Search

This paper focuses on remainder estimates of the magnetic $L^p$-Hardy inequalities for $1

This paper focuses on optimal constants and optimizers of the second order Caffarelli-Kohn-Nirenberg inequalities. Firstly, we aim to study optimal constants and optimizers for the following second order Caffarelli-Kohn-Nirenberg inequality in radial space: let $N\ge1$, $t\ge p>1$, \begin{equation}\label{0.1} \left(\int_{\mathbb{R}^N} \frac{|\Delta u|^p}{|x|^{p\alpha}} \mathrm{d}x\right)^{\frac{1}{p}} \left[\int_{\mathbb{R}^N} \frac{\left|\nabla u\right|^{\frac{p(t-1)}{p-1}}} {|x|^{\frac{p(t-1)}{p-1}\beta}} \mathrm{d}x\right]^{\frac{p-1}{p}} \ge C(N,p,t,\alpha,\beta) \int_{\mathbb{R}^N} \frac{\left|\nabla u\right|^t}{|x|^{t\gamma}} \mathrm{d}x. \end{equation} Secondly, we establish second order $L^p$-Caffarelli-Kohn-Nirenberg identities, and obtain optimal constants and optimizers of the second order $L^p$-Caffarelli-Kohn-Nirenberg inequalities (i.e., $p=t$ in \eqref{0.1}) in general space. Lastly, under some more general assumptions, we consider the optimal weighted second order Heisenberg Uncertainty Principles, which complements the recent work [``The sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates for the sharp second order uncertainty principle'', 2022, arXiv:2102.01425]. This paper's main novelty lies in the fact that we research the optimal versions of the second order Caffarelli-Kohn-Nirenberg inequalities \eqref{0.1} in radial space or in general space, and also establish the second order $L^p$-Caffarelli-Kohn-Nirenberg identities.

Stimulated by the recent experimental results on the fully-charm tetraquark states, we systematically calculate the mass spectra of the fully-charm tetraquark states in $8_{[c\bar{c}]}\otimes8_{[c\bar{c}]}$ color configuration via QCD sum rules. By constructing nine $8_{[c\bar{c}]}\otimes8_{[c\bar{c}]}$ type currents with quantum numbers $J^{PC}=0^{-+},0^{--},1^{-+},1^{+-},1^{--}$ and $2^{++}$, we perform analytic calculation up to dimension six in the Operator Product Expansion (OPE). We find the fully-charm tetraquark states with $J^{PC}=1^{+-},2^{++}$ lie around 6.48 $\sim$ 6.62 GeV while the fully-charm tetraquark states with $J^{PC}=0^{-+},0^{--},1^{--},1^{-+}$ are about 6.85 $\sim$ 7.02 GeV. Notably, the mass predictions for the $c\bar{c}c\bar{c}$ tetraquarks, specifically those with $J^{PC}=2^{++}$, align with the broad structure identified by LHCb. Moreover, the masses of fully-charm tetraquarks with $J^{PC}=0^{-+}$ and $1^{-+}$ are anticipated to match closely with the mass of X(6900), considering the margin of error. Such findings hint at the presence of some $8_{[c\bar{c}]}\otimes8_{[c\bar{c}]}$ components within the di-$J/\psi$ structures observed by LHCb. The predictions for tetraquark states with $J^{PC}=0^{--},1^{+-},1^{--}$ may be accessible in the future BelleII, Super-B, PANDA, and LHCb experiments., Comment: 19 pages, 4 figures, 1 table. To match the published version

In the present paper, we study the following Schr\"{o}dinger-Maxwell equation with combined nonlinearities \begin{align*} \displaystyle - \Delta u+\lambda u+ \left(|x|^{-1}\ast |u|^2\right)u =|u|^{p-2}u +\mu|u|^{q-2}u\quad \text{in} \ \mathbb{ R}^3 \quad \quad \text{and}\quad \quad \int_{\mathbb{R}^3}|u|^2dx=a^2, \end{align*} where $a>0$, $\mu\in \mathbb{R}$, $2

