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Jianfeng Lin

Publications and source records attributed to Jianfeng Lin.

At least 19 recordsLinked to original sources
arXiv2026

Unsteady Thin-Airfoil Theory Revisited: An Approximate Analytical Solution and the Self-Similar Wagner Effect in Viscous Flows

An approximate analytical solution for the unsteady lift of a thin airfoil with a general unsteady motion is derived from a viscous-flow perspective, where the wake vortex-sheet strength is given in an explicit convolution-type expression as an approximate solution of the Wagner integral equation. For validation, this analytical solution is applied to the Wagner and Theodorsen problems, giving the explicit integral forms of the Wagner and Theodorsen functions as the reduced cases. Further, this analytical solution is applied to the starting flow with a finite timescale in the generalized Wagner problem, revealing the self-similarity of the re-normalized circulatory lift coefficient and its equivalence to the re-normalized Wagner function in a finite time domain. More importantly, the self-similar Wagner effect is found in numerical simulation of the flow over a starting flat-plate airfoil at low Reynolds numbers even when the flow is moderately separated. This self-similarity represents the Reynolds-number-invariance.

physics.flu-dyn↗
arXiv2026

GameXpert-Bench: How Far Are Coding Agents from Expert Game Development?

Recent large language models (LLMs) can operate as coding agents that build complete games from natural language requests. Game development is especially demanding because program logic, visual and audio content, interfaces, interaction and playability must function together in one executable artifact. Measuring this capability therefore requires evaluation of both game product and the development process. Existing benchmarks often assess the game development capabilities of LLMs by evaluating the final artifact or an isolated development stage. Our analysis of complete human-agent development trajectories identifies three stages that together span the lifecycle of game development with a coding agent: initial game generation, bug diagnosis and repair, and optimization over multiple turns. Therefore, we introduce GameXpert-Bench, which operationalizes the three lifecycle stages as three complementary benchmark tracks. GameGen evaluates complete game creation from a single request in an empty workspace. GameFix evaluates diagnosis and repair when defects are reported or left for the agent to discover. GameOpt evaluates cumulative optimization through request chains seeded by real development trajectories between users and agents. We evaluate each track using live game interaction, deterministic behavioral tests, or final product criteria with regression checks. The suite contains 97 generation tasks across 11 genres; 100 repair tasks from 50 game levels verified by humans, each with 19-27 injected bugs; and 17 optimization chains with six turns and 102 requests. Across the three tracks, current agents are more reliable at producing playable foundations and implementing explicit requirements than at discovering defects, verifying runtime behavior, and preserving functionality across changes.

cs.AI↗
arXiv2026

Splitting spheres for $S^2$-links in $S^4$

We prove that every smooth two-component split sphere link $L\sqcup R\subset S^4$ admits infinitely many smooth splitting $3$-spheres that are topologically non-isotopic. This generalizes a theorem of Tatsuoka from the two-component sphere unlink to split links with arbitrarily knotted sphere components. In the course of the proof, we establish a general sufficient condition under which a connected sum of smooth $4$-manifolds admits infinitely many topologically non-isotopic splitting $3$-spheres. This criterion may be of independent interest; in particular, it applies to all previously known examples of nonuniqueness for splitting $3$-spheres of positive-genus surface links.

math.GT↗
arXiv2026

Three-dimensional hydro-cluttered locomotion by an undulatory robot

Aquatic robots have expanded human access to underwater environments, yet many underwater spaces contain obstacles that can disrupt open-water locomotion. In "hydro-cluttered" environments, water is interspersed with rigid and flexible clutter, making body-obstacle contact unavoidable. Operating in these spaces requires robots that can regulate and exploit contact, but this regime remains difficult to model or simulate. Building on recent advances in mechanical intelligence in terradynamically capable limbless robotics, we develop principles for 3D aquatic locomotion using AquaMILR, an elongate limbless robot that combines bilateral cable-driven actuation, programmable body compliance, distributed depth regulation, corrosion-resistant enclosures, and onboard power and electronics for untethered field operation. Systematic robophysical experiments reveal that programmable body compliance regulates body deformation and converts body-environment interactions into fast, robust, forward progression across increasing hydro-clutter constraint strength. Depth regulation provides three-dimensional access, allowing the robot to bypass clutter, recover from obstruction, and continue through otherwise inaccessible routes. In potential jamming scenarios, emergent inertia-induced rolling acts as a spontaneous recovery mechanism, freeing the robot from clutter that would otherwise lead to failure and allowing locomotion to continue without additional control. Tests of the robot in an aquatic mangrove field demonstrate that these principles transfer to practical operation, enabling navigation and onboard visual inspection of inaccessible root zones. These results establish principles for hydro-cluttered locomotion and a design paradigm in which aquatic robots exploit environmental complexity as a locomotor resource.

