A 10-year time horizon from the perspective of Malaysian health care providers was used in this analysis. The model parameters, including transition probabilities and costs, were based on Malaysian sources. Treatment efficacy data were obtained from a network meta-analysis. The study outcomes were presented as incremental cost per quality-adjusted life-year (QALY) gained. Sensitivity analyses were performed to ensure the robustness of the results. A cost-effectiveness threshold was set at MYR 21,438 (USD 5175) per QALY. RESULTS: Denosumab was found to be a cost-effective option for postmenopausal osteoporotic women aged 60 and older. The incremental cost-effectiveness ratios (ICERs) for denosumab versus alendronate ranged from MYR 16,955 (USD 4093) per QALY at age 60 to MYR 4380 (USD 1057) per QALY at age 80. The cost-effectiveness of denosumab improved monotonically with increasing age. Denosumab was 72.8-92.7% likely to be cost-effective at the cost-effectiveness threshold. Sensitivity analyses demonstrated that the results were robust across all parameter variations, with the annual cost of denosumab being the most sensitive. CONCLUSIONS: From the perspective of the Malaysian health care provider, denosumab appears to be a cost-effective treatment choice for postmenopausal osteoporotic women over 60 years of age.

Elastic-plastic Rayleigh-Taylor instability at a cylindrical interface.

The boundaries of stability are determined for the Rayleigh-Taylor instability at a cylindrical interface between an ideal fluid in the interior and a heavier elastic-plastic solid in the outer region. The stability maps are given in terms of the maximum dimensionless initial amplitude ξ_{th}^{*} that can be tolerated for the interface to remain stable, for any particular value of the dimensionless radius B of the surface, and for the different spatial modes m of the perturbations. In general, for the smallest dimensionless radius and larger modes m, the interface remains stable for larger values of ξ_{th}^{*}. In particular, for m>1 and B→0, it turns out ξ_{th}^{*}→1, and a cylindrical geometry equivalent to Drucker's criterion is found, which indeed ends up being independent of the interface geometry.

Rayleigh-Taylor instability in elastic-plastic solid slabs bounded by a rigid wall.

The linear evolution of the incompressible Rayleigh-Taylor instability for the interface between an elastic-plastic slab medium and a lighter semi-infinite ideal fluid beneath the slab is developed for the case in which slab is attached to a rigid wall at the top surface. The theory yields the maps for the stability in the space determined by the initial perturbation amplitude and wavelength, as well as for the transition boundary from the elastic to the plastic regimes for arbitrary thicknesses of the slab and density contrasts between the media. In particular, an approximate but very accurate scaling law is found for the minimum initial perturbation amplitude required for instability and for the corresponding perturbation wavelength at which it occurs. These results allows for an interpretation of the recent experiments by Maimouni et al. [Phys. Rev. Lett. 116, 154502 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.154502].

Studies of equation of state properties of high-energy-density matter generated by intense ion beams at the facility for antiprotons and ion research.

The work presented in this paper shows with the help of two-dimensional hydrodynamic simulations that intense heavy-ion beams are a very efficient tool to induce high energy density (HED) states in solid matter. These simulations have been carried out using a computer code BIG2 that is based on a Godunov-type numerical algorithm. This code includes ion beam energy deposition using the cold stopping model, which is a valid approximation for the temperature range accessed in these simulations. Different phases of matter achieved due to the beam heating are treated using a semiempirical equation-of-state (EOS) model. To take care of the solid material properties, the Prandl-Reuss model is used. The high specific power deposited by the projectile particles in the target leads to phase transitions on a timescale of the order of tens of nanosecond, which means that the sample material achieves thermodynamic equilibrium during the heating process. In these calculations we use Pb as the sample material that is irradiated by an intense uranium beam. The beam parameters including particle energy, focal spot size, bunch length, and bunch intensity are considered to be the same as the design parameters of the ion beam to be generated by the SIS100 heavy-ion synchrotron at the Facility for Antiprotons and Ion Research (FAIR), at Darmstadt. The purpose of this work is to propose experiments to measure the EOS properties of HED matter including studies of the processes of phase transitions at the FAIR facility. Our simulations have shown that depending on the specific energy deposition, solid lead will undergo phase transitions leading to an expanded hot liquid state, two-phase liquid-gas state, or the critical parameter regime. In a similar manner, other materials can be studied in such experiments, which will be a very useful addition to the knowledge in this important field of research.

