Longitudinal Pressures Research Articles

Holographic Gubser flow. A combined analytic and numerical study

Gubser flow is an evolution with cylindrical and boost symmetries, which can be best studied by mapping the future wedge of Minkowski space (R3,1) to dS3 × ℝ in a conformal relativistic theory. Here, we sharpen our previous analytic results and validate them via the first numerical exploration of the Gubser flow in a holographic conformal field theory.Remarkably, the leading generic behavior at large de Sitter time is free-streaming in transverse directions and the sub-leading behavior is that of a color glass condensate. We also show that Gubser flow can be smoothly glued to the vacuum outside the future Minkowski wedge generically given that the energy density vanishes faster than any power when extrapolated to early proper time or to large distances from the central axis. We find that at intermediate times the ratio of both the transverse and longitudinal pressures to the energy density converge approximately to a fixed point which is hydrodynamic only for large initial energy densities. We argue that our results suggest that the Gubser flow is better applied to collective behavior in jets rather than the full medium in the phenomenology of heavy ion collisions and can reveal new clues to the mechanism of confinement.

Rapid Pressure Hemostatic Drug Delivery and Microsystem Design Based on Battlefield Trauma

The battlefield rapid pressure hemostatic microsystem maximizes hemostasis efficiency. Battlefield wound has the characteristics of rapid blood loss and irregular surface, which needs to be treated in a very short time. The existing rapid hemostasis method has poor efficiency and no sterilization and disinfection effect. Therefore, we reported a wound pressure hemostatic microsystem based on gas generated by rapid chemical reaction. Before the device is used, the two chemicals in the device are isolated. During hemostasis, the flexible device is applied to the wound surface, and the two chemicals in the device are mixed and chemically reacted. And the large amount of gas generated by the reaction causes the balloon in the device to expand and exert lateral and longitudinal pressure on the surface of the wound, so that the wound quickly closed. At the same time, the drug storage unit in the device is under pressure to release the drug to the wound surface. In addition, the chemical reaction of the device has an endothermic effect, which can rapidly cool the wound surface. The lateral and longitudinal pressures of the flexible microsystem in the process of hemostasis were analyzed by numerical simulation. In the experiment, the maximum longitudinal pressure reached 270mmHg, meeting the requirements of surface wound hemostasis.

Applying a homogeneous pressure distribution to the upper vertebral endplate: Validation of a new loading system, pilot application to human vertebral bodies, and finite element predictions of DIC measured displacements and strains

Image-based personalized Finite Element Models (pFEM) could detect alterations in physiological deformation of human vertebral bodies, but their accuracy has been seldom reported. Meaningful validation experiments should allow vertebral endplate deformability and ensure well-controlled boundary conditions. This study aimed to (i) validate a new loading system to apply a homogeneous pressure on the vertebral endplate during vertebral body compression regardless of endplate deformation; (ii) perform a pilot study on human vertebral bodies measuring surface displacements and strains with Digital Image Correlation (DIC); (iii) determine the accuracy of pFEM of the vertebral bodies.Homogeneous pressure application was achieved by pressurizing a fluid silicone encased in a rubber silicone film acting on the cranial endplate. The loading system was validated by comparing DIC-measured longitudinal strains and lower-end contact pressures, measured on three homogeneous pseudovertebrae of constant transversal section at 2.0 kN, against theoretically calculated values. Longitudinal strains and contact pressures were rather homogeneous, and their mean values close to theoretical calculations (5% underestimation).DIC measurements of surface longitudinal and circumferential displacements and strains were obtained on three human vertebral bodies at 2.0 kN. Complete displacement and strain maps were achieved for anterolateral aspects with random errors ≤0.2 μm and ≤30 μstrain, respectively. Venous plexus and double curvatures limited the completeness and accuracy of DIC data in posterior aspects.pFEM of vertebral bodies, including cortical bone mapping, were built from computed tomography images. In anterolateral aspects, pFEM accuracy of the three vertebrae was: (i) comparable to literature in terms of longitudinal displacements (R2>0.8); (ii) extended to circumferential displacements (pooled data: R2>0.9) and longitudinal strains (zero median error, 95% error: <27%). Circumferential strains were overestimated (median error: 39%).The new methods presented may permit to study how physiological and pathologic conditions influence the ability of vertebral endplates/bodies to sustain loads.