In this article, we study the mass spectrum of the low-lying triply heavy hybrid baryon, which consists of three valence heavy quarks in a color octet and one valence gluon, with spin-parity $J^P=(\frac{1}{2})^+$ via QCD sum rules. This is the first study on the triply heavy hybrid baryons in the framework of QCD sum rules. After performing the QCD sum rule analysis, we find that the mass of $cccg$ hybrid baryon lies in $M_{cccg}= 5.91-6.13$ GeV. As a byproduct, the mass of the triply bottom hybrid baryon state is extracted to be around $M_{bbbg}=14.62-14.82$ GeV. The contributions up to dimension eight at the leading order of $\alpha_s$ (LO) in the operator product expansion are taken into account in the calculation. The triply charmed hybrid baryon predicted in this work can decay into one doubly charmed baryon and one charmed meson. Especially, we propose to search for $cccg$ hybrid baryon with $J^{P}= (1/2)^+$ in the P-wave decay channels $\Xi_{cc}^{++} D^0$, $\Xi_{cc}^{+} D^+$, and $\Xi_{ccs}^{+} D_s^+$, which may be accessible in future BelleII, Super-B, PANDA, and LHCb experiments., Comment: 20 pages, 4 figures, 2 tables. To match the published version

In present paper, we study the following nonlinear Schr\"{o}dinger equation with combined power nonlinearities \begin{align*} - \Delta u+V(x)u+\lambda u=|u|^{2^*-2}u+\mu |u|^{q-2}u \quad \quad \text{in} \ \mathbb{ R}^N, \ N\geq 3 \end{align*} having prescribed mass \begin{align*} \int_{ \mathbb{ R}^N}u^2dx=a^2, \end{align*} where $\mu, a>0$, $q\in(2, 2^*)$, $2^*=\frac{2N}{N-2}$ is the critical Sobolev exponent, $V$ is an external potential vanishing at infinity, and the parameter $\lambda\in \mathbb{R}$ appears as a Lagrange multiplier. Under some mild assumptions on $V$, for the $L^2$-subcritical perturbation $q\in(2, 2+\frac{4}{N})$, we prove that there exists $a_0>0$ such that the normalized solution with negative energy to the above problem with $\mu>0$ can be obtained for $a\in (0, a_0)$; for the $L^2$-critical perturbation $q=2+\frac{4}{N}$, by limiting the range of $\mu$, the positive ground state normalized solution to the above problem for any $a>0$ is also found with the aid of the Poho\v{z}aev constraint; moreover, for the $L^2$-supercritical perturbation $q\in( 2+\frac{4}{N}, 2^*)$, we get a positive ground state normalized solution for the above problem with $a>0$ and $\mu>0$ by using the Poho\v{z}aev constraint. At the same time, the exponential decay property of the positive normalized solution is established, which is important for the instability analysis of the standing waves. Furthermore, we give a description of the ground state set and obtain the strong instability of the standing waves for $q\in[2+\frac{4}{N}, 2^*)$. This paper can be regarded as a generalization of Soave [J. Funct. Anal. (2020)] in a sense., Comment: arXiv admin note: text overlap with arXiv:2111.01687 by other authors

In this paper, we are concerned with the following Schr\"{o}dinger-Poisson system with critical nonlinearity and critical nonlocal term due to the Hardy-Littlewood-Sobolev inequality \begin{equation}\begin{cases} -\Delta u+u+\lambda\phi |u|^3u =|u|^4u+ |u|^{q-2}u,\ \ &\ x \in \mathbb{R}^{3},\\[2mm] -\Delta \phi=|u|^5, \ \ &\ x \in \mathbb{R}^{3}, \end{cases} \end{equation} where $\lambda\in \mathbb{R}$ is a parameter and $q\in(2,6)$. If $\lambda\ge (\frac{q+2}{8})^2$ and $q\in(2,6)$, the above system has no nontrivial solution. If $\lambda\in (\lambda^*,0)$ for some $\lambda^*<0$, we obtain a least energy radial sign-changing solution $u_\lambda$ to the above system. Furthermore, we consider $\lambda$ as a parameter and analyze the asymptotic behavior of $u_\lambda$ as $\lambda\to 0^-$.

