Evolution Of Energy Density Research Articles

Energy evolution properties and strength failure criterion of coal-fired slag concrete based on energy dissipation

Coal-fired slag concrete is gradually used in underground projects such as coal mines. Due to the differences between concrete composites and rocks, the failure of coal-fired slag concrete cannot be predicted from the essence through the stress–strain curve. However, studying the deformation and failure law of concrete from the perspective of energy can be closer to the essence of concrete deformation and failure. Therefore, in this paper, with the help of RLJW-2000 testing machine, the uniaxial compression test of C15 strength grade coal-fired slag concrete is carried out, the energy evolution law in the process of deformation and failure of coal-fired slag concrete is analyzed, and the failure criterion based on energy consumption ratio is established. The results show that with the increase of slag-cement ratio, the total energy and elastic strain energy at the peak point gradually decrease. The evolution of peak energy density satisfies the exponential function relation with e as the base. The process that the elastic energy consumption ratio changes from the stable state tending to 0 to the beginning of growth, or the process that the elastic energy consumption ratio changes from negative value to 0, and then gradually increases to positive value can be used as the energy criterion for the strength failure of coal-fired slag concrete. The research results can essentially analyze the instability and failure of coal-fired slag concrete, which is of great significance to ensure the safety of coal-fired slag concrete in engineering application.

Understanding of the fatigue crack nucleation in metallic sealing rings by explicitly incorporating the deformation history from manufacturing to service

Fatigue cracking in metallic sealing rings has been a concern for the aerospace industry because the formation of even a micro-crack may cause an aviation accident. In this study, an integrated three-point bending fatigue experiment and dislocation-based crystal plasticity finite element modeling was used to determine the threshold for fatigue crack nucleation. Subsequently, the fatigue lives of the rings under different service conditions were evaluated based on the local stored energy density evolution. The conclusions of this work can provide theoretical guidance for the manufacturing of high-performance metallic sealing rings.

Entropy-conserving Scheme for Modeling Nonthermal Energies in Fluid Dynamics Simulations

We compare the performance of energy-based and entropy-conserving schemes for modeling nonthermal energy components, such as unresolved turbulence and cosmic rays, using idealized fluid dynamics tests and isolated galaxy simulations. While both methods are aimed to model advection and adiabatic compression or expansion of different energy components, the energy-based scheme numerically solves the nonconservative equation for the energy density evolution, while the entropy-conserving scheme uses a conservative equation for modified entropy. Using the standard shock tube and Zel’dovich pancake tests, we show that the energy-based scheme results in a spurious generation of nonthermal energy on shocks, while the entropy-conserving method evolves the energy adiabatically to machine precision. We also show that, in simulations of an isolated L ⋆ galaxy, switching between the schemes results in ≈20%–30% changes of the total star formation rate and a significant difference in morphology, particularly near the galaxy center. We also outline and test a simple method that can be used in conjunction with the entropy-conserving scheme to model the injection of nonthermal energies on shocks. Finally, we discuss how the entropy-conserving scheme can be used to capture the kinetic energy dissipated by numerical viscosity into the subgrid turbulent energy implicitly, without explicit source terms that require calibration and can be rather uncertain. Our results indicate that the entropy-conserving scheme is the preferred choice for modeling nonthermal energy components, a conclusion that is equally relevant for Eulerian and moving-mesh fluid dynamics codes.

Acoustic emission characteristics and energy mechanism of CFRP-jacketed coal specimens under uniaxial compression

Fiber-reinforced polymer (FRP) wrapping is a potentially attractive coal-pillar reinforcement technique. To study the effect of carbon fiber-reinforced polymer (CFRP) jacketing on mechanical properties, crack evolution, and energy dissipation mechanism of coal specimens, a series of uniaxial compression tests with acoustic emission (AE) monitoring were conducted on coal specimens with 0–2 CFRP-jacket layers. The results showed that the CFRP jacket had visible effects on the core failure process of coal specimens. (1) With an increase in the number of CFRP-jacketed layers, the specimens showed stronger strain-softening characteristics in the unstable crack growth stage, and the damage stress threshold increased significantly. (2) The correlation analysis between average frequency (AF) and rise angle (RA) demonstrated that with an increase in the number of CFRP-jacketed layers, the tendency of crack classification to change from tensile mode to shear mode increased. (3) The spatiotemporal evolution of AE event locations showed that CFRP jackets changed the AE event location concentration mode from a longitudinal distribution along the coal specimen to a distribution near the fracture. Moreover, the strain energy density evolution of coal specimens with 0–2 layers of CFRP jacketing was analyzed based on the mechanical equilibrium and energy conservation of CFRP-jacketed coal specimens. The dissipation strain energy ratio was introduced to define the damage variable, and the damage constitutive model with regards to CFRP jackets was constructed; the model describes the CFRP-jacketed coal specimen stress–strain relationship for strain-hardening, strain-softening, and sudden failure.