Isotropization of a Rotating and Longitudinally Expanding ϕ4 Scalar System.

We study numerically the evolution of an expanding system of scalar fields. The initial configuration is non-isotropic and rotating. We calculate the energy-momentum tensor and angular momentum vector of the system. We compare the time scales associated with the isotropization of the transverse and longitudinal pressures, and the decay of the initial angular momentum. We show that even a fairly large initial angular momentum decays significantly faster than the pressure anisotropy.

Nonextensive hydrodynamics of boost-invariant plasmas

We use quasiparticle anisotropic hydrodynamics to study the non-conformal and non-extensive dynamics of a system undergoing boost-invariant Bjorken expansion. To introduce nonextensivity, we use an underlying Tsallis distribution with a time-dependent nonextensivity parameter q. By taking moments of the quasiparticle Boltzmann equation in the relaxation-time approximation, we obtain dynamical equations which allow us to determine the time evolution of all microscopic parameters including q. We compare numerical solutions for bulk observables obtained using the nonextensive evolution with results obtained using quasiparticle anisotropic hydrodynamics with a Boltzmann distribution function (q rightarrow 1). We show that the evolution of the temperature, pressure ratio, and scaled energy density, are quite insensitive to which distribution function is assumed. However, we find significant differences in the early-time evolution of the bulk pressure which are observed for even small deviations from the Boltzmann distribution function. Finally, we discuss the existence of non-conformal hydrodynamic attractors for the longitudinal and transverse pressures, the bulk and shear viscous corrections, and the nonextensivity parameter q.

Physical characteristics of glasma from the earliest stage of relativistic heavy ion collisions

We present analytic results that describe the gluon field, or glasma, at very early times after a collision of relativistic heavy ions at proper time $\tau=0$. We use a Colour Glass Condensate approach, and perform an expansion in $\tau$. The full details of our method are described in our previous paper [1]. In this paper we present an analysis of various physical quantities that can be obtained from the energy-momentum tensor. We show that the expansion to order $\tau^6$ can be trusted to about $\tau=0.05$ fm. For times small enough that the expansion converges, the transverse and longitudinal pressures move towards their equilibrium values of one third of the energy density. The Fourier coefficients of the azimuthal flow are larger than expected, which contradicts the usual assumption that anisotropy is mostly generated during the hydrodynamic evolution of the plasma. We find a significant correlation between the elliptic flow coefficient and the eccentricity, which indicates that the spatial asymmetry introduced by the initial geometry is effectively transmitted to the azimuthal distribution of the gluon momentum field, even at very early times. This result is interesting because correlations of this kind are characteristic of the onset of hydrodynamic behaviour. We show that the angular momentum of the glasma is orders of magnitude smaller than the angular momentum of the initial system of ions colliding with non-zero impact parameter. This indicates that most of the angular momentum carried by the valence quarks is not transmitted to the glasma, and contradicts the picture of a rapidly rotating initial glasma state that has been proposed by several authors, but agrees with the current lack of experimental evidence for a significant polarization effect of the hyperons and vector mesons produced in heavy ion collisions at the highest accessible energies.