In this work, we study the $1^{--}$ double-gluon charmonium ($\bar{c}ggc$) and bottomonium ($\bar{b} gg b$) hybrids in terms of QCD sum rules. We find that the mass of $\bar{c}ggc$ hybrid lies in $M_{H_{c}}$ = $5.33 \sim 5.90$ GeV, while in the bottom sector the mass of $\bar{b}ggb$ hybrid may be situated in $M_{H_b} = 11.20 \sim 11.68$ GeV. The contributions up to dimension eight at leading order of $\alpha_s$ (LO) in the operator product expansion are taken into account in the calculation. The double-gluon charmonium hybrid meson predicted in this work can decay into a pair of charmed mesons or a pair of charmed mesons together with a light meson. Especially, we propose to search for $\bar{c}ggc$ hybrid with $I^G(J^{PC})= 0^-(1^{--})$ in their decay channels $D \bar{D}/D^* \bar{D}/D^{*} \bar{D}^{*}$ with P wave and $D^* \bar{D}^{*} \pi/D^* \bar{D}^*\eta/D \bar{D}\rho/D \bar{D}\omega$ with S wave, which may be accessible in Belle II, PANDA, Super-B, GlueX, and LHCb experiments., Comment: 25 pages, 7 figures, 4 tables; revised version to be published in PRD

In this paper, we consider the quasilinear Schr\"{o}dinger equation \begin{equation*} -\Delta u+V(x)u-u\Delta(u^2)=g(u),\ \ x\in \mathbb{R}^{3}, \end{equation*} where $V$ and $g$ are continuous functions. Without the coercive condition on $V$ or the monotonicity condition on $g$, we show that the problem above has a least energy sign-changing solution and infinitely many sign-changing solutions. Our results especially solve the problem above in the case where $g(u)=|u|^{p-2}u$ ($2

In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly convergent algorithm is proposed. The initial iteration point can be chosen arbitrarily for the algorithm. At each iteration, the new algorithm solves one quadratic programming subproblem which is always feasible, and one or two systems of linear equations with a common coefficient matrix. Moreover, the coefficient matrix is uniformly nonsingular. After finite iterations, the iteration points can always enter into the feasible set of the problem, and the search direction is obtained by solving one quadratic programming subproblem and only one system of linear equations. The new algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some preliminary numerical experiments are reported to show that the algorithm is promising.

NASA's Descent System Studies (DSS) Program is studying various concept vehicles to enable landing of heavy payloads on the surface of Mars. While it is desirable to run high-fidelity CFD simulations to accurately assess the aerodynamic and aerothermal effects of various design changes during EDL, it is usually difficult to quickly generate high-quality grids suitable for such analyses. One approach to address this bottleneck in mesh generation is through the use oversetting grids. Although the overset approach is efficient and powerful in solving partial differential equations on complex geometries, new users often find it challenging to apply overset concepts for their simulations. For example, generating hyperbolic grids with sufficient overlap; priority in hole-cutting on multiple overlapping grids; and fixes to assemble overlapping viscous grids at the body surface. The objective of this presentation is to introduce a simple process that combines the advantages of near-body, point-matched, structured grids with oversetting background grids suitable for grid alignment. This approach allows for grids that can be sequenced, reclustering of mesh spacing at the wall, and grid alignment with the bow shock. The current methodology is tested on a Mid-L/D configuration using the overset DPLR code.