Energy characteristics of sandstones with different crack angles under true triaxial cyclic loading and unloading

AbstractThe effect of crack angle on energy evolution during sandstone failure subjected to true triaxial cyclic loading and unloading is of great concern. However, the energy consumed in the crack initiation and compaction process is generally referred to the dissipated energy, which is inaccurate. To reveal the energy law in the breaking process of sandstone, a complex cyclic loading and unloading test is carried out on precast angled sandstone samples by employing the triaxial test system. The area integral methodology is exploited to evaluate the evolution of total energy density, elastic energy density, dissipated energy density, and plastic energy density of the rock samples of different crack angles. The variations of these four energy density levels in terms of the number of loading and unloading cycles and the upper limit of stress are explained and discussed. The obtained results reveal that during the entire cycle of loading and unloading, the variations of the above‐mentioned factors of the rock sample fairly do not rely on the crack angle. The energy density increases with the number of cycles, and the total energy density and elastic energy density significantly increase faster than the consumption mode. The growth rate of the dissipative energy density is greater than that of the plastic energy density. Additionally, the aforementioned four energy quantities grow in a quadratic manner as a function of the upper limit of the loading stress. The releasable elastic energy gradually magnifies by increasing the upper limit of the loading stress. The plasticity density first decreases and then increases, reflecting the change law of the irreversible plastic deformation caused by newly developed cracks in the rock sample. The elastic energy density, the fitting coefficient of the dissipated energy density, and the total energy density are employed to define the characteristic coefficients of the rock energy storage and energy dissipation. The results indicate that the larger the rock crack angle, the stronger the energy storage energy and the weaker the energy dissipation capacity. It also explains that how the strength of the rock sample becomes higher as the crack angle increases.

Effects of Smooth Divergence-Free Flows on Tracer Gradients and Spectra: Eulerian Prognosis Description

AbstractOcean eddies play an important role in the transport of heat, salt, nutrients, or pollutants. During a finite-time advection, the gradients of these tracers can increase or decrease, depending on a growth rate and the angle between flow gradients and initial tracer gradients. The growth rate is directly related to finite-time Lyapunov exponents. Numerous studies on mixing and/or tracer downscaling methods rely on satellite altimeter-derived ocean velocities. Filtering most oceanic small-scale eddies, the resulting smooth Eulerian velocities are often stationary during the characteristic time of tracer gradient growth. While smooth, these velocity fields are still locally misaligned, and thus uncorrelated, to many coarse-scale tracer observations amendable to downscaling [e.g., sea surface temperature (SST), sea surface salinity (SSS)]. Using finite-time advections, the averaged squared norm of tracer gradients can then only increase, with local growth rate independent of the initial coarse-scale tracer distribution. The key mixing processes are then only governed by locally uniform shears and foldings around stationary convective cells. To predict the tracer deformations and the evolution of their second-order statistics, an efficient proxy is proposed. Applied to a single velocity snapshot, this proxy extends the Okubo–Weiss criterion. For the Lagrangian-advection-based downscaling methods, it further successfully predicts the evolution of tracer spectral energy density after a finite time, and the optimal time to stop the downscaling operation. A practical estimation can then be proposed to define an effective parameterization of the horizontal eddy diffusivity.Significance StatementAn analytical formalism is adopted to derive new exact and approximate relations that express the clustering of tracers transported by upper-ocean flows. This formalism bridges previous Eulerian and Lagrangian approaches. Accordingly, for slow and smooth upper-ocean flows, a rapid prognosis estimate can solely be performed using single-time velocity field observations. Well suited to satellite-altimeter measurements, it will help rapidly identify and monitor mixing regions occurring in the vicinity of ocean eddy boundaries.