Stability boundaries for the Rayleigh-Taylor instability in accelerated elastic-plastic solid slabs.

The linear theory of the incompressible Rayleigh-Taylor instability in elastic-plastic solid slabs is developed on the basis of the simplest constitutive model consisting in a linear elastic (Hookean) initial stage followed by a rigid-plastic phase. The slab is under the action of a constant acceleration, and it overlays a very thick ideal fluid. The boundaries of stability and plastic flow are obtained by assuming that the instability is dominated by the average growth of the perturbation amplitude and neglecting the effects of the higher oscillation frequencies during the stable elastic phase. The theory yields complete analytical expressions for such boundaries for arbitrary Atwood numbers and thickness of the solid slabs.

Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width.

The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number A_{T}=1 and for sufficiently small values of A_{T}. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids.

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number A_{T}=1, the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998)10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.

Economic burden of osteoporosis-related hip fracture in Asia: a systematic review.

This review analyzes the economic costs of HF in Asia. The availability and quality of studies on the burden of osteoporosis in Asia are very scarce. There is a need to encourage more quality cost of osteoporosis studies based on standardized methods to convince healthcare authorities in implementing appropriate strategies. INTRODUCTION: Osteoporosis fractures, especially hip fractures, impose large economic costs to governments and societies. This review aimed to systematically analyze available evidence on healthcare costs associated with osteoporosis-related hip fractures (HF) in Asia. METHODS: Articles were systematically sought from databases including PubMed, EMBASE, and EBSCOHost between 2000 and 2015. Total costs associated with HF care, the cost components, and length of stays were retrieved and analyzed. Study designs were also qualitatively analyzed. RESULTS: The availability of published studies on economic burden of HF in Asia is severely lacking with only 15 articles met the inclusion criteria. Even among the included studies, only two studies reported comprehensive costs evaluating all costs including indirect or intangible costs. Most studies satisfactorily reported criteria for conducting economic evaluation, but large variations existed in the methodological design. Due to study design and other influencing factors, large variation in the cost of HF treatment from US$774 to US$14,198.90 (median S$2943), representing an average of 18.95% (range: 3.58-57.05%) of the countries' 2014 GDP/capita, was observed. This highlighted the heavy burden of managing HF in Asia with about 40% of the included studies reported using more than one third of GDP/capita. CONCLUSION: There is a paucity of burden of illness studies of osteoporosis in the Asian region. For the few available studies, there was a lack of standardization in methodological approach in evaluating the economic burden of the disease. There is a need to encourage more quality burden of illness studies of osteoporosis to inform policymakers in healthcare planning.

Rayleigh-Taylor instability in accelerated elastic-solid slabs.

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ_{2}, shear modulus G, and thickness h, placed over a semi-infinite ideal fluid of density ρ_{1}<ρ_{2}. It extends previous results for Atwood number A_{T}=1 [B. J. Plohr and D. H. Sharp, Z. Angew. Math. Phys. 49, 786 (1998)ZAMPA80044-227510.1007/s000330050121] to arbitrary values of A_{T} and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ_{2}gh/G≤2(1-A_{T})/A_{T}.

Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration.

A model is presented for the linear Rayleigh-Taylor instability taking place at the early stage of acceleration of an elastic-plastic solid, when the shock wave is still running into the solid and is driven by a time varying pressure on the interface. When the the shock is formed sufficiently close to the interface, this stage is considered to follow a previous initial phase controlled by the Ritchmyer-Meshkov instability that settles new initial conditions. The model reproduces the behavior of the instability observed in former numerical simulation results and provides a relatively simpler physical picture than the currently existing one for this stage of the instability evolution.

Rayleigh-Taylor linear growth at an interface between an elastoplastic solid and a viscous liquid.