This presentation will discuss the current state of each of the main measurements systems for MEDLI2. The first system is a network of pressure transducers, the Mars Entry Atmospheric Data System (MEADS). Improving upon MEDLI, separate MEDLI2 pressure transducers span the measurement range suitable for both hypersonic and supersonic flows. The MEADS will also measure pressure on the backshell of the vehicle to better characterize the contribution of backshell pressure on the overall forces and moments on the entry probe. The second system is the thermal instrumentation, or Mars Instrumented Sensor Plugs. This system includes a network of high-temperature thermocouples embedded in the thermal protection system across the heatshield and backshell. The MISP also includes two types of sensors for directly measuring incident heatflux on the backshell of the vehicle. In addition, a radiometer is included on the backshell to measure radiative heating. The presentation will also cover the current state of the MEDLI2 hardware, expected environments that will be measured, and data analysis techniques being developed to infer vehicle entry performance from both the MISP and MEADS sensor systems.

The Mars Entry, Descent, and Landing Instrumentation 2 (MEDLI2) sensor suite for the Mars 2020 mission includes a radiometer on the backshell to measure the radiative heating during entry into the Martian atmosphere. Thermal Protection System (TPS) ablation products may be deposited on the radiometer window which would degrade the transmission and thus alter the accuracy of the radiometer readings. Testing in NASA Ames Research Center's miniature arc jet (mARC) facility was conducted to deposit TPS ablation products on radiometer windows in an effort to characterize how the ablation products change the window transmission and thus alter radiometer performance. Heat flux and stagnation pressure characterization of the mARC facility in a 90 percent CO2, 10 percent N2 (by mass) Mars-like environment are presented. The spectral transmission of the radiometer windows before and after mARC testing are compared. Additionally, a discussion of how flight-like these test conditions were and future work to further characterize the effect of TPS ablation on radiometer performance are presented.

Short course on Introduction to DPLR for a general audience at TFAWS 2016.

An overview of aerodynamic models for the Low Density Supersonic Decelerator (LDSD) Supersonic Flight Dynamics Test (SFDT) campaign test vehicle is presented, with comparisons to reconstructed flight data and discussion of model updates. The SFDT campaign objective is to test Supersonic Inflatable Aerodynamic Decelerator (SIAD) and large supersonic parachute technologies at high altitude Earth conditions relevant to entry, descent, and landing (EDL) at Mars. Nominal SIAD test conditions are attained by lifting a test vehicle (TV) to 36 km altitude with a helium balloon, then accelerating the TV to Mach 4 and 53 km altitude with a solid rocket motor. Test flights conducted in June of 2014 (SFDT-1) and 2015 (SFDT-2) each successfully delivered a 6 meter diameter decelerator (SIAD-R) to test conditions and several seconds of flight, and were successful in demonstrating the SFDT flight system concept and SIAD-R technology. Aerodynamic models and uncertainties developed for the SFDT campaign are presented, including the methods used to generate them and their implementation within an aerodynamic database (ADB) routine for flight simulations. Pre- and post-flight aerodynamic models are compared against reconstructed flight data and model changes based upon knowledge gained from the flights are discussed. The pre-flight powered phase model is shown to have a significant contribution to off-nominal SFDT trajectory lofting, while coast and SIAD phase models behaved much as predicted.

Aerothermal modeling is inherently entwined with TPS design. Aerothermal, radiation, and TPS material response are coupled so it's important to check modeling assumptions. Validation of numerical models using ground and flight tests is important to quantify uncertainties. A margin policy based on statistical methods may provide greater insight in the key drivers and overall reliability of the design

Presentation provides an overview of the process to generate aerothermal databases for the Orion MPCV usingcomputational fluid dynamics (CFD) tools.