Investigation of the Energy Evolution of Tectonic Coal under Triaxial Cyclic Loading with Different Loading Rates and the Underlying Mechanism

It is of great significance to ascertain the mechanical characteristics and deformation laws of tectonic coal that is under complex stress conditions for safe production, but the targeted research in this area is still insufficient at present. This paper performed triaxial tests under cyclic multi-level loading at different rates by using an MTS-815 Rock Mechanics Testing System. The strain characteristics, elastic modulus and energy evolution were obtained in order to explore the effects of the mechanism of loading rate on the evolution of deformation and energy parameters of tectonic coal. The results showed that the irreversible strain and plastic energy increased exponentially with the increase in the deviatoric stress, but the growth rate decreased with the increase in loading rate. Furthermore, the elastic strain increased linearly and the growth rate was essentially unaffected by the loading rate. During the compaction stage, the variation of each parameter was not sensitive to the loading rate; during the elastic and damage stage, the rate increase inhibited secondary defect propagation and improved rock strength. In addition, the stepwise and cumulative energy ratio was defined in order to describe the energy distribution during cyclic loading and unloading. It was found that the decrease in the loading rate was beneficial to the transformation of the total energy into plastic energy. The elastic modulus was the most sensitive to sample damage, but the energy density evolution was able to be used to describe the deformation damage process of tectonic coal in more detail. These findings provide important theoretical support for the tectonic coal deformation law and action mechanism in the damage process that occurs under complex stress conditions.

Kinetic energy cascade in stably stratified open-channel flows

In this paper, the kinetic energy cascade in stably stratified open-channel flows is investigated. A mathematical framework to incorporate vertical scales into the conventional kinetic energy spectrum and its budget is introduced. This framework defines kinetic energy density in horizontal spectral and vertical scale space. The energy cascade is studied by analysing the evolution of kinetic energy density. It is shown that energetic streamwise scales ($\lambda _x$) become larger with increasing vertical scale. For the strongest stratification, for which the turbulence becomes intermittent, the energetic streamwise scales are suppressed, and energy density resides in $\lambda _x$ of the size of the domain. It is shown that, in an unstratified case, vertical scales of the size comparable to the height of the logarithmic layer connect viscous regions to the outer layer. By contrast, in stratified cases, such a connection is not observed. Moreover, it is shown that nonlinear transfer for streamwise scales is dominated by in-plane triad interactions and inter-plane transfer is more active in transferring energy density among small vertical scales of the size comparable to the height of viscous sublayer. The vertical scales of size comparable to the height of the viscous sublayer and buffer layer are the most active scales in the viscous term and the production term in the energy density budget, respectively.

Energy conditions for inhomogeneous EOS and its thermodynamics analysis with the resolution on finite time future singularity problems

In this paper, we study two different cases of inhomogeneous EOS of the form [Formula: see text]. We derive the energy density of dark fluid and dark matter component for both the cases. Further, we calculate the evolution of energy density, gravitational constant and cosmological constant. We also explore the finite time singularity and thermodynamic stability conditions for the two cases of EOS. Finally, we discuss the thermodynamics of inhomogeneous EOS with the derivation of internal energy, Temperature and entropy and also show that all the stability conditions are satisfied for the two cases of EOS.

Inertia-gravity-wave scattering by three-dimensional geostrophic turbulence

In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with geostrophically balanced turbulent flows. Advection and refraction by such flows lead to wave scattering, redistributing IGW energy in the position–wavenumber phase space. We give a detailed description of this process by deriving a kinetic equation governing the evolution of the IGW phase-space energy density. The derivation relies on the smallness of the Rossby number characterising the geostrophic flow, which is treated as a random field with known statistics, makes no assumption of spatial scale separation, and neglects wave–wave interactions. It extends previous work restricted to near-inertial waves, barotropic flows or waves much shorter than the flow scales. The kinetic equation describes energy transfers that are restricted to IGWs with the same frequency, as a result of the time scale separation between waves and flow. We formulate the kinetic equation on the constant-frequency surface – a double cone in wavenumber space – using polar spherical coordinates, and we examine the form of the two scattering cross-sections involved, which quantify energy transfers between IGWs with, respectively, the same and opposite directions of vertical propagation. The kinetic equation captures both the horizontal isotropisation and the cascade of energy across scales that result from scattering. We focus our attention on the latter to assess the predictions of the kinetic equation against direct simulations of the three-dimensional Boussinesq equations, finding good agreement.

