Time-dependent Density Profiles Research Articles

Gyrokinetic flux-driven simulations in mixed TEM/ITG regime using a delta-f PIC scheme with evolving background

In the context of global gyrokinetic simulations of turbulence using a particle-in-cell framework, verifying the delta-f assumption with a fixed background distribution becomes challenging when determining quasi-steady state profiles corresponding to given sources over long time scales, where plasma profiles can evolve significantly. The advantage of low relative sampling noise afforded by the delta-f scheme is shown to be retained by considering the background as a time-evolving Maxwellian with time-dependent density and temperature profiles. Implementation of this adaptive scheme to simulate electrostatic collisionless flux-driven turbulence in tokamak plasmas show small and nonincreasing sampling noise levels, which would otherwise increase indefinitely with a stationary background scheme. The adaptive scheme furthermore allows one to reach numerically converged results of quasi-steady state with much lower marker numbers.

Capturing the mechanosensitivity of cell proliferation in models of epithelium

Despite the primary role of cell proliferation in tissue development and homeostatic maintenance, the interplay between cell density, cell mechanoresponse, and cell growth and division is not yet understood. In this article, we address this issue by reporting on an experimental investigation of cell proliferation on all time- and length-scales of the development of a model tissue, grown on collagen-coated glass or deformable substrates. Through extensive data analysis, we demonstrate the relation between mechanoresponse and probability for cell division, as a function of the local cell density. Motivated by these results, we construct a minimal model of cell division in tissue environment that can recover the data. By parameterizing the growth and the dividing phases of the cell cycle, and introducing such a proliferation model in dissipative particle dynamics simulations, we recover the mechanoresponsive, time-dependent density profiles in 2D tissues growing to macroscopic scales. The importance of separating the cell population into growing and dividing cells, each characterized by a particular time scale, is further emphasized by calculations of density profiles based on adapted Fisher-Kolmogorov equations. Together, these results show that the mechanoresponse on the level of a constitutive cell and its proliferation results in a matrix-sensitive active pressure. The latter evokes massive cooperative displacement of cells in the invading tissue and is a key factor for developing large-scale structures in the steady state.

Scalar field dark matter: impact of supernova-driven blowouts on the soliton structure of low-mass dark matter haloes

ABSTRACT We present the first study on the gravitational impact of supernova feedback in an isolated soliton and a spherically symmetric dwarf scalar field dark matter (SFDM) halo of virial mass $1\times 10^{10}\,\mathrm{M_\odot }$. We use a boson mass $m=10^{-22}\,\mathrm{eV\,c^{-2}}$ and a soliton core $r_\mathrm{ c} \approx 0.7$ kpc, comparable to typical half-light radii of Local Group dwarf galaxies. We simulate the rapid gas removal from the centre of the soliton by a concentric external time-dependent Hernquist potential. We explore two scenarios of feedback blowouts: (i) a massive single burst and (ii) multiple consecutive blowouts injecting the same total energy to the system, including various magnitudes for the blowouts in both scenarios. In all cases, we find one single blowout has a stronger effect on reducing the soliton central density. Feedback leads to central soliton densities that oscillate quasi-periodically for an isolated soliton and stochastically for an SFDM halo. The range in the density amplitude depends on the strength of the blowout; however, we observe typical variations of a factor of $\geqslant$2. One important consequence of the stochastic fluctuating densities is that, if we had no prior knowledge of the system evolution, we can only know the configuration profile at a specific time within some accuracy. By fitting soliton profiles at different times to our simulated structures, we found the (1$\sigma$) scatter of their time-dependent density profiles. For configurations within the 1$\sigma$ range, we find the inferred boson mass is typically less than 20 per cent different from the real value used in our simulations. Finally, we compare the observed dynamical masses of field dwarf galaxies in our Local Group with the implied range of viable solitons from our simulations and find good agreement.

Accessing the free expansion of a crystalline colloidal drop by optical experiments.