NASA's Low Density Supersonic Decelerator Program is developing new technologies that will enable the landing of heavier payloads in low density environments, such as Mars. A recent flight experiment conducted high above the Hawaiian Islands has demonstrated the performance of several decelerator technologies. In particular, the deployment of the Robotic class Supersonic Inflatable Aerodynamic Decelerator (SIAD-R) was highly successful, and valuable data were collected during the test flight. This paper outlines the Computational Fluid Dynamics (CFD) analysis used to estimate the aerodynamic and aerothermal characteristics of the SIAD-R. Pre-flight and post-flight predictions are compared with the flight data, and a very good agreement in aerodynamic force and moment coefficients is observed between the CFD solutions and the reconstructed flight data.

An overview of pre-flight aerodynamic models for the Low Density Supersonic Decelerator (LDSD) Supersonic Flight Dynamics Test (SFDT) campaign is presented, with comparisons to reconstructed flight data and discussion of model updates. The SFDT campaign objective is to test Supersonic Inflatable Aerodynamic Decelerator (SIAD) and large supersonic parachute technologies at high altitude Earth conditions relevant to entry, descent, and landing (EDL) at Mars. Nominal SIAD test conditions are attained by lifting a test vehicle (TV) to 36 km altitude with a large helium balloon, then accelerating the TV to Mach 4 and and 53 km altitude with a solid rocket motor. The first flight test (SFDT-1) delivered a 6 meter diameter robotic mission class decelerator (SIAD-R) to several seconds of flight on June 28, 2014, and was successful in demonstrating the SFDT flight system concept and SIAD-R. The trajectory was off-nominal, however, lofting to over 8 km higher than predicted in flight simulations. Comparisons between reconstructed flight data and aerodynamic models show that SIAD-R aerodynamic performance was in good agreement with pre-flight predictions. Similar comparisons of powered ascent phase aerodynamics show that the pre-flight model overpredicted TV pitch stability, leading to underprediction of trajectory peak altitude. Comparisons between pre-flight aerodynamic models and reconstructed flight data are shown, and changes to aerodynamic models using improved fidelity and knowledge gained from SFDT-1 are discussed.

Detached Eddy Simulations have been performed to investigate the effects of high-fidelity turbulence modeling on roughness-induced transition to turbulence during Mars entry. Chemically reacting flow solutions will be obtained for a gap filler of Mars Science Laboratory at the peak heating condition.

The NEQAIR line-by-line radiation code has been incorporated into the DPLR Navier-Stokes flow solver such that the NEQAIR subroutines are now callable functions of DPLR. The coupled DPLR-NEQAIR code was applied to compute the convective and radiative heating rates over high-mass Mars entry vehicles. Two vehicle geometries were considered - a 15 m diameter 70-degree sphere cone configuration and a slender, mid-L/D vehicle with a diameter of 5 m called an Ellipsled. The entry masses ranged from 100 to 165 metric tons. Solutions were generated for entry velocities ranging from 6.5 to 9.1 km/s. The coupled fluids-radiation solutions were performed at the peak heating location along trajectories generated by the Traj trajectory analysis code. The impact of fluids-radiation coupling is a function of the level of radiative heating and the freestream density and velocity. For the high-mass Mars vehicles examined in this study, coupling effects were greatest for entry velocities above 8.5 km/s where the surface radiative heating was reduced by up 17%. Generally speaking, the Ellipsled geometry experiences a lower peak radiative heating rate but a higher peak turbulent convective heating rate than the MSL-based vehicle.

The NEQAIR line-by-line radiation code has been incorporated into the DPLR Navier-Stokes flow solver such that the NEQAIR subroutines are now callable functions of DPLR. The coupled DPLR-NEQAIR code was applied to compute the convective and radiative heating rates over high-mass Mars entry vehicles. Two vehicle geometries were considered - a 15 m diameter 70-degree sphere cone configuration and a slender, mid-L/D vehicle with a diameter of 5 m called an Ellipsled. The entry masses ranged from 100 to 165 metric tons. Solutions were generated for entry velocities ranging from 6.5 to 9.1 km/s. The coupled fluids-radiation solutions were performed at the peak heating location along trajectories generated by the Traj trajectory analysis code. The impact of fluids-radiation coupling is a function of the level of radiative heating and the freestream density and velocity. For the high-mass Mars vehicles examined in this study, coupling effects were greatest for entry velocities above 8.5 km/s where the surface radiative heating was reduced by up 17%. Generally speaking, the Ellipsled geometry experiences a lower peak radiative heating rate but a higher peak turbulent convective heating rate than the MSL-based vehicle.

