Collapse Of Shell Research Articles

Generating interstitial water within the persisting tetrahedral H-bond network explains density increase upon compressing liquid water

Despite its ubiquitous nature, the atomic structure of water in its liquid state is still controversially debated. We use a combination of X-ray Raman scattering spectroscopy in conjunction with ab initio and path integral molecular dynamics simulations to study the local atomic and electronic structure of water under high pressure conditions. Systematically increasing fingerprints of non-hydrogen-bonded H[Formula: see text]O molecules in the first hydration shell are identified in the experimental and computational oxygen K-edge excitation spectra. This provides evidence for a compaction mechanism in terms of a continuous collapse of the second hydration shell with increasing pressure via generation of interstitial water within locally tetrahedral hydrogen-bonding environments.

Mass fluctuations in non-rotating BTZ black holes

We investigate the impact of oscillations of a black hole's mass around its average value on the three-dimensional black hole geometry. Drawing on a classical framework that conceptualizes fluctuations near an event horizon as mass variations, we introduce a model where the metric of a black hole, formed from the collapse of a massive null shell, exhibits oscillatory behavior in spherical modes. This dynamic is encapsulated by a non-rotating BTZ-Vaidya solution, characterized by the black hole mass fluctuating at a resonant frequency ω and a small amplitude parameter μ0. Using a perturbative approach, solutions to the null geodesic equation are determined up to the second order in μ0. The temporal fluctuations of the event horizon's location induce alterations in the thermodynamic variables' values. Upon calculating the time-averaged values, the mean Hawking temperature experiences a slight decrease due to these fluctuations, while the mean entropy exhibits an increase. Furthermore, the study explores the influence of these fluctuations on the trajectories of null rays near the horizon, which ultimately reach the anti-de Sitter boundary at late times. The analytical computation of the general solution for the perturbed rays up to the second order underscores the novel approach of this study in examining the effects of mass oscillations on black hole thermodynamics and geometry, thereby contributing a unique perspective to the field.

A method to represent the strain hardening effect in the hyper-elastic model within a fully Eulerian framework

We propose a method to treat the strain hardening effect in the hyperelastic model. Coupled with the level set interface capturing method and a real ghost fluid method, it is formulated in a fully Eulerian framework. The HLLD approximate Riemann solver is used to obtain the interface state. We use the elastic inverse deformation gradient tensor to track the material deformation state. Once the solid starts to yield, along the normal direction in stress space, an iterative algorithm is used to relax the elastic inverse deformation gradient tensor to target value where the equivalent stress meets the requirement of consistency condition in plasticity. This approach is intuitive and can avoid the use of the physical delay time, which is difficult to calibrate from experiments. We use the Wilkins flying plate impact, cylindrical shell collapse, Taylor impact and the conical-nosed projectile penetration test cases to validate the method. The results show good agreement with the theoretical analysis and experiments. This approach can also apply without further extension when thermal softening effect or damage models are considered.

The structure of water from hot to supercooled temperatures based on analysis of experimental X-ray scattering data

An increasing number of studies support the existence of a liquid–liquid critical point (LLCP) in water, implying that under ambient conditions, water is a supercritical mixture of low-density (LDL) and high-density liquid (HDL) structures. Here, we analyse X-ray scattering data in terms of this model. Small-angle X-ray scattering data shows that anomalies are seen at temperatures as high as 360 K. By assuming the local structure in LDL-domains resembles that of the corresponding amorphous solid, we estimate the population of LDL-domains at different temperatures from pair-correlation functions (PCFs). By subtracting the LDL contribution, we isolate the PCF of the HDL component. The temperature-dependent HDL-PCFs show a feature around 4 Å in the supercooled regime, interpreted as interstitials resulting from collapse of the second coordination shell. We define the first coordination shell as neighbours up to 3.3 Å, based on an isosbestic point in the running coordination number. Our analysis shows that the HDL-domains have on average two strongly and two weakly H-bonded neighbours. The LDL population in TIP4P/2005-water is less temperature dependent than in real water, and the HDL component contains more structures with three strongly H-bonded neighbours, leading to a slight overestimation of the first peak of the PCF.

Real-time swelling-collapse kinetics of nanogels driven by XFEL pulses.

Stimuli-responsive polymers are an important class of materials with many applications in nanotechnology and drug delivery. The most prominent one is poly-N-isopropylacrylamide (PNIPAm). The characterization of the kinetics of its change after a temperature jump is still a lively research topic, especially at nanometer-length scales where it is not possible to rely on conventional microscopic techniques. Here, we measured in real time the collapse of a PNIPAm shell on silica nanoparticles with megahertz x-ray photon correlation spectroscopy at the European XFEL. We characterize the changes of the particles diffusion constant as a function of time and consequently local temperature on sub-microsecond timescales. We developed a phenomenological model to describe the observed data and extract the characteristic times associated to the swelling and collapse processes. Different from previous studies tracking the turbidity of PNIPAm dispersions and using laser heating, we find collapse times below microsecond timescales and two to three orders of magnitude slower swelling times.