We study poly-crystalline spherical drops of an aqueous suspension of highly charged colloidal spheres exposed to a colloid-free aqueous environment. Crystal contours were obtained from standard optical imaging. The crystal spheres first expand to nearly four times their initial volume before slowly shrinking due to dilution-induced melting. Exploiting coherent multiple-scattering by (110) Bragg reflecting crystals, time-dependent density profiles were recorded within the drop interior. These show a continuously flattening radial density gradient and a decreasing central density. Expansion curves and density profiles are qualitatively consistent with theoretical expectations based on dynamical density functional theory for the expansion of a spherical crystallite made of charged Brownian spheres. We anticipate that our study opens novel experimental access to density determination in turbid crystals.

A novel density functional study on the freezing mechanism of a nanodroplet under an external electric field

An electric field is one of the most favorable means to control the microscopic behavior of a nanodroplet/nanocluster, but the mechanisms to do so are still not very clear. In this work, we proposed dynamic density functional theory (DDFT) to mimic the freezing process of a nanodroplet under an external electric field (EEF). The molecular interaction is modeled by a Lennard–Jones potential plus a dipole–dipole interaction that is induced by the EEF. We found that the electric field could induce a series of structural transitions and that the droplet could form into a layered structure or a discrete lattice depending on the intensity of the EEF. Compared to molecular simulation, the transition EEF predicted from DDFT agrees more with reality. The time-dependent density profile indicates that the freezing process is nonlinear and irreversible, especially for the strong electric field case. These findings may provide insights into the control of nanodroplets and the preparation of nanoclusters.

High-energy neutrino emission from magnetized jets of rapidly rotating protomagnetars

ABSTRACT Relativistic jets originating from protomagnetar central engines can lead to long duration gamma-ray bursts (GRBs) and are considered potential sources of ultra-high-energy cosmic rays and secondary neutrinos. We explore the propagation of such jets through a broad range of progenitors, from stars which have shed their envelopes to supergiants which have not. We use a semi-analytical spin-down model for the strongly magnetized and rapidly rotating protoneutron star (PNS) to investigate the role of central engine properties such as the surface dipole field strength, initial rotation period, and jet opening angle on the interactions and dynamical evolution of the jet-cocoon system. With this model, we determine the properties of the relativistic jet, the mildly relativistic cocoon, and the collimation shock in terms of system parameters such as the time-dependent jet luminosity, injection angle, and density profile of the stellar medium. We also analyse the criteria for a successful jet breakout, the maximum energy that can be deposited into the cocoon by the relativistic jet, and structural stability of the magnetized outflow relative to local instabilities. Lastly, we compute the high-energy neutrino emission as these magnetized outflows burrow through their progenitors. Precursor neutrinos from successful GRB jets are unlikely to be detected by IceCube, which is consistent with the results of previous works. On the other hand, we find that high-energy neutrinos may be produced for extended progenitors like blue and red supergiants, and we estimate the detectability of neutrinos with next generation detectors such as IceCube-Gen2.

Spatially heterogeneous dynamics and locally arrested density fluctuations from first principles

We present a first-principles formalism for studying dynamical heterogeneities in glass-forming liquids. Based on the non-equilibrium self-consistent generalized Langevin equation theory, we were able to describe the time-dependent local density profile during the particle interchange among small regions of the fluid. The final form of the diffusion equation contains both the contribution of the chemical potential gradient written in terms of a coarse-grained density and a collective diffusion coefficient as well as the effect of a history-dependent mobility factor. With this diffusion equation, we captured interesting phenomena in glass-forming liquids such as the cases when a strong density gradient is accompanied by a very low mobility factor attributable to the denser part: in such circumstances, the density profile falls into an arrested state even in the presence of a density gradient. On the other hand, we also show that above a certain critical temperature, which depends on the volume fraction, any density heterogeneity relaxes to a uniform state in a finite time, known as equilibration time. We further show that such equilibration time varies little with the temperature in diluted systems but can change drastically with temperature in concentrated systems.

