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Santosh Bhattarai

Publications and source records attributed to Santosh Bhattarai.

10 recordsLinked to original sources

Photons x Force: Differentiable Radiation Pressure Modeling

We propose a system to optimize parametric designs subject to radiation pressure, \ie the effect of light on the motion of objects. This is most relevant in the design of spacecraft, where radiation pressure presents the dominant non-conservative forcing mechanism, which is the case beyond approximately 800 km altitude. Despite its importance, the high computational cost of high-fidelity radiation pressure modeling has limited its use in large-scale spacecraft design, optimization, and space situational awareness applications. We enable this by offering three innovations in the simulation, in representation and in optimization: First, a practical computer graphics-inspired Monte-Carlo (MC) simulation of radiation pressure. The simulation is highly parallel, uses importance sampling and next-event estimation to reduce variance and allows simulating an entire family of designs instead of a single spacecraft as in previous work. Second, we introduce neural networks as a representation of forces from design parameters. This neural proxy model, learned from simulations, is inherently differentiable and can query forces orders of magnitude faster than a full MC simulation. Third, and finally, we demonstrate optimizing inverse radiation pressure designs, such as finding geometry, material or operation parameters that minimizes travel time, maximizes proximity given a desired end-point, minimize thruster fuel, trains mission control policies or allocated compute budget in extraterrestrial compute.

cs.GR

Evaluating Near-Real Time Thermospheric Density Retrieval Methods from Precise Low Earth Orbit Spacecraft Ephemerides During Geomagnetic Storms

Characterizing the density of the thermosphere during geomagnetic storms is critical for both thermosphere modelling efforts and satellite operations. Accurate near-real time density estimates can feed into data assimilation schemes and provide operators with an early warning system for storm-triggered drag increases. This study evaluates two methods for generating near-real time thermospheric density estimates: the Energy Dissipation Rate (EDR) method and the Precise Orbit Determination (POD)-accelerometry method. Using accelerometer-derived densities from the Gravity Recovery And Climate Experiment Follow-On (GRACE-FO) and Challenging Minisatellite Payload (CHAMP) spacecraft as truth over 45 geomagnetic storms, the POD accelerometry method was found to surpass EDR density retrieval as well as one commonly used atmospheric density model (DTM2000) in terms of mean absolute percentage error (by 113.30\% and 130.64\%, respectively). The POD accelerometry method is comparable, albeit slightly worse, than two other models: JB2008 (-8.74\%) and NRLMSISE-00 (-22.74\%). These results highlight the potential for near-real-time density inversion to rival models driven by post-processed indices, which outperform these same models in an operational setting, where they rely on forecasted or nowcasted indices. By applying the POD accelerometry method along the orbits of three LEO satellite orbits during 80 geomagnetic storms (2001--2024), this study illustrates the potential of POD accelerometry as a near-real-time resource for the thermosphere and satellite operations community. The accompanying codebase facilitates broader adoption of these techniques, advancing both storm-time modelling and operational response capabilities.

physics.space-ph

Existence and stability of standing waves for coupled nonlinear Hartree type equations

We study existence and stability of standing waves for coupled nonlinear Hartree type equations \[ -i\frac{\partial}{\partial t}ψ_j=Δψ_j+\sum_{k=1}^m \left(W\star |ψ_k|^p \right)|ψ_j|^{p-2}ψ_j, \] where $ψ_j:\mathbb{R}^N\times \mathbb{R}\to \mathbb{C}$ for $j=1, \ldots, m$ and the potential $W:\mathbb{R}\to [0, \infty)$ satisfies certain assumptions. Our method relies on a variational characterization of standing waves based on minimization of the energy when $L^2$ norms of component waves are prescribed. We obtain existence and stability results for two and three-component systems and for a certain range of $p$. In particular, our argument works in the case when $W(x)=|x|^{-α}$ for some $α>0.$

math.AP

On fractional Schrodinger systems of Choquard type

In this article, we first employ the concentration compactness techniques to prove existence and stability results of standing waves for nonlinear fractional Schrödinger-Choquard equation \[ i\partial_tΨ+ (-Δ)^αΨ= a |Ψ|^{s-2}Ψ+λ\left( \frac{1}{|x|^{N-β}} \star |Ψ|^p \right)|Ψ|^{p-2}Ψ \ \ \mathrm{in}\ \mathbb{R}^{N+1}, \] where $N\geq 2$, $α\in (0,1)$, $β\in (0, N)$, $s\in (2, 2+\frac{4α}{N})$, $p\in [2, 1+\frac{2α+β}{N})$, and the constants $a, λ$ are nonnegative satisfying $a+λ> 0.$ We then extend the arguments to establish similar results for coupled standing waves of nonlinear fractional Schrödinger systems of Choquard type. The same argument works for equations with an arbitrary number of combined nonlinearities and when $|x|^{β-N}$ is replaced by a more general convolution potential $\mathcal{K}:\mathbb{R}^N\to [0, \infty)$ under certain assumptions. The same arguments can be applied and the results are identical for the case $α=1$ as well.