The energy-momentum tensor at the earliest stage of relativistic heavy-ion collisions

Nuclear collisions at high energies produce a gluon field that can be described using the Colour Glass Condensate (CGC) effective theory at proper times \(\tau \lesssim 1\) fm. The theory can be used to calculate the gluon energy-momentum tensor, which provides information about the early time evolution of the chromo-electric and chromo-magnetic fields, energy density, longitudinal and transverse pressures, and other quantities. We obtain an analytic expression for the energy-momentum tensor using an expansion in the proper time, and working to sixth order. The calculation is technically difficult, in part because the number of terms involved grows rapidly with the order of the \(\tau \) expansion, but also because of several subtle issues related to the definition of event-averaged correlators, the method chosen to regulate these correlators, and the dependence of results on the parameters introduced by the regularization and nuclear density profile functions. All of these issues are crucially related to the important question of the extent to which we expect a CGC approach to be able to accurately describe the early stages of a heavy-ion collision. We present some results for the evolution of the energy density and the longitudinal and transverse pressures. We show that our calculation gives physically meaningful results up to values of the proper time which are close to the regime at which hydrodynamic simulations are initialized. In a companion paper [1] we give a detailed analysis of several other experimentally relevant quantities that can be calculated from the energy-momentum tensor.

Bjorken flow attractors with transverse dynamics

In the context of the longitudinally boost-invariant Bjorken flow with transverse expansion, we use three different numerical methods to analyze the emergence of attractor solutions in an ideal gas of massless particles exhibiting constant shear viscosity to entropy density ratio $\eta / s$. The fluid energy density is initialized using a Gaussian profile in the transverse plane, while the ratio $\chi = \mathcal{P}_L / \mathcal{P}_T$ between the longitudinal and transverse pressures is set at initial time $\tau_0$ to a constant value $\chi_0$ throughout the system employing the Romatschke-Strickland distribution. We introduce the hydrodynamization time $\delta \tau_H = (\tau_H - \tau_0)/ \tau_0$ based on the time $\tau_H$ when the standard deviation $\sigma(\chi)$ of a family of solutions with different $\chi_0$ reaches a minimum value at the point of maximum convergence of the solutions. In the $0+1{\rm D}$ setup, $\delta \tau_H$ exhibits scale invariance, being a function only of $(\eta / s) / (\tau_0 T_0)$. With transverse expansion, we find a similar $\delta \tau_H$ computed with respect to the local initial temperature, $T_0(r)$. We highlight the transition between the regimes where the longitudinal and transverse expansions dominate. We find that the hydrodynamization time required for the attractor solution to be reached increases with the distance from the origin, as expected based on the properties of the $0+1{\rm D}$ system defined by the local initial conditions. We argue that hydrodynamization is predominantly the effect of the longitudinal expansion, being significantly influenced by the transverse dynamics only for small systems or for large values of $\eta / s$.

Analytical canonical partition function of a quasi-one-dimensional system of hard disks.

The exact canonical partition function of a hard disk system in a narrow quasi-one-dimensional pore of given length and width is derived analytically in the thermodynamic limit. As a result, the many body problem is reduced to solving the single transcendental equation. The pressures along and across the pore, distributions of contact distances along the pore, and disks' transverse coordinates are found analytically and presented in the whole density range for three different pore widths. The transition from the solidlike zigzag to the liquidlike state is found to be quite sharp in the density scale but shows no genuine singularity. This transition is quantitatively described by the distribution of zigzag's windows through which disks exchange their positions across the pore. The windowlike defects vanish only in the densely packed zigzag, which is in line with a continuous Kosterlitz-Thouless transition.

Measurement of admittance and acoustic augmentation of burning rate of composite solid propellants using Laser Doppler Velocimetry

The present work involves the use of Laser Doppler Velocimetry (LDV) technique to measure the acoustic admittance of aluminized composite solid propellant (AP/HTPB/Al) by experimentally measuring the instantaneous velocities of the particles of solid propellant during burning while the acoustic pressure oscillations are being imposed. Both velocity fluctuations and pressure fluctuations are measured synchronously. The probe volume of the laser is maintained at a constant distance from the burning surface by using a linear actuator. Tests were conducted for two aluminized composite solid propellants at low frequency ranges (130-312 Hz) of the longitudinal acoustic modes and mean chamber pressures ranging from 1 to 4 MPa. A rotary valve is designed to acoustically excite the chamber to the required resonant frequency. It was found that admittance rises with frequency and peaks around 260 Hz and then falls. The use of linear actuator mechanism significantly improves the velocity data rate (number of data points). Maintaining the probe volume at 800 to 900 µm above the propellant surface is very crucial to determine the admittance accurately. Test results revealed that a good agreement between the steady state mean burning rates with the window bomb experiments is achieved. The measured mean burn rates under imposed acoustic pressure oscillations shows the augmentation up to 55%. The admittance measured for the metallized composite propellant using this technique and the comparison with T-burner shows good agreement. The comparison of responses with LDV and T-burner and the augmentation factor due to acoustic oscillations using LDV are reported for the first time.

Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism

We investigate the implications of the general frame approach for conformal Bjorken flow beyond the earlier studies. We show that the power series solution at late times is not unique and is accompanied by an exact solution of the form $1/\tau$, which becomes unphysical if taken on shell. In contrast to the M\"uller-Israel-Stewart formalism, a matching between $\NFSYM$ results and the hydro expansion is only possible up to the first order, which gives rise to $\eta/s=1/4\pi$. Matching the results to the next order gives rise to causality/stability-violating values. Furthermore, we show that the pressure anisotropy in the general frame cannot capture the hydrodynamization, and we introduce an alternative measure to find the attractor. Using slow-roll expansion, we find an analytical approximation form for the attractor. We also show that the early-time behavior of attractors is related to stability and causality conditions. The attractor solutions outside the stable and causal regime give rise to reheating and negative longitudinal pressures in early times, in contrast to the stable and causal ones. We also comment on the violation of the second law of thermodynamics by the off-shell parameters. We show that for the stable and causal choice of parameters, the off-shell canonical entropy of the attractors, which is not a physical quantity, has a negative divergence in early times before tending to its on-shell limit. On the other hand, the unstable and acausal attractors have non-negative entropy divergence. We speculate that the violation of the second law by stable and causal off-shell parameters is required for stability of the first-order hydrodynamics. We investigate the analytical structure of the Borel-transformed series and find the proper relation between the poles and nonhydro modes.

Description of Large-Scale Processes in the Near-Earth Space Plasma

We suggest a solution of the problem of the description of magnetic and electric fields occurring during large-scale nonradiative processes in the collisionless space plasma. The key idea is that the quasi-neutrality condition and the field-aligned force equilibrium of electrons should be taken into account. Equations describing the plasma are divided into two parts, namely, a system of transport equations which describes the plasma motion, and a system of equations for fields. The fields are defined in the instantaneous action approximation via the current spatial distributions of hydrodynamic plasma parameters and boundary conditions obtained from the system of elliptic equations containing no partial time derivatives. Three forms of the generalized Ohm’s law corresponding to different levels of plasma magnetization are considered. It is shown that, depending on the form of a system of transport equations derived for each plasma component, five key variants of the equation system describing the plasma can be obtained from the three forms of the Ohm’s law. The first form of the generalized Ohm’s law refers to the general case in which all plasma components unmagnetized and the system of transport equations represents the Vlasov equations for each plasma component. The second form of the Ohm’s law corresponds to the case of unmagnetized ionic plasma components, while electrons are magnetized and their pressure tensor is expressed through their longitudinal and transverse pressures as well as through the magnetic field. In the latter case two variants of the system of transport equations are possible, and the ions are described by Vlasov equations in both of them. In the first variant, the electrons are described by the Vlasov equation in the drift approximation. In the second variant, the electrons are described by the system of Chew–Goldberger–Low equations of magnetogasdynamics. The third variant of Ohm’s law corresponds to the case in which all plasma components are magnetized, and the pressure tensor of each component is replaced by its expression through the longitudinal and transverse pressure, as well as through the magnetic field. In this case, two variants of the transport equation system are also possible. In the first variant, each component is described by the Vlasov equation in the drift approximation. In the second variant, each component is described by the system of the Chew–Goldberger–Low equations of magnetogasdynamics.