The Cosmic Thermal History Probed by Sunyaev–Zeldovich Effect Tomography

Abstract The cosmic thermal history, quantified by the evolution of the mean thermal energy density in the universe, is driven by the growth of structures as baryons get shock heated in collapsing dark matter halos. This process can be probed by redshift-dependent amplitudes of the thermal Sunyaev–Zeldovich (SZ) effect background. To do so, we cross-correlate eight sky intensity maps in the Planck and Infrared Astronomical Satellite missions with two million spectroscopic redshift references in the Sloan Digital Sky Surveys. This delivers snapshot spectra for the far-infrared to microwave background light as a function of redshift up to z ∼ 3. We decompose them into the SZ and thermal dust components. Our SZ measurements directly constrain 〈 bP e 〉 , the halo bias-weighted mean electron pressure, up to z ∼ 1. This is the highest redshift achieved to date, with uncorrelated redshift bins thanks to the spectroscopic references. We detect a threefold increase in the density-weighted mean electron temperature T ¯ e from 7 × 105 K at z = 1 to 2 × 106 K today. Over z = 1–0, we witness the build-up of nearly 70% of the present-day mean thermal energy density ρ th, with the corresponding density parameter Ωth reaching 1.5 × 10−8. We find the mass bias parameter of Planck's universal pressure profile of B = 1.27 (or 1 − b = 1/B = 0.79), consistent with the magnitude of nonthermal pressure in gas motion and turbulence from mass assembly. We estimate the redshift-integrated mean Compton parameter y ∼ 1.2 × 10−6, which will be tested by future spectral distortion experiments. More than half originates from the large-scale structure at z < 1, which we detect directly.

Scalar characterisations of three-dimensional shock-flame interactions: similarity and inhomogeneity

ABSTRACTThree-dimensional shock-flame interactions are simulated by the ninth-order WENO scheme to study the characterisations of scalar under Richtmyer-Meshkov instability (RMI) with reaction. Initially, a planar incident shock with Ma = 1.7 accelerates the single-mode diffusive flame interface with initial wavelength 4 mm and amplitude 0.4 mm from the reactant C2H4+3O2+4N2 medium with temperature 293 K and pressure 13.3 kPa; then the transmitting shock branch during incident shock-flame interaction is reflected at the end boundary to form a reflected shock which disturbs the flame interface again. The reflected shock-flame interaction will form transmitting and reflecting shock branches where the reflecting branch reflects at the end boundary and accelerates the flame interface again. During successive interactions between flame interface and shocks, a large range of flow is generated. Physical processes in the flame interface are examined related to the evolution of reactant density and internal energy density, including convection, molecule diffusion, reaction, pressure-dilatation, and heat conduction. Similarity in scalars and velocity is examined in both spatial and spectral spaces and inhomogeneity related to similarity is provided.

Sulphur doped iron cobalt oxide nanocaterpillars: An electrode for supercapattery with ultrahigh energy density and oxygen evolution reaction

Inclusion of sulphur in metal oxide nanostructure can alter the electrochemical performance by minimizing its resistance for charge transfer. Herein, We report the synthesis of sulphur doped iron cobalt oxide nanocaterpillars (FCS) and their utilization in supercapatteries and for oxygen evolution reaction (OER). These nanocaterpillars (FCS) demonstrate a high specific capacitance of 1809 F g−1 at 2 A g−1 along with an exceptional stability of 138% after 15,000 cycles in alkaline media. Considering them in the fabrication of a supercapattery (with iron cobalt oxide (FCO) as a negative electrode), we achieve an ultrahigh energy density of 140 Wh kg−1 at 1434 W kg−1 with an excellent cycling stability (95% till 5000 cycles). To our surprise, it even outshines as an electrocatalyst (OER) attaining a current density of 10 mA cm−2 at a low overpotential of 300 mV. As a consequence of the extremely high roughness factor (Rf = 1135) these nanocaterpillars deliver a best Tafel slope of 56 mV/dec. Henceforth, these sulphur doped iron cobalt oxide nanocaterpillars (FCS) display enormous potential in storing and converting energy.

FRW viscous modified cosmic Chaplygin gas cosmology in the presence of cosmological constant

In this paper, we study viscous Modified Cosmic Chaplygin Gas (MCCG) in the presence of cosmological constant in flat FRW universe. We assume that bulk viscosity [Formula: see text] and cosmological constant [Formula: see text] are the linear combinations of two terms, one is constant and other is a function of dark energy density [Formula: see text]. In this framework, we solve the non-linear differential equation analytically and numerically and obtain time dependent dark energy density. We also consider two separate cases of early and late universe and discussed the evolution of dark energy density. We investigate the effect of viscosity and cosmological constant to the evolution of universe and discuss the stability of the model by square of speed of sound. Finally, we compare our model with Cardassian universe.