Collapse of helical cylindrical shells subjected to external hydrostatic pressure

ABSTRACT The present study investigated the collapse performance of helical cylindrical shells subjected to external pressure. Helical cylindrical shells, cylindrical shells, and helically stiffened cylindrical shells were designed, fabricated, geometrically measured, and hydrostatically tested. Linear eigenvalue and nonlinear Riks analyses were performed to evaluate the collapse properties of the fabricated shells. The experimental and numerical results of this study were in agreement. In addition, the existing shapes of shells were used to make a comparison with the helical cylindrical shell. The effects of the spiral rib and wall thickness on the collapse properties of helical cylindrical shells were investigated numerically. The results indicated that a helical cylindrical shell with a spiral cambered surface and spiral rib has considerably higher loading capacity than an ordinary cylindrical shell does. A spiral rib can improve the collapse behaviour of helical cylindrical shells and change their collapse modes.

Experimental investigations on the collapse of spiral-stiffened cylindrical shells under external hydrostatic pressure

This paper presents a comprehensive experimental investigation into the collapse behavior of spiral stiffened cylindrical shells under external hydrostatic pressure. Spiral stiffened cylindrical shells with two different pitches and cylindrical shells were designed and fabricated. The fabricated specimens were divided into three groups. Each group has two identical specimens. Test specimens were welded from stainless steel. The shell was formed by cold bending, and the spiral ribs were welded to the surface of the shell to form a spiral stiffened cylindrical shell. Measurements of initial geometric imperfections and shell thickness were performed on the fabricated specimens to verify the accuracy of fabricating. Subsequently, the specimens were placed in a pressure chamber and pressurized until collapsed to obtain the ultimate collapse pressure and collapse modes. In addition, a uniaxial tensile test was conducted on the shell material to obtain its material properties. Experimental results indicated that the fabricated specimens had excellent repeatability and reasonable precision. The presence of a spiral rib effectively boosted the ultimate collapse pressure of the cylindrical shell with a more pronounced strengthening effect observed as the rib density increased.

Cold-formed steel strength predictions for torsion and bending–torsion interaction

Locally slender cross-section members, such as cold-formed steel open sections, are susceptible to significant twisting and high warping torsion stresses. Torsion considerations are complicated by whether it is derived as a first-order effect from loading or a second-order effect from instability. Previous direct torsion experiments on lipped Cee sections have shown significant inelastic reserve. Furthermore, the current design for combined bending–torsion interaction has limitations, including only considering the first yield and ignoring the cross-section slenderness in torsion. Two parametric studies were conducted to predict both the torsion capacity and the combined bending–torsion interaction in locally slender cross-sections. Shell finite element analysis of lipped Cee and Zee sections for both the torsion only and the combined bending–torsion cases were created using a validated model. For the torsion-only study, various cross-section geometries, steel grades, and member lengths covering the range of practically expected torsional slenderness were investigated. A set of bimoment parameters, including yield, buckling, and plastic bimoments, were calculated and the ultimate bimoment was determined by shell finite element collapse analyses. A simple uniform equation predicting the bimoment capacity was adopted and two bimoment strength curves are proposed for local and distortional buckling-controlled cases respectively. For the combined bending–torsion case, various practical cross-sections and bracing conditions were investigated with various ratios of applied torsion and bending. Shell finite element buckling and collapse analyses were performed to determine the critical and ultimate moments and bimoments. It was found that the current AISI standard is conservative under most scenarios. Updated torsion–bending interaction equations incorporating bimoment and bending moments are proposed. The interaction equations are dependent on the cross-section, the direction of the applied torsion, and the bracing condition.

Interplay of shell evolution and oxidation depth on the ignition and combustion behavior of aluminum nanoparticles

Shell morphology and oxidation depth can significantly affect the combustion effectiveness of aluminum nanoparticles (ANPs). This study presents an approach to dynamically detect and reconstruct irregular ANP surfaces using the Alpha Shape algorithm. We also introduce a visualization technique to observe nanoscale density, per-atom stress, charge, and temperature distribution of ANPs. Our findings reveal a striking phenomenon where a transitory cavity forms in the particle center during ignition, playing a significant role in the overall ignition and combustion process of ANPs. The reaction rate is found to be closely associated with the formation and collapse of the cavity, with over half of the energy being released in this process. Furthermore, the study highlights the impact of oxidation depth on ANP combustion behavior. In cases of mild oxidation, a breach in the weak area of the shell leads to the leakage of aluminum atoms from the core and the eventual shell collapse. The duration of physiochemical stages during ignition and combustion varies with oxidation depth but generally conforms to established principles. This study is expected to offer valuable insight into the interplay between shell morphology and oxidation depth on the ignition and combustion behavior of ANPs for researchers and engineers in the field of material science and combustion technology.