A previously developed model for the Rayleigh-Taylor instability at an interface between an elastoplastic solid and a viscous fluid [Piriz, Sun, and Tahir, Phys. Rev. E 88, 023026 (2013)] has been used for calculating the time evolution of the perturbations in terms of the mechanical properties of the solid and the liquid, as well as of the initial amplitude ξ_{0} and the wavelength λ of the perturbation. Four kinds of possible evolution are found: two stable and two unstable, depending on their positions in the space of parameters (ξ_{0},λ). All of them present some features that are independent of the solid properties and that are determined only by the liquid viscosity.

Simulations of beam-matter interaction experiments at the CERN HiRadMat facility and prospects of high-energy-density physics research.

In a recent publication [Schmidt et al., Phys. Plasmas 21, 080701 (2014)], we reported results on beam-target interaction experiments that have been carried out at the CERN HiRadMat (High Radiation to Materials) facility using extended solid copper cylindrical targets that were irradiated with a 440-GeV proton beam delivered by the Super Proton Synchrotron (SPS). On the one hand, these experiments confirmed the existence of hydrodynamic tunneling of the protons that leads to substantial increase in the range of the protons and the corresponding hadron shower in the target, a phenomenon predicted by our previous theoretical investigations [Tahir et al., Phys. Rev. ST Accel. Beams 25, 051003 (2012)]. On the other hand, these experiments demonstrated that the beam heated part of the target is severely damaged and is converted into different phases of high energy density (HED) matter, as suggested by our previous theoretical studies [Tahir et al., Phys. Rev. E 79, 046410 (2009)]. The latter confirms that the HiRadMat facility can be used to study HED physics. In the present paper, we give details of the numerical simulations carried out to understand the experimental measurements. These include the evolution of the physical parameters, for example, density, temperature, pressure, and the internal energy in the target, during and after the irradiation. This information is important in order to determine the region of the HED phase diagram that can be accessed in such experiments. These simulations have been done using the energy deposition code fluka and a two-dimensional hydrodynamic code, big2, iteratively.

Rayleigh-Taylor stability boundary at solid-liquid interfaces.

A previous model for the Rayleigh-Taylor instability [A. R. Piriz, J. J. López Cela, and N. A. Tahir, Phys. Rev. E 80, 046305 (2009)] has been extended in order to study an interface between an elastic-plastic solid and a Newtonian liquid and determine the stability region given by the initial perturbation amplitude ξ(0) and wavelength λ. The stability region is found to be enhanced by the effect of the liquid viscosity, but it reaches an asymptote for a sufficiently high viscosity. In addition, it is also found that the boundary for the transition from the elastic to the plastic regime get closer to the stability boundary up to both boundaries coincide for a high enough liquid viscosity, thus making the onset of plastic flow a sufficient condition for instability.

Dynamic stabilization of Rayleigh-Taylor instability in newtonian fluids.

Dynamic stabilization of incompressible and immiscible newtonian fluids is studied by means of an approximate analytical model that considers the vertical vibration of the interface between the fluids. The force driving the vibration is modeled by periodic sequences of Dirac deltas. The model shows the roles played by surface tension and viscosity in determining the stability boundaries and the relevant similarity parameters are found. The results are compared with previous theoretical and experimental studies that used a sinusoidal vibration and they are found to present the same qualitative features provided a symmetric sequence of Dirac deltas is considered. Instead, important differences are observed when an asymmetric driving is used.

Linear analysis of incompressible Rayleigh-Taylor instability in solids.

The study of the linear stage of the incompressible Rayleigh-Taylor instability in elastic-plastic solids is performed by considering thick plates under a constant acceleration that is also uniform except for a small sinusoidal ripple in the horizontal plane. The analysis is carried out by using an analytical model based on the Newton second law and it is complemented with extensive two-dimensional numerical simulations. The conditions for marginal stability that determine the instability threshold are derived. Besides, the boundary for the transition from the elastic to the plastic regime is obtained and it is demonstrated that such a transition is not a sufficient condition for instability. The model yields complete analytical solutions for the perturbation amplitude evolution and reveals the main physical process that governs the instability. The theory is in general agreement with the numerical simulations and provides useful quantitative results. Implications for high-energy-density-physics experiments are also discussed.