Angular mode expansion of the Boltzmann equation in the small-angle approximation

We use an expansion in angular mode functions in order to solve the Boltzmann equation for a gluon plasma undergoing longitudinal expansion. By comparing with the exact solution obtained numerically by other means we show that the expansion in mode functions converges rapidly for all cases of practical interest, and represents a substantial gain in numerical effort as compared to more standard methods. We contrast the cases of a non expanding plasma and of longitudinally expanding plasmas, and follow in both cases the evolutions towards thermalization. In the latter case, we observe that, although the spherical mode function appears to be well reproduced after some time by a local equilibrium distribution function depending on slowly varying temperature and chemical potential, thereby suggesting thermalization of the system, the longitudinal and transverse pressures take more time to equilibrate. This is because the expansion hinders the relaxation of the first angular mode function. This feature was also observed in a simpler context where the Boltzmann equation is solved in terms of special moments within the relaxation time approximation, and attributed there to the particular coupling between the first two moments of the distribution function. The present analysis confirms this observation in a more realistic setting.

Magnetized neutron matter and deformed neutron stars

In this work, we study the influences of density-dependent magnetic field on the equation of state (EoS) of neutron matter using the lowest order constraint variational method. We consider the effects of neutron mass reduction due to the strong magnetic field on the EoS and perform our calculations applying magnetic field-dependent neutron mass (MFD model) and magnetic field-independent neutron mass (MFI model). In this paper, the longitudinal and transverse pressures with respect to the direction of magnetic field are calculated. According to our results for longitudinal pressure of magnetized neutron matter, the upper limit of the magnetic field strength in the neutron star is about G. Furthermore, we investigate the structure of deformed neutron stars by solving Einstein equations and expanding the metric up to the quadrupole term in spherical harmonics. The maximum gravitational mass obtained is about 1.79 M⊙ for the MFI model and 1.93 M⊙ for the MFD model. We find that the oblateness of the neutron star increases by enhancing field strength.

IP-Glasma Phenomenology Beyond 2D

We present a novel formulation of the IP-Glasma initial state model in 3+1D in which the 2+1D boost invariant IP-Glasma is generalized through JIMWLK rapidity evolution of the pre-collision Wilson lines [B. Schenke and S. Schlichting, Phys. Rev. C 94, no. 4, 044907 (2016) doi:10.1103/PhysRevC.94.044907]. In order to consistently accommodate a non-boost-invariant system, the initial conditions are generalized to 3+1D. By breaking boost invariance, the 3+1D model no longer trivially satisfies Gauss' law at the initial time, and we now enforce it locally. We compare the time evolution of the chromo-electric and chromo-magnetic fields as well as the transverse and longitudinal pressures in the 3+1D case with the boost invariant result.

Investigation of the regularities of vortical flows in a cyclone-bed chamber

Experimental investigation of the radial distributions of tangential and longitudinal velocities, total and static pressures in the vortex zone of a cyclone-bed chamber of diameter 0.21 m has been carried out. The experiments were carried out at various regime parameters (fraction of bottom blast, total air volume flow) and geometric parameters (diameter and shape of the outlet) of the chamber, and also in the presence of a fixed or fluidized bed of granular material. The influence of nonisotherm of bottom and tangential blast on the distribution pattern of velocity and pressure in the vortex zone of the cyclone-bed chamber is investigated. There was determined the influence of bottom blast temperature on the longitudinal velocity of air in the central part of the vortex zone chamber. It is shown that the diameter of the outlet has a significant effect on the pressure in the chamber. The longitudinal velocity in the central part of the chamber is practically independent of the shape of the outlet. The presence of the fluidized bed has an effect on the hydrodynamics of the cyclone-bed chamber vortex zone. In the presence of the fluidized bed there has been a violation of the self-similarity of hydrodynamic dimensionless parameters distribution in the vortex zone. The obtained experimental data were summarized within the framework of the similarity theory with the use of a dimensionless quantity characterizing the hydrodynamics of an inhomogeneous fluidized bed – the Froude number (Fr). The use of the Froude number makes it possible to take into account the effect of the fluidized bed hydrodynamics on the features of air velocity and pressure distributions in the vortex zone, and also takes into account the influence of such an important factor as the fraction of bottom blast.