Computational Fluid Dynamics (CFD) simulations were used to study the possible effects that the Boundary Layer Transition (BLT) Flight Experiments may have on the heating environment of the Space Shuttle during its entry to Earth. To investigate this issue, hypersonic calculations using the Data-Parallel Line Relaxation (DPLR) and Langley Aerothermodynamic Upwind Relaxation (LAURA) CFD codes were computed for a 0.75 tall protuberance at flight conditions of Mach 15 and 18. These initial results showed high surface heating on the BLT trip and the areas surrounding the protuberance. Since the predicted peak heating rates would exceed the thermal limits of the materials selected to construct the BLT trip, many changes to the geometry were attempted in order to reduce the surface heat flux. The following paper describes the various geometry revisions and the resulting heating environments predicted by the CFD codes.

Surface temperature measurements from the STS-119 boundary-layer transition experiment on the space shuttle orbiter Discovery provide a rare opportunity to assess turbulent CFD models at hypersonic flight conditions. This flight data was acquired by on-board thermocouples and by infrared images taken off-board by the Hypersonic Thermodynamic Infrared Measurements (HYTHIRM) team, and is suitable for hypersonic CFD turbulence assessment between Mach 6 and 14. The primary assessment is for the Baldwin-Lomax and Cebeci-Smith algebraic turbulence models in the DPLR and LAURA CFD codes, respectively. A secondary assessment is made of the Shear-Stress Transport (SST) two-equation turbulence model in the DPLR code. Based upon surface temperature comparisons at eleven thermocouple locations, the algebraic-model turbulent CFD results average 4% lower than the measurements for Mach numbers less than 11. For Mach numbers greater than 11, the algebraic-model turbulent CFD results average 5% higher than the three available thermocouple measurements. Surface temperature predictions from the two SST cases were consistently 3 4% higher than the algebraic-model results. The thermocouple temperatures exhibit a change in trend with Mach number at about Mach 11; this trend is not reflected in the CFD results. Because the temperature trends from the turbulent CFD simulations and the flight data diverge above Mach 11, extrapolation of the turbulent CFD accuracy to higher Mach numbers is not recommended.

The current status of aerothermal analysis for Mars entry missions is reviewed. The aeroheating environment of all Mars missions to date has been dominated by convective heating. Two primary uncertainties in our ability to predict forebody convective heating are turbulence on a blunt lifting cone and surface catalysis in a predominantly CO2 environment. Future missions, particularly crewed vehicles, will encounter additional heating from shock-layer radiation due to a combination of larger size and faster entry velocity. Localized heating due to penetrations or other singularities on the aeroshell must also be taken into account. The physical models employed to predict these phenomena are reviewed, and key uncertainties or deficiencies inherent in these models are explored. Capabilities of existing ground test facilities to support aeroheating validation are also summarized. Engineering flight data from the Viking and Pathfinder missions, which may be useful for aerothermal model validation, are discussed, and an argument is presented for obtaining additional flight data. Examples are taken from past, present, and future Mars entry missions, including the twin Mars Exploration Rovers and the Mars Science Laboratory, scheduled for launch by NASA in 2011.