Quantum vacuum effects on the formation of black holes

We study the backreaction of quantum fields induced through the vacuum polarization and the conformal anomaly on the collapse of a thin shell of dust. It is shown that the final fate of the collapse process depends on the physical properties of the shell, including its rest and gravitational masses. Investigating the conditions for the formation of black holes, we notice that quantum effects modify the geometry and structure of Schwarzschild space-time in such a way that black holes have two horizons, an inner and an outer horizon. If the gravitational mass of the shell is about that of an ordinary star, then in most cases, the semi-classical collapse will terminate in a singularity, and in general, quantum fluctuations are not strong enough to prevent the creation of the singularity. Although under certain conditions, it is possible to form a non-singular black hole, i.e., a regular black hole. In this way, the collapse stops at a radius much larger than the Planck length below the inner horizon, and the shell bounces and starts an expansion.

An analytic model for gravitational collapse of spherical matter under mixed pressure

In this paper, we investigate spherically symmetric gravitational collapse of thick matter shell without radiation in the Einstein gravity with cosmological constant. The orbit of the infalling thick matter is determined by imposing an equation of state for the matter near interface, where pressure constituted of the transverse component and the longitudinal one is proportional to energy density. We present analytic solutions for the equation of state and discuss parameter region to satisfy physical conditions such as the absence of the shell crossing singularity, the monotonic increase of the emergent infinite redshift surface and energy conditions. We finally show that adopting the definition presented in arXiv:2005.13233 the total energy in this time-dependent system is invariant under the given time evolution.

Permanent irreversible structural color based on core-shell chemically bonded SiO2@P(St-BA) particles.

Novel core-shell chemically bonded SiO2@P(St-BA) particles were designed and self-assembled to prepare photonic crystals. Due to the irreversible collapse of polymer shells during hot-pressing, SiO2@P(St-BA) particles could provide new ideas for high-stability and bright red-shifted structural color patterns.

Modeling Dynamic Compaction of Porous Materials

To model dynamic compaction of a porous material we need: 1) an equation of state (EOS) for the porous material in terms of the EOS of its matrix; and 2) a compaction law. For an EOS people usually use Hermann's suggestion, as in his Pα [1] model. For a compaction law people usually use the results of a spherical shell collapse analysis (Carroll and Holt model [2]). In their original paper Carroll and Holt do both: the quasi-static shell collapse and the dynamic shell collapse. In their dynamic analysis, however, they ignore density changes of the matrix. In what follows we: 1) revisit the spherical shell collapse problem but with density changes taken into account; 2) develop a dynamic compaction law based on our overstress principle; 3) implement the different compaction laws mentioned above in a hydro-code; and 4) run a planar impact problem and compare histories and profiles obtained with the different compaction laws. We find that: 1) dynamic compaction laws give entirely different results from quasi-static compaction laws; 2) taking density changes into account do make a certain difference.

Thin shell dynamics in Lovelock gravity

We study matching conditions for a spherically symmetric thin shell in Lovelock gravity which can be read off from the variation of the corresponding first-order action. In point of fact, the addition of Myers’ boundary terms to the gravitational action eliminates the dependence on the acceleration in this functional and such that the canonical momentum appears in the surface term in the variation of the total action. This procedure leads to junction conditions given by the discontinuity of the canonical momentum defined for an evolution normal to the boundary.In particular, we correct existing results in the literature for the thin shell collapse in generic Lovelock theories, which were mistakenly drawn from an inaccurate analysis of the total derivative terms in the system.

Fibre-Based modelling for predicting the progressive collapse of cylindrical shells under combined axial compression and bending moment

Cylindrical shell is a fundamental building block of many engineering structures. They are usually designed to be the primary load-carrying components to withstand different combinations of environmental loads. This paper presents a fibre-based approach to modelling the progressive collapse of cylindrical shells under combined axial compression and bending moment. In this method, the progressive collapse behaviour of cylindrical shells is incrementally evaluated by accounting for the local response of each fibre element. This approach offers a computationally efficient and robust scheme to compute the ultimate strength of cylindrical shells. Moreover, it enables the modelling of load-shedding between the buckled and intact shell elements on the compressive side, and the yielding failure on the tensile side, which appears to be ignored in existing design codes. Analyses are performed on cylindrical shells with a wide range of design parameters. Validation using the finite element method demonstrates a reasonably well performance of the proposed fibre-based modelling technique.