Effect of Nonparallel End Face on Energy Dissipation Analyses of Rocklike Materials Based on SHPB Tests

To evaluate the effect of nonparallel end face of rocklike specimens in SHPB tests, the characteristics of energy dissipation are analyzed based on numerical simulations for end‐face nonparallelism from 0% to 0.40% and Young’s modulus from 14 GPa to 42 GPa. With the increment of end‐face nonparallelism, both energy consumption density and dissipated energy density show a slight increase trend, while releasable elastic strain energy density presents a slight decrease trend. Existence of elastic unloading in the damaged rocklike specimen leads to a reduction of energy consumption density and a constant dissipated energy density during total strain shrinkage. At peak dynamic stress, dissipated energy density presents a linear upward trend with the increment of end‐face nonparallelism and Young’s modulus, while releasable elastic strain energy density shows an inverse trend. A binary linear regression equation is deduced to estimate the energy dissipation ratio. Mechanical damage evolution of the rocklike specimen is divided into two regions in line with the two regions in dynamic stress‐strain curves, and the transition between the slow‐growth region and rapid‐growth region is shifted to the right with the increment of end‐face nonparallelism. Due to the presence of nonparallel end face, fluctuation presents in energy density evolution and mechanical damage evolution. The fluctuation is enhanced with the increment of end‐face nonparallelism and weakened with the increase of Young’s modulus. Based on energy density evolution and mechanical damage evolution analyses, the maximum end‐face nonparallelism should be controlled within 0.20%, twice the value in ISRM suggested methods, which reduces the cost and time for processing rocklike specimens.

Effective quintessence from string landscape

Recently, Vafa et al. proposed two string swampland criteria, and studying the constraints imposed by the two string swampland criteria on cosmology, they found that the inflationary models are generally difficult to be compatible with these two criteria. Applying these two criteria to the accelerated expansion of the universe during the current period, it was found that the specific quintessence model can satisfy these constraints while satisfying the constraints imposed by the current observations. Applying the gravitational theory of large scale Lorentz violation to cosmology, the vacuum energy density is not the only cause of the accelerated expansion of the universe. The large scale Lorentz violation combined with the cosmological constant term results in the observed accelerated expansion of the late universe. The vacuum energy density is a bit like a naked cosmological constant. The equivalent energy density considering the large scale Lorentz violation effect is the effective cosmological constant that determines the evolution of the universe. In this way, we find that the negative cosmological constant in the string landscape can also accelerate the expansion of the universe, and compared with the <inline-formula><tex-math id="M2">\begin{document}$ {\varLambda _{{\rm{CDM}}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20190282_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20190282_M2.png"/></alternatives></inline-formula> model, it leads to a cosmological constant as an effective vacuum energy density. Effective vacuum energy density behaves as a monotonically decreasing quintessence potential energy for the string landscape, for most of the naked positive vacuum energy densities in the swampland, the evolution of effective cosmological constant with time will show a local minimum. Comparing the calculated results of the distance modulus withthe astronomical observations, we can obtain that a negative cosmological constant also accelerates the expansion of the universe. Thus, the vacuum energy density derived from the string landscape will give quintessence potential that satisfies the swampland criterion, while the evolution of vacuum energy density given by the swampland model of the metastable dS vacuum is not quintessence potential, so it cannot satisfy the second de Sitter criterion. Therefore, the effective potential leading to the accelerated expansion of the late universe can only come from the string landscape, which is naturally UV completion. Therefore, it gives that the accelerated expansion of the late universe is the feature of early quantum gravity. It is not necessary to use the metastable de Sitter vacuum to explain the accelerated expansion of the late universe. The difficulty of incompatibility between the swampland model and the accelerated expansion of the late universe caused by the swampland conjecture will be eliminated.