Aerothermodynamic design environments are presented for the Mars Science Laboratory entry capsule backshell and parachute cone. The design conditions are based on Navier-Stokes flowfield simulations on shallow (maximum total heat load) and steep (maximum heat flux) design entry trajectories from a 2009 launch. Transient interference effects from reaction control system thruster plumes were included in the design environments when necessary. The limiting backshell design heating conditions of 6.3 W/sq cm for heat flux and 377 J/sq cm for total heat load are not influenced by thruster firings. Similarly, the thrusters do not affect the parachute cover lid design environments (13 W/sq cm and 499 J/sq cm). If thruster jet firings occur near peak dynamic pressure, they will augment the design environments at the interface between the backshell and parachute cone (7 W/sq cm and 174 J/sq cm). Localized heat fluxes are higher near the thruster fairing during jet firings, but these areas did not require additional thermal protection material. Finally, heating bump factors were developed for antenna radomes on the parachute cone

Aerothermodynamic design environments are presented for the Mars Science Laboratory entry capsule heatshield. The design conditions are based on Navier-Stokes flowfield simulations on shallow (maximum total heat load) and steep (maximum heat flux, shear stress, and pressure) entry trajectories from a 2009 launch. Boundary layer transition is expected prior to peak heat flux, a first for Mars entry, and the heatshield environments were defined for a fully-turbulent heat pulse. The effects of distributed surface roughness on turbulent heat flux and shear stress peaks are included using empirical correlations. Additional biases and uncertainties are based on computational model comparisons with experimental data and sensitivity studies. The peak design conditions are 197 W/sq cm for heat flux, 471 Pa for shear stress, 0.371 Earth atm for pressure, and 5477 J/sq cm for total heat load. Time-varying conditions at fixed heatshield locations were generated for thermal protection system analysis and flight instrumentation development. Finally, the aerothermodynamic effects of delaying launch until 2011 are previewed.

An investigation of effectiveness of the reaction control system (RCS) of Mars Science Laboratory (MSL) entry capsule during atmospheric flight has been conducted. The reason for the investigation is that MSL is designed to fly a lifting actively guided entry with hypersonic bank maneuvers, therefore an understanding of RCS effectiveness is required. In the course of the study several jet configurations were evaluated using Langley Aerothermal Upwind Relaxation Algorithm (LAURA) code, Data Parallel Line Relaxation (DPLR) code, Fully Unstructured 3D (FUN3D) code and an Overset Grid Flowsolver (OVERFLOW) code. Computations indicated that some of the proposed configurations might induce aero-RCS interactions, sufficient to impede and even overwhelm the intended control torques. It was found that the maximum potential for aero-RCS interference exists around peak dynamic pressure along the trajectory. Present analysis largely relies on computational methods. Ground testing, flight data and computational analyses are required to fully understand the problem. At the time of this writing some experimental work spanning range of Mach number 2.5 through 4.5 has been completed and used to establish preliminary levels of confidence for computations. As a result of the present work a final RCS configuration has been designed such as to minimize aero-interference effects and it is a design baseline for MSL entry capsule.

An overview of the aerothermodynamic environments definition status is presented for the Mars Science Laboratory entry vehicle. The environments are based on Navier-Stokes flowfield simulations on a candidate aeroshell geometry and worst-case entry heating trajectories. Uncertainties for the flowfield predictions are based primarily on available ground data since Mars flight data are scarce. The forebody aerothermodynamics analysis focuses on boundary layer transition and turbulent heating augmentation. Turbulent transition is expected prior to peak heating, a first for Mars entry, resulting in augmented heat flux and shear stress at the same heatshield location. Afterbody computations are also shown with and without interference effects of reaction control system thruster plumes. Including uncertainties, analysis predicts that the heatshield may experience peaks of 225 W/sq cm for turbulent heat flux, 0.32 atm for stagnation pressure, and 400 Pa for turbulent shear stress. The afterbody heat flux without thruster plume interference is predicted to be 7 W/sq cm on the backshell and 10 W/sq cm on the parachute cover. If the reaction control jets are fired near peak dynamic pressure, the heat flux at localized areas could reach as high as 76 W/sq cm on the backshell and 38 W/sq cm on the parachute cover, including uncertainties. The final flight environments used for hardware design will be updated for any changes in the aeroshell configuration, heating design trajectories, or uncertainties.