arXiv subjects

Liqiang Hou

Publications and source records attributed to Liqiang Hou.

5 recordsLinked to original sources

arXiv2026

Fuel-Optimal Low-Thrust Trajectory Design under High-Fidelity Dynamics: A State Transition Matrix-Based Sensitivity Approach

A straightforward and computationally efficient indirect method based on STM sensitivity analysis is introduced for designing fuel-optimal low-thrust transfers under high-fidelity dynamics. Conventional indirect approaches require explicit expressions for the partial derivatives of the system dynamics to formulate the costate equations, making the derivation process complex for high-fidelity trajectory design. In this work, the costate equations are reformulated as ordinary differential equations involving only the state variables and their time derivatives. High-order dynamical effects are treated as black-box components, avoiding the need to derive partial derivatives of the system dynamics. A standard gradient-based or interior-point optimizer is used to determine the optimal costates and transfer parameters. The equivalence between the proposed method and conventional approaches is demonstrated through a classic Earth-Mars transfer scenario. An Earth-Mars transfer under high-fidelity dynamics is then presented, including perturbations from solar radiation pressure, solar J2 oblateness, Jupiter third-body gravity, and relativistic effects. Finally, the method is applied to a multiple-revolution Earth-Venus transfer under high-fidelity dynamics.

math.OC↗

arXiv2025

Cosmology of Single Species Hidden Dark Matter

Cosmology and astrophysics provide various ways to study the properties of dark matter even if they have negligible non-gravitational interactions with the Standard Model particles and remain hidden. We study a type of hidden dark matter model in which the dark matter is completely decoupled from the Standard Model sector except gravitationally, and consists of a single species with conserved comoving particle number and conserved comoving entropy. This category of hidden dark matter includes models that act as warm dark matter but is more general. In particular, in addition to having an independent temperature from the Standard Model sector, it includes cases in which dark matter is in its own kinetic equilibrium or is free-streaming, obeys fermionic or bosonic statistics, and processes a chemical potential that controls the particle occupation number. While the usual parameterization using the free-streaming scale or the particle mass no longer applies, we show that all cases can be well approximated by a set of functions parameterized by only one parameter as long as the chemical potential is nonpositive: the characteristic scale factor at the time of the relativistic-to-nonrelativistic transition. We study the constraints from Big Bang Nucleosynthesis, the cosmic microwave background, the Lyman-$α$ forest, and the smallest halo mass. We show that the most significant phenomenological impact is the suppression of the small-scale matter power spectrum -- a typical feature when the dark matter has a velocity dispersion or pressure at early times. So far, the Lyman-$α$ forest and the small dark matter halo population provide the strongest constraints, limiting the transition redshift to be larger than $\sim6.2\times10^7$.

astro-ph.CO↗

arXiv2025

The Effects of Dark Matter Annihilation and Dark Matter-Baryon Velocity Offsets at Cosmic Dawn

Dark matter annihilation has the potential to leave an imprint on the properties of the first luminous structures at Cosmic Dawn as well as the overall evolution of the intergalactic medium (IGM). In this work, we employ a semi-analytic method to model dark matter annihilation during Cosmic Dawn (approximately redshift $z=20$ to $40$), examining potential modifications to IGM evolution as well as gas collapse, cooling, and star formation in mini-halos. Our analysis takes into account the effects of dark matter-baryon velocity offsets, utilizing the public 21cmvFAST code, and producing predictions for the 21cm global signal. The results from our simplified model suggest that dark matter annihilation can suppress the gas fraction in small halos and alter the molecular cooling process, while the impact on star formation might be positive or negative depending on parameters of the dark matter model as well as the redshift and assumptions about velocity offsets. This underscores the need for more comprehensive simulations of the effects of exotic energy injection at Cosmic Dawn as observational probes are providing us new insights into the process of reionization and the formation of first stars and galaxies.

astro-ph.CO↗

arXiv2021

A New Continuous Optimization Method for Mixed Integer Space Travelling Salesman Problem

The travelling salesman problem (TSP) of space trajectory design is complicated by its complex structure design space. The graph based tree search and stochastic seeding combinatorial approaches are commonly employed to tackle the time-dependent TSP due to their combinatorial nature. In this paper, a new continuous optimization strategy for the mixed integer combinatorial problem is proposed. The space trajectory combinatorial problem is tackled using continuous gradient based method. A continuous mapping technique is developed to map the integer type ID of targets on the sequence to a set of continuous design variables. Expected flyby targets are introduced as references and used as priori to select the candidate target to fly by. Bayesian based analysis is employed to model accumulated posterior of the sequence and a new objective function with quadratic form constraints is constructed. The new introduced auxiliary design variables of expected targets together with the original design variables are set to be optimized. A gradient based optimizer is used to search optimal sequence parameter. Performances of the proposed algorithm are demonstrated through a multiple debris rendezvous problem and a static TSP benchmark.

math.OC↗

arXiv2020

Investigating the Hubble Constant Tension -- Two Numbers in the Standard Cosmological Model

The current Hubble constant tension is usually presented by comparing constraints on $H_0$ only. However, the post-recombination background cosmic evolution is determined by two parameters in the standard $Λ$CDM model, the Hubble constant ($H_0$) and today's matter energy fraction ($Ω_{\rm{m}}$). If we therefore compare all constraints individually in the $H_0$-$Ω_{\rm{m}}$ plane, (1) various constraints can be treated as independently as possible, (2) single-sided constraints are easier to consider, (3) compatibility among different constraints can be viewed in a more robust way, (4) the model dependence of each constraint is clear, and (5) whether or not a nonstandard model is able to reconcile all constraints in tension can be seen more effectively. We perform a systematic comparison of different constraints in the $H_0$-$Ω_{\rm{m}}$ space based on a flat $Λ$CDM model, treating them as separately as possible. Constraints along different degeneracy directions consistently overlap in one region of the space, with the local measurement from Cepheid variable-calibrated supernovae being the most outlying, followed by the time-delay strong-lensing result. Considering the possibility that some nonstandard physics may reconcile the constraints, we provide a general discussion on nonstandard models with modifications at high, mid, or low redshifts, and the effect of local environmental factors. Due to the different responses of individual constraints to a modified model, it is not easy for nonstandard models to reconcile all constraints if none of them have unaccounted-for systematic effects.

astro-ph.CO↗