math.AP

Existence and stability of standing waves for nonlinear Schrodinger systems involving the fractional Laplacian

In the present paper we consider the coupled system of nonlinear Schrödinger equations with the fractional Laplacian \[ \left\{ \begin{aligned} (-Δ)^αu_1 & = λ_1u_1+f_1(u_1)+\partial_1F(u_1,u_2)\ \ \mathrm{in}\ \mathbb{R}^N, \\ (-Δ)^αu_2 & = λ_2u_2+f_2(u_2)+\partial_2F(u_1,u_2)\ \ \mathrm{in}\ \mathbb{R}^N, \end{aligned} \right. \] where $u_1, u_2:\mathbb{R}^N\to \mathbb{C},\ N\geq 2,$ and $0<α<1.$ By studying an appropriate family of constrained minimization problems, we obtain the existence of solutions in the space $H^α(\mathbb{R}^N) \times H^α(\mathbb{R}^N)$ satisfying \[ \int_{\mathbb{R}^N}|u_1|^2\ dx = σ_1\ \ \textrm{and}\ \ \int_{\mathbb{R}^N}|u_2|^2\ dx=σ_2 \] for given $σ_j>0.$ The numbers $λ_1$ and $λ_2$ in the system appear as Lagrange multiplier. The method is based on the concentration compactness arguments, but introduces a new way to verify some of the properties of the variational problem that are required in order for the concentration compactness method to work. We consider the case when $f_j(s)=μ_j|s|^{p_j-2}s$ and $F(s,t)=β|s|^{r_1}|t|^{r_2}$ with $μ_j>0, β>0,$ and the values $r_i>1, 2<p_j, r_1+r_2<2+\frac{4α}{N}.$ The method also enables us to prove the stability result of standing wave solutions associated with the set of global minimizers.

math.AP

Well-posedness for multicomponent Schrodinger-gKdV systems and stability of solitary waves with prescribed mass

In this paper we prove the well-posedness issues of the associated initial value problem, the existence of nontrivial solutions with prescribed $L^2$-norm, and the stability of associated solitary waves for two classes of coupled nonlinear dispersive equations. The first problem here describes the nonlinear interaction between two Schrödinger type short waves and a generalized Korteweg-de Vries type long wave and the second problem describes the nonlinear interaction of two generalized Korteweg-de Vries type long waves with a common Schrödinger type short wave. The results here extend many of the previously obtained results for two-component coupled Schrödinger-Korteweg-de Vries systems.

math.AP

Stability of normalized solitary waves for three coupled nonlinear Schrodinger equations

In this paper we establish existence and stability results concerning fully nontrivial solitary-wave solutions to 3-coupled nonlinear Schrödinger system \[ i\partial_t u_{j}+\partial_{xx}u_{j}+ \left(\sum_{k=1}^{3} a_{kj} |u_k|^{p}\right)|u_j|^{p-2}u_j = 0, \ j=1,2,3, \] where $u_j$ are complex-valued functions of $(x,t)\in \mathbb{R}^{2}$ and $a_{kj}$ are positive constants satisfying $a_{kj}=a_{jk}$ (symmetric attractive case). Our approach improves many of the previous known results. In all methods used previously to study solitary waves, which we are aware of, the variational problem has consisted of finding the extremum of an energy functional subject to the constraints that were not independently chosen. Here we study a problem of minimizing the energy functional subject to three independent $L^2$ mass constraints and establish existence and stability results for a true three-parameter family of solitary waves.

math.AP

Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities

This paper proves existence and stability results of solitary-wave solutions to coupled nonlinear Schrödinger equations with power-type nonlinearities arising in several models of modern physics. The existence of solitary waves is obtained by solving a variational problem subject to two independent constraints and using the concentration-compactness method. The set of minimizers is shown to be stable and further information about the structures of this set are given. The paper extends the results previously obtained by Cipolatti and Zumpichiatti, Nguyen and Wang, and Ohta.

math.AP

Existence and stability of a two-parameter family of solitary waves for an NLS-KdV system

We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schrödinger type is coupled to an equation of Korteweg-de Vries type. Such systems model interactions between short and long dispersive waves. The results extend earlier results of Angulo, Albert and Angulo, and Chen. Our proof involves the characterization of solitary-wave solutions as minimizers of an energy functional subject to two constraints. To establish the precompactness of minimizing sequences via concentrated compactness, we establish the sub-additivity of the problem with respect to both constraint variables jointly.

math.AP