Gravitational collapse of spherical shells of fluid in the isotropic homogeneous universe

We investigate gravitational collapse of thick shell of fluid in the isotropic homogeneous universe without radiation described by the Einstein gravity with cosmological constant. We construct analytic solutions of this kind interpolating the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric and the de-Sitter Schwarzschild black hole one by the Gullstrand-Painlevé one. After determining the scale factor for a perfect fluid coexisting with cosmological constant, we determine the orbit of the collapsing shells of fluid from the continuity condition for density and the perpendicular component of pressure at interface. However the continuity condition cannot fix the orbit when there does not exist a perfect fluid inside the shells. In this case we determine the orbit from an equation of state for the fluid consisting a shell near the surface. Finally we confirm that the total energy defined in arXiv:2005.13233 is independent of the given time evolution in this system.

Quantum thin shell surrounding a black hole

In a previous work we obtained exact solutions for the proper time quantum mechanics of a thin dust shell, collapsing in a vacuum. We extend these results to the quantum collapse of a dust shell surrounding a preexisting black hole. In lieu of exact solutions, which have so far proved difficult to obtain for this system, we establish the essential features of the quantum shell through a Wentzel-Kramers-Brillouin approximation, which is valid only when the mass of the shell is much greater than the Planck mass. There are many similarities with the vacuum collapse: only bound states exist and the proper energy spectrum of the shell is unaffected by the presence of the central black hole to this order. There are no peculiar or distinguishing features of the wave function near the black hole horizon. It vanishes at the center and oscillates between the origin and the classically forbidden region, beyond which it decays exponentially.

Spin transfer from dark matter to gas during halo formation

ABSTRACT In the protogalactic density field, diffuse gas and collision-less cold dark matter (DM) are often assumed sufficiently mixed that both components experience identical tidal torques. However, haloes in cosmological simulations consistently end up with a higher specific angular momentum (sAM) in gas, even in simulations without radiative cooling and galaxy formation physics. We refine this result by analysing the spin distributions of gas and DM in ∼50 000 well-resolved haloes in a non-radiative cosmological simulation from the SURFS suite. The sAM of the halo gas on average ends up ∼40 per cent above that of the DM. This can be pinned down to an excess AM in the inner halo (<50 per cent virial radius), paralleled by a more coherent rotation pattern in the gas. We uncover the leading driver for this AM difference through a series of control simulations of a collapsing ellipsoidal top-hat, where gas and DM are initially well mixed. These runs reveal that the pressurized inner gas shells collapse more slowly, causing the DM ellipsoid to spin ahead of the gas ellipsoid. The arising torque generally transfers AM from the DM to the gas. The amount of AM transferred via this mode depends on the initial spin, the initial axes ratios, and the collapse factor. These quantities can be combined in a single dimensionless parameter, which robustly predicts the AM transfer of the ellipsoidal collapse. This simplistic model can quantitatively explain the average AM excess of the gas found in the more complex non-radiative cosmological simulation.

Possible connection between time-splitting parameter and surface tension in Casimir-type problems

We discuss four different, though related, fundamental topics related to the Casimir effect: (1) We suggest that the application of Casimir theory to real dielectric materials, thus implying the atomic spacing as a course-grained length parameter, makes it natural to assume that this parameter is of the same order of magnitude as the QFT time-splitting parameter multiplied with the velocity of light. (2) We show that application of Casimir theory to a thick fluid shell (apparently a closed mechanical system) leads actually to an unstable situation if no extra mechanical forces, typically surface tension forces, are brought into consideration. (3) We analyze how the presence of a radial Casimir repulsive pressure modifies the filling process of a spherical vacuum hole in an infinite fluid (the Reynolds problem), with the result that a bounce occurs at a finite though very small radius. (4) As a comment on an apparently similar situation in general relativity, we consider the gravitational collapse of a singular shell. It might seem natural to allow for the presence of a repulsive Casimir pressure in this case also, thereby obtaining a bounce-like situation again. However, we have to conclude that such a procedure implies an omission of the Casimir field’s gravitational energy, and is therefore hardly tenable, although it is in our opinion worth mentioning.

Quantum collapse of a thin shell revisited

There are several possible choices of the time parameter for the canonical description of a self-gravitating thin shell, but quantum thories built on different time parameters lead to unitarily inequivalent descriptions. We compare the quantum collapse of a thin dust shell in two different times {\it viz.,} the time coordinate in the interior of the shell (originally addressed in \cite{hajicek92a}) and the time coordinate of the comoving observer (proper time). In each case, we obtain exact solutions to the Wheeler-DeWitt equation requiring only a finite and well behaved $U(1)$ current. The two quantum theories are complementary and each highlights the role played by the Planck mass: stationary states of positive energy in interior time exist only if the shell rest mass in smaller than the Planck mass. In proper time they exist only when the shell rest mass is {\it greater} than the Planck mass. In coordinate time there are both scattering states and bound states with a well defined energy spectrum. In the proper time description there are only bound states, whose spectrum we determine.