cs.RO↗
arXiv2026

Flexible exponent of geometric 3-manifolds and Legendrian maps of Seifert spaces

A classical question in quantitative topology is to bound the mapping degree $\operatorname{deg}(f)$ in terms of its Lipchitz constant $\operatorname{Lip}(f)$. For a closed, oriented manifold $M$, the flexible exponent $\alpha(M)$ is the infimum of $\alpha\geq 0$ such that $|\operatorname{deg} f|\leq C(\operatorname{Lip} f)^\alpha$ holds for all differentiable map $f:M\to M$. The flexible exponent measures how effectively a manifold can wrap itself through self-maps. For geometric 3-manifolds $M$ in the sense of Thurston, we give the complete result for $\alpha(M)$: \[ \alpha(M)= \begin{cases} 3 & M \text{ modeled on } \mathbb S^3,\mathbb E^3,\mathbb S^2\times\mathbb E^1,\\ \frac83 & M \text{ modeled on Nil},\\ 2 & M \text{ modeled on Sol},\\ 1 & M \text{ modeled on }\mathbb H^2\times\mathbb E^1,\\ 0 & M \text{ modeled on } \mathbb H^3,\widetilde{\rm SL_2}. \end{cases} \] To prove $\alpha(M)=8/3$ for Nil 3-manifold $M$, we construct the so-called Legendrian map: a smooth self-map $f: M\to M$ such that $f$ is homotopic to the identity and $f$ maps all $S^1$-fibers into the orthogonal contact plane field simultaneously. Moreover, we prove that any Legendrian map must not be a diffeomorphism.

math.GT↗
arXiv2026

Flexible exponents of non-geometric 3-manifolds

A classical question in quantitative topology is to bound the mapping degree $\operatorname{deg}(f)$ in terms of its Lipchitz constant $\text{Lip}(f)$. For a closed, orientable, Riemannian manifold $M$, the flexible exponent $\alpha(M)$ is the infimum of $\alpha\geqslant 0$ such that $|\text{deg}(f)|\leqslant C\cdot (\text{Lip}(f))^\alpha$ holds for any Lipschitz map $f:M\to M$. For a geometric 3-manifold $M$ in the sense of Thurston, $\alpha(M)$ is determined in \cite{DLWWW}. In this paper, we determine $\alpha(M)$ for non-geometric 3-manifolds.

math.GT↗
arXiv2026

Non-isotopic surfaces in $T^4\#(S^2\times S^2)$: an example

We prove that there exist infinitely many embedded tori with a common geometric dual in $T^4\#(S^2\times S^2)$ that are homotopic, diffeomorphic, but not isotopic to each other, even after arbitrary many external stabilizations. These surfaces are obtained by applying the Norman trick to a fixed immersed surface, using non-homotopic tubing arcs. The isotopy classes of these surfaces are distinguished by homotopy classes of the 2-handles (relative to the boundary) in the complement of the image of the $0$- and $1$-handles.

math.GT↗
arXiv2026

Non-Existence of Smooth Full-Holonomy Cayley Fibrations

We prove that every Cayley fibration of a compact torsion-free Spin(7)-manifold with full holonomy must have singular fibers. This confirms a long-standing expectation in the study of calibrated fibrations with exceptional holonomy. Our argument first uses the rigidity of the Spin(7)-structure to reduce any hypothetical nonsingular Cayley fibration to two possible topological configurations. We then exclude both by proving a new spinnability theorem for smooth fiber bundles over simply-connected 4-manifolds with fiber homeomorphic to the elliptic surfaces E(2) or E(4). The E(4) case, which constitutes the main new difficulty, is established by combining families Seiberg--Witten theory with parametrized equivariant homotopy theory and equivariant K-theory.

math.DG↗
arXiv2026

A Robust Antenna Provides Tactile Feedback in a Multi-legged Robot

Multi-legged elongate robots hold promise for maneuvering through complex environments. Prior work has demonstrated that reliable locomotion can be achieved using open-loop body undulation and foot placement on rugose terrain. However, robust navigation through confined spaces remains challenging when body-environment contact is extensive and terrain rheology varies rapidly. To address this challenge, we develop a pair of tactile antennae for multi-legged robots that enable real-time sensing of surrounding geometry, modeling the morphology and function of biological centipede antennae. Each antenna features gradient compliance, with a stiff base and soft tip, allowing repeated deformation and elastic recovery. Robophysical experiments reveal a relationship between continuous antenna curvature and contact force, leading to a simplified mapping from antenna deformation to inferred discrete collision states. We incorporate this mapping into a controller that selects among a set of locomotor maneuvers based on the inferred collision state. Experiments in obstacle-rich and confined environments demonstrate that tactile feedback enables reliable steering and allows the robot to recover from near-stuck conditions without requiring global environmental information or real-time vision. These results highlight how mechanically tuned tactile appendages can simplify sensing and enhance autonomy in elongate multi-legged robots operating in constrained spaces.