Anisotropic pressure in strange quark matter in the presence of a strong nonuniform magnetic field

Thermodynamic properties of strange quark matter (SQM) in a nonuniform magnetic field are studied within the phenomenological MIT bag model under the charge neutrality and beta equilibrium conditions, relevant to the interior of strange quark stars. The spatial dependence of the magnetic field strength is modeled by the dependence on the baryon chemical potential in the exponential and power forms. The total energy density, longitudinal and transverse pressures in magnetized SQM are found as functions of the baryon chemical potential. It is clarified that the central magnetic field strength in a strange quark star is bound from above by the critical value at which the derivative of the longitudinal pressure with respect to the baryon chemical potential vanishes first somewhere in the interior of a star under varying the central field. Above this upper bound, the instability along the magnetic field is developed in magnetized SQM. The change in the form of the dependence of the magnetic field strength on the baryon chemical potential between the exponential and power ones has a nonnegligible effect on the critical magnetic field strength while the variation of the bag pressure within the absolute stability window for magnetized SQM has a little effect on the critical field.

( 3+1 )-dimensional anisotropic fluid dynamics with a lattice QCD equation of state

Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections nonperturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade description of the final collision stage. We present a new dissipative hydrodynamic formulation for nonconformal fluids where both of these effects are treated nonperturbatively. The evolution equations are derived from the Boltzmann equation in the 14-moment approximation, using an expansion around an anisotropic leading-order distribution function with two momentum-space deformation parameters, accounting for the longitudinal and transverse pressures. To obtain their evolution we impose generalized Landau matching conditions for the longitudinal and transverse pressures. We describe an approximate anisotropic equation of state that relates the anisotropy parameters with the macroscopic pressures. Residual shear stresses are smaller and are treated perturbatively, as in standard second-order dissipative fluid dynamics. The resulting optimized viscous anisotropic hydrodynamic evolution equations are derived in $3+1$ dimensions and tested in a ($0+1$)-dimensional Bjorken expansion, using a state-of-the-art lattice equation of state. Comparisons with other viscous hydrodynamical frameworks are presented.

Coupled kinetic equations for fermions and bosons in the relaxation-time approximation

Kinetic equations for quarks and gluons are solved numerically in the relaxation time approximation for the case of one-dimensional boost-invariant geometry. Quarks are massive and described by the Fermi-Dirac statistics, while gluons are massless and obey Bose-Einstein statistics. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions which specify the coupling between the quark and gluon sectors and determine the proper-time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a non-equlibrium mixture of quarks and gluons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients. The shear viscosity of a mixture is the sum of the shear viscosities of quark and gluon components, while the bulk viscosity is given by the formula known for a gas of quarks, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless gluons contribute in a non-trivial way to the bulk viscosity of a mixture, provided quarks are massive. We further observe the hydrodynamization effect which takes place earlier in the shear sector than in the bulk one. The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behaviour is connected with the existence of an attractor solution for conformal systems.

Paths to equilibrium in non-conformal collisions

We extend our previous analysis of holographic heavy ion collisions in non-conformal theories. We provide a detailed description of our numerical code. We study collisions at different energies in gauge theories with different degrees of non-conformality. We compare four relaxation times: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value), the isotropization time (when the longitudinal and transverse pressures approach each other) and the condensate relaxation time (when the expectation value of a scalar operator approaches its equilibrium value). We find that these processes can occur in several different orderings. In particular, the condensate can remain far from equilibrium even long after the plasma has hydrodynamized and EoSized. We also explore the rapidity distribution of the energy density at hydrodynamization. This is far from boost-invariant and its width decreases as the non-conformality increases. Nevertheless, the velocity field at hydrodynamization is almost exactly boost-invariant regardless of the non-conformality. This result may be used to constrain the initialization of hydrodynamic fields in heavy ion collisions.