The effect of concentration-dependent diffusion on double-diffusive instability

The article studies the stability of a two-layer miscible system to the double-diffusive instability. The system is placed in a vertical Hele–Shaw cell and is composed of two homogeneous aqueous solutions initially separated by a narrow transient zone. We have restricted our consideration to the initially stable density stratification that precludes the Rayleigh–Taylor instability. The main objective of the study is to elucidate the effect of a concentration-dependent diffusion coefficient, which has been commonly ignored by researchers. Assuming linear dependence of the diffusion coefficient of each solute and using Picard's iteration scheme, we have derived a closed-form analytical expression for the time-dependent density profile. This permits the stability boundary to be established for a two-layer system with respect to the double-diffusive instability by taking into account the effect of a concentration-dependent diffusion coefficient. The obtained analytical result has been substantiated by the results of direct numerical simulation. The experiments have shown that a successive increase in the concentrations of both solutes, with their ratio remaining unchanged, can lead to opposite results. In the case of a NaNO3-H2SO4 pair, the two-layer system, being stable at low concentrations, becomes unstable as the concentrations proportionally increase, giving rise to convective motion in the form of salt fingers. On the contrary, a two-layer system consisting of LiCl and NaNO3 solutions is stabilized with increasing concentrations of dissolved substances. A further increase in the concentrations of these substances causes mechanical equilibrium breaking and subsequent formation of the so-called diffusive-layer convection. The experimental results are in good agreement with the theoretical predictions.

Density relaxation in conserved Manna sandpiles.

We study relaxation of long-wavelength density perturbations in a one-dimensional conserved Manna sandpile. Far from criticality where correlation length ξ is finite, relaxation of density profiles having wave numbers k→0 is diffusive, with relaxation time τ_{R}∼k^{-2}/D with D being the density-dependent bulk-diffusion coefficient. Near criticality with kξ≳1, the bulk diffusivity diverges and the transport becomes anomalous; accordingly, the relaxation time varies as τ_{R}∼k^{-z}, with the dynamical exponent z=2-(1-β)/ν_{⊥}<2, where β is the critical order-parameter exponent and ν_{⊥} is the critical correlation-length exponent. Relaxation of initially localized density profiles on an infinite critical background exhibits a self-similar structure. In this case, the asymptotic scaling form of the time-dependent density profile is analytically calculated: we find that, at long times t, the width σ of the density perturbation grows anomalously, σ∼t^{w}, with the growth exponent ω=1/(1+β)>1/2. In all cases, theoretical predictions are in reasonably good agreement with simulations.

Probing episodic accretion with chemistry: CALYPSO observations of the very-low-luminosity Class 0 protostar IRAM 04191+1522

Context. The process of mass accretion in the earliest phases of star formation is still not fully understood: does the accretion rate smoothly decline with the age of the protostar or are there short, intermittent accretion bursts? The latter option would also yield the possibility for very low-luminosity objects (VeLLOs) to be precursors of solar-type stars, even though they do not seem to have sufficiently high accretion rates to reach stellar masses during their protostellar lifetime. Nevertheless, probing such intermittent events in the deeply embedded phase is not easy. Chemical signatures in the protostellar envelope can trace a past accretion burst. Aims. We aim to explore whether or not the observed C18O and N2H+ emission pattern towards the VeLLO IRAM 04191+1522 can be understood in the framework of a scenario where the emission is chemically tracing a past accretion burst. Methods. We used high-angular-resolution Plateau de Bure Interferometer (PdBI) observations of C18O and N2H+ towards IRAM 04191+1522 that were obtained as part of the CALYPSO IRAM Large Program (Continuum And Lines in Young ProtoStellar Objects). We model these observations using a chemical code with a time-dependent physical structure coupled with a radiative transfer module, where we allow for variations in the source luminosity. Results. We find that the N2H+ line emission shows a central hole, with the N2H+ emission peaking at a radius of about 10′′ (1400 au) from the source, while the C18O emission is compact (1.3′′ FWHM, corresponding to 182 au). The morphology of these two lines cannot be reproduced with a constant luminosity model based on the present-day internal luminosity (0.08 L⊙). However, the N2H+ peaks are consistent with a constant-luminosity model of 12 L⊙. Using a model with time-dependent temperature and density profiles, we show that the observed N2H+ peak emission could indeed be caused by a past accretion burst with a luminosity 150 times higher than the present-day luminosity. Such a burst should have occurred a couple of hundred years ago. Conclusions. We suggest that an accretion burst occurred in IRAM 04191+1522 in the recent past. If such bursts are common and sufficiently long in VeLLOs, they could lead to higher accretion onto the central object than their luminosity suggests. For IRAM 04191 in particular, our results yield an estimated final mass of 0.2–0.25 M⊙ by the end of the Class 0 phase, which would make this object a low-mass star rather than a brown dwarf. More generally, our analysis demonstrates that the combination of observations of N2H+ and C18O is a more reliable diagnostic of past outburst activity than C18O or N2H+ emission alone.