cs.RO↗
arXiv2026

Pseudo-isotopies of 3-manifolds with infinite fundamental groups

Suppose $Y$ is a compact, connected, oriented 3-manifold possibly with boundary, such that $\pi_1(Y)$ is infinite. Let $\operatorname{Diff}_\partial(I\times Y)$ denote the group of self-diffeomorphisms of $I\times Y$ that are equal to the identity near the boundary. Let $\operatorname{Diff}_{PI}(I\times Y)$ denote the subgroup of $\operatorname{Diff}_\partial(I\times Y)$ consisting of elements pseudo-isotopic to the identity. Define $\operatorname{Homeo}_\partial(I\times Y)$, $\operatorname{Homeo}_{PI}(I\times Y)$ similarly for homeomorphisms. We show that the canonical map $\pi_0\operatorname{Diff}_{PI}(I\times Y) \to \pi_0\operatorname{Homeo}_{PI}(I\times Y)$ is of infinite rank. As a consequence, $\pi_0\operatorname{Diff}_{PI}(I\times Y)$, $\pi_0\operatorname{Diff}_{\partial}(I\times Y)$, $\pi_0\operatorname{Homeo}_{PI}(I\times Y)$, $\pi_0\operatorname{Homeo}_{\partial}(I\times Y)$ are all abelian groups of infinite rank. We also prove that $\pi_0\,C(Y)$ contains an abelian subgroup of infinite rank, and $\pi_0\,C(I\times Y)$ admits a surjection to an abelian group of infinite rank, where $C(X)$ denotes the concordance automorphism group $\operatorname{Diff}(I\times X, \{0\}\times X\cup I\times \partial X)$ or $\operatorname{Homeo}(I\times X, \{0\}\times X\cup I\times \partial X)$. These results are proved by studying the actions of barbell diffeomorphisms on the spaces of embedded arcs and configuration spaces.

math.GT↗
arXiv2025

Constraints on Lefschetz fibrations with four-dimensional fibers from Seiberg-Witten theory

We establish constraints on the topology of smooth Lefschetz fibrations with $4$-dimensional fibers, by studying the family Bauer-Furuta invariant. To compute this invariant, we analyze the framed bordism class of 1-dimensional Seiberg-Witten moduli spaces using the local index theorem by Bismut-Freed. Using this, we deduce new obstructions to the smooth isotopy to the identity for compositions of Dehn twists on $(-2)$-spheres in closed $4$-manifolds. We obtain several applications: (1) We exhibit the first examples of closed simply-connected symplectic $4$-manifolds admitting Torelli symplectomorphisms which are smoothly non-trivial. In particular, their symplectic Torelli mapping class group is not generated by squared Dehn-Seidel twists on Lagrangian spheres -- providing a negative answer to a question of Donaldson. (2) We provide the first examples of irreducible closed $4$-manifolds (both symplectic and non-symplectic) that admit exotic diffeomorphisms given by Seifert-fibered Dehn twist.

math.GT↗
arXiv2025

The Omega Turn: A General Turning Template for Elongate Robots

Elongate limbless robots have the potential to locomote through tightly packed spaces for applications such as search-and-rescue and industrial inspections. The capability to effectively and robustly maneuver elongate limbless robots is crucial to realize such potential. However, there has been limited research on turning strategies for such systems. To achieve effective and robust turning performance in cluttered spaces, we take inspiration from a microscopic nematode, C. elegans, which exhibits remarkable maneuverability in rheologically complex environments partially because of its ability to perform omega turns. Despite recent efforts to analyze omega turn kinematics, it remains unknown if there exists a wave equation sufficient to prescribe an omega turn, let alone its reconstruction on robot platforms. Here, using a comparative theory-biology approach, we prescribe the omega turn as a superposition of two traveling waves. With wave equations as a guideline, we design a controller for limbless robots enabling robust and effective turning behaviors in lab and cluttered field environments. Finally, we show that such omega turn controllers can also generalize to elongate multi-legged robots, demonstrating an alternative effective body-driven turning strategy for elongate robots, with and without limbs.

cs.RO↗
arXiv2025

Optimal swimming with body compliance in an overdamped medium

Elongate animals and robots use undulatory body waves to locomote through diverse environments. Geometric mechanics provides a framework to model and optimize such systems in highly damped environments, connecting a prescribed shape change pattern (gait) with locomotion displacement. However, the practical applicability of controlling compliant physical robots remains to be demonstrated. In this work, we develop a framework based on geometric mechanics to predict locomotor performance and search for optimal swimming strategies of compliant swimmers. We introduce a compliant extension of Purcell's three-link swimmer by incorporating series-connected springs at the joints. Body dynamics are derived using resistive force theory. Geometric mechanics is incorporated into movement prediction and into an optimization framework that identifies strategies for controlling compliant swimmers to achieve maximal displacement. We validate our framework on a physical cable-driven three-link limbless robot and demonstrate accurate prediction and optimization of locomotor performance under varied programmed, state-dependent compliance in a granular medium. Our results establish a systematic, physics-based approach for modeling and controlling compliant swimming locomotion