Non-linear coupling in the dark sector as a running vacuum model

In this work we study a phenomenological non-gravitational interaction between dark matter and dark energy. The scenario studied in this work extends the usual interaction model proportional to the derivative of the dark component density adding to the coupling a non-linear term of the form $Q = \rho'/3(\alpha + \beta \rho)$. This dark sector interaction model could be interpreted as a particular case of a running vacuum model of the type $\Lambda(H) = n_0 + n_1 H^2 + n_2 H^4$ in which the vacuum decays into dark matter. For a flat FRW Universe filled with dark energy, dark matter and decoupled baryonic matter and radiation we calculate the energy density evolution equations of the dark sector and solve them. The different sign combinations of the two parameters of the model show clear qualitative different cosmological scenarios, from basic cosmological insights we discard some of them. The linear scalar perturbation equations of the dark matter were calculated. Using the CAMB code we calculate the CMB and matter power spectra for some values of the parameters $\alpha$ and $\beta$ and compare it with $\Lambda$CDM. The model modify mainly the lower multipoles of the CMB power spectrum remaining almost the same the high ones. The matter power spectrum for low wave numbers is not modified by the interaction but after the maximum it is clearly different. Using observational data from Planck, and various galaxy surveys we obtain the constraints of the parameters, the best fit values obtained are the combinations $\alpha = (3.7 \pm 7 )\times 10^{-4} $, $-(1.5\times10^{-5} {\rm eV}^{-1})^{4} \ll \beta < (0.07 {\rm eV}^{-1})^4$.

Super-Eddington accreting massive black holes explore high- z cosmology: Monte-Carlo simulations

In this paper, we simulate Super-Eddington accreting massive black holes (SEAMBHs) as the candles to probe cosmology for the first time. SEAMBHs have been demonstrated to be able to provide a new tool for estimating cosmological distance. Thus, we create a series of mock data sets of SEAMBHs, especially in the high redshift region, to check their abilities to probe the cosmology. To fulfill the potential of the SEAMBHs on the cosmology, we apply the simulated data to three projects. The first is the exploration of their abilities to constrain the cosmological parameters, in which we combine different data sets of current observations such as the cosmic microwave background from {\it Planck} and type Ia supernovae from Joint Light-curve Analysis (JLA). We find that the high redshift SEAMBHs can help to break the degeneracies of the background cosmological parameters constrained by {\it Planck} and JLA, thus giving much tighter constraints of the cosmological parameters. The second uses the high redshift SEAMBHs as the complements of the low redshift JLA to constrain the early expansion rate and the dark energy density evolution in the cold dark matter frame. Our results show that these high redshift SEAMBHs are very powerful on constraining the early Hubble rate and the evolution of the dark energy density; thus they can give us more information about the expansion history of our Universe, which is also crucial for testing the $\Lambda$CDM model in the high redshift region. Finally, we check the SEAMBH candles' abilities to reconstruct the equation of state of dark energy at high redshift. In summary, our results show that the SEAMBHs, as the rare candles in the high redshift region, can provide us a new and independent observation to probe cosmology in the future.

Chiral magnetic effect in the presence of electroweak interactions as a quasiclassical phenomenon

We elaborate the quasiclassical approach to obtain the modified chiral magnetic effect (CME) in the case when the massless charged fermions interact with electromagnetic fields and the background matter by the electroweak forces. The derivation of the anomalous current along the external magnetic field involves the study of the energy density evolution of chiral particles in parallel electric and magnetic fields. We consider both the particle acceleration by the external electric field and the contribution of the Adler anomaly. The condition of the validity of this method for the derivation of the CME is formulated. We obtain the expression for the electric current along the external magnetic field, which appears to coincide with our previous results based on the purely quantum approach. Our results are compared with the findings of other authors.

Dynamic Monte Carlo simulations of radiatively accelerated GRB fireballs

We present a novel Dynamic Monte Carlo code (DynaMo code) which self-consistently simulates the Compton scattering driven dynamic evolution of a plasma. We use the DynaMo code to investigate the time-dependent expansion and acceleration of dissipationless GRB fireballs by varying their initial opacities and baryonic content. We study the opacity and energy density evolution of an initially optically thick, radiation-dominated fireball across its entire phase space - in particular during the $R_{\rm ph} < R_{\rm sat}$ regime. Our results reveal new phases of fireball evolution: a transition phase with a radial extent of several orders of magnitude - the fireball transitions from $\Gamma \propto R$ to $\Gamma \propto R^0$, a post-photopsheric acceleration phase - where fireballs accelerate beyond the photosphere, and a Thomson-dominated acceleration phase - characterized by slow acceleration of optically thick, matter-dominated fireballs due to Thomson scattering. We quantify the new phases by providing analytical expressions of Lorentz factor evolution, which will be useful for deriving jet parameters.