Noise limits on ITER plasma vertical stabilization system imposed by tungsten divertor monoblock thermal fatigue

Abstract Tokamak plasmas with vertically elongated cross-sections are unstable due to vertical displacements. Feedback stabilization of the ITER plasma current centre will be performed using the speed of its vertical displacements, dZ/dt, as input. Inevitable noise in the diagnostic signal for dZ/dt leads to “noisy” components in the feedback voltage and current in the stabilizing coils. This leads to noisy components in the vertical position of the plasma current centre and the divertor strike points. For burning plasma conditions on ITER, these strike point displacements may be a concern for thermal fatigue at the water cooling interface of the tungsten monoblocks constituting the divertor targets. A study is presented here in which this concern is examined for the first time. The baseline 15 MA scenario (fusion power of 500 MW with a 500 s flattop and fusion power gain, QDT = 10) is simulated with the DINA code, assuming low frequency noise in the dZ/dt diagnostic signal. The noise has uniform spectrum with a given root mean square (RMS) value ( =0.6 ms−1 or 0.2 ms−1) in the frequency band (0, 1 kHz). The results of these DINA simulations are combined with dissipative divertor plasma solutions obtained with the SOLPS-ITER plasma boundary code to provide a time dependent divertor target heat flux density profile. The latter is then imposed on a finite element model of the target monoblocks to assess the temporal evolution of the 3D temperature field in the block, including the Cu-W and Cu-CuCrZr joints at the cooling interface. These joints represent the points of the Cu and CuCrZr materials that see the largest temperature changes and are thus at greatest risk of failure. To evaluate an acceptance criterion on the non-cyclic and non-uniform thermal loads at the joints, an approach is developed which combines a Rainflow counting technique with Palmgren-Miner’s rule for fatigue accumulation. Analysis of the temperature evolution at the Cu-W joint shows that the RMS value of noise ∼0.6 ms−1 is unacceptable from the point of view of thermal fatigue for the expected total exposure time under burning plasma conditions that the first ITER divertor must survive. The lower value ( ∼0.2 ms−1) is found to be acceptable. A subsequent parametric study concludes that ≲ 0.44 ms−1 is just consistent with fatigue lifetime for the prescribed divertor power flux density profile, but should be kept lower than this to allow for some margin. Regarding the monoblock surface temperature, the natural power spreading caused by the separatrix movements is found to be beneficial from the point of view of recrystallization. For the level of noise in the dZ/dt diagnostic required to stay below joint fatigue limits, the average surface temperature on the most loaded monoblocks is reduced by ∼100 °C compared to the case with stationary strike points and the amount of time spent at this temperature at any one block by over 80 %.

Activated diffusiophoresis.

Perturbations of fluid media can give rise to non-equilibrium dynamics, which may, in turn, cause motion of immersed inclusions or tracer particles. We consider perturbations ("activations") that are local in space and time, of a fluid density which is conserved, and study the resulting diffusiophoretic phenomena that emerge at a large distance. Specifically, we consider cases where the perturbations propagate diffusively, providing examples from passive and active matter for which this is expected to be the case. Activations can, for instance, be realized by sudden and local changes in interaction potentials of the medium or by local changes in its activity. Various analytical results are provided for the case of confinement by two parallel walls. We investigate the possibility of extracting work from inclusions, which are moving through the activated fluid. Furthermore, we show that a time-dependent density profile, created via suitable activation protocols, allows for the conveyance of inclusions along controlled and stable trajectories. In contrast, in states with a steady density, inclusions cannot be held at stable positions, reminiscent of Earnshaw's theorem of electrostatics. We expect these findings to be applicable in a range of experimental systems. The phenomena described here are argued to be distinct from other forms of phoresis such as thermophoresis.

Simulation of Wetting and Interfacial Behavior of Quaternary Ammonium and Phosphonium Ionic Liquid Nanodroplets Over Face-Centered Cubic Metal Surfaces.

We studied the behavior of quaternary ammonium- and phosphonium-based ([N2225][NTf2] and [P2225][NTf2]) ionic liquid (IL) nanodroplets on copper (Cu) and platinum (Pt) metal surfaces using classical molecular dynamics simulations. Solid-liquid interactions were underpinned by studying the dynamic spreading, contact angle, time-dependent binding energies, mean-square displacements, number and charge density profiles, and orientational distribution of these two IL nanodroplets. In particular, the role and importance of different crystallographic facets of face-centered cubic metal surface [Cu(100), Cu(111), Pt(100), and Pt(111)] were investigated. The results indicate a vast variety of properties that are dictated highly by the structure of different crystallographic facets of the metal substrate. The nature of the facet (e.g., the atomic arrangement symmetry, the extent of closed packed, and the unit cell size) leads to an extended scale spreading of the ILs on the surface with the (111) index but not with the (100) index, while the nature of metals itself plays a role.

Super-transition-array calculations for synthetic spectra and opacity of high-density, high-temperature germanium plasmas

The synthetic emission spectra and opacity of high-density, high-temperature germanium (Z=32) plasma from super-transition-array (STA) calculations are presented. The viability of the STA model, which is based on a statistical superconfigurations accounting approach for calculating the atomic and radiative properties, is examined by comparing and contrasting its results against the available experimental data and other theoretical calculations. First, we focus on the emission data. To model the data, the Eulerian radiation-hydrodynamics code FastRad3D is used in conjunction with STA to obtain the STA-required inputs, namely, the time-dependent temperature and density profiles of the Ge plasmas. Consequently, we find that STA results fit the experimental spectrum reasonably well, reproducing the main spectral features of 2p−3d,2s−3p, and 2p−4d transitions from the laser-heated germanium layer buried in plastic [High Energy Density Phys., 6 (2010) 105]. However, careful comparison between experimental and theoretical results in the photon-energy regions of ~ 1.7 keV shows some degrees of disparity between the two. This may be due to the non-LTE effects and the presence of spatial gradients in the sample. Limitations of STA to model the experimental spectrum precisely is expected and underscoring the difficulty of the present attempts as the model assumed local thermodynamics equilibrium population dynamics. Second, we examine the STA calculated multi-frequency opacities for a broad range of Ge plasma conditions covering the L- and M-shell spectral range. Comparing with a hybrid LTE opacity code which combines the statistical super-transition-array and fine-structure methods [High Energy Density Phys., 7 (2011) 234], impressively good agreement is found between the two calculations. In addition, the sensitivity of the opacity results in various plasma temperatures and mass densities is discussed. The ionized population fraction and average ionization of the Ge plasma are also described. Comparisons of STA results in the observed spectrum and opacity are considerably close while offering the advantage of computational speed and its capability of treating hot and dense high-Z plasmas.

Symmetric exclusion process under stochastic resetting.

We study the behavior of a symmetric exclusion process (SEP) in the presence of stochastic resetting where the configuration of the system is reset to a steplike profile with a fixed rate r. We show that the presence of resetting affects both the stationary and dynamical properties of SEPs strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a nontrivial inhomogeneous profile in contrast to the flat one for r=0. We also show that for r>0 the average diffusive current grows linearly with time t, in stark contrast to the sqrt[t] growth for r=0. In addition to the underlying diffusive current, we identify the resetting current in the system which emerges due to the sudden relocation of the particles to the steplike configuration and is strongly correlated to the diffusive current. We show that the average resetting current is negative, but its magnitude also grows linearly with time t. We also compute the probability distributions of the diffusive current, resetting current, and total current (sum of the diffusive and the resetting currents) using the renewal approach. We demonstrate that while the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behavior.

Experimental investigation of the compression and heating of an MHD-driven jet impacting a target cloud

Adiabatic compression has been investigated by having an MHD-driven plasma jet impact a gas target cloud. Compression and heating of the jet upon impact were observed and compared to theoretical predictions. Diagnostics for comprehensive measurements included a Thomson scattering system, a fast movie camera, a translatable fiber-coupled interferometer, a monochromator, a visible-light photodiode, and a magnetic probe array. Measurements using these diagnostics provided the time-dependent electron density, electron temperature, continuum emission, line emission, and magnetic field profile. Increases in density and magnetic field and a decrease in jet velocity were observed during the compression. The electron temperature had a complicated time dependence, increasing at first, but then rapidly declining in less than 1 μs which is less than the total compression time. Analysis indicates that this sudden temperature drop is a consequence of radiative loss from hydrogen atoms spontaneously generated via three-body recombination in the high-density compressed plasma. A criterion for how fast compression must be to outrun radiative loss is discussed not only for the Caltech experiment but also for fusion-grade regimes. In addition, the results are analyzed in the context of shocks the effects of which are compared to adiabatic compression.

Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench

We use a semiclassical approach to study out of equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low energy quasiparticles, the system is described in terms of a classical gas of colored hard-core particles. Starting from an inhomogeneous initial state, in this limit we give analytic expressions for the space and time dependent spin density and spin current profiles. Depending on the initial state, the spin transport is found to be ballistic or diffusive. In the ballistic case we identify a `second front' that moves more slowly than the maximal quasiparticle velocity. Our analytic results also capture the diffusive broadening of this ballistically propagating front. To go beyond the universal limit, we study the effect of non-trivial scattering processes in the $O(3)$ non-linear sigma model by performing Monte Carlo simulations, and observe local equilibration around the second front in terms of the densities of the particle species.

An overabundance of black hole X-ray binaries in the Galactic Centre from tidal captures

A large population of X-ray binaries (XRBs) was recently discovered within the central parsec of the Galaxy by Hailey et al. While the presence of compact objects on this scale due to radial mass segregation is, in itself, unsurprising, the fraction of binaries would naively be expected to be small because of how easily primordial binaries are dissociated in the dynamically hot environment of the nuclear star cluster (NSC). We propose that the formation of XRBs in the central parsec is dominated by the tidal capture of stars by black holes (BHs) and neutron stars (NSs). We model the time-dependent radial density profiles of stars and compact objects in the NSC with a Fokker-Planck approach, using the present-day stellar population and rate of in situ massive star (and thus compact object) formation as observational constraints. Of the ~10,000-40,000 BHs that accumulate in the central parsec over the age of the Galaxy, we predict that ~60 - 200 currently exist as BH-XRBs formed from tidal capture, consistent with the population seen by Hailey et al. A somewhat lower number of tidal capture NS-XRBs is also predicted. We also use our observationally calibrated models for the NSC to predict rates of other exotic dynamical processes, such as the tidal disruption of stars by the central supermassive black hole (~0.0001 per year at z=0).

Validation of TOKES vapor shield simulations against experiments in the 2MK-200 facility

Measurements of tungsten (W) plasma shield dynamics have been performed in the 2MK-200 facility under ITER relevant disruptive plasma heat flux densities of ∼100GW/m2. Plasma temperature profiles at two time instants and time dependent electron density profiles are available from these experiments. These data have been used to validate TOKES code simulations of the W plasma shield which is computed to form in front of the ITER W divertor targets during disruptions. The experimental and simulated temperature profiles are in a good agreement for the measurement points at distances of 1–5cm from the target. An important feature of the W plasma shield seen in the code simulations is the sharp electron temperature drop very close to the target. This region is not resolved in the 2MK-200 facility because of unacceptably low signal/noise ratio. Further experiments in a new, larger plasma gun are planned for experimental validation of this feature.

Separation of Time Scales in a Quantum Newton's Cradle.

We provide detailed modeling of the Bragg pulse used in quantum Newton's-cradle-like settings or in Bragg spectroscopy experiments for strongly repulsive bosons in one dimension. We reconstruct the postpulse time evolution and study the time-dependent local density profile and momentum distribution by a combination of exact techniques. We further provide a variety of results for finite interaction strengths using a time-dependent Hartree-Fock analysis and bosonization-refermionization techniques. Our results display a clear separation of time scales between rapid and trap-insensitive relaxation immediately after the pulse, followed by slow in-trap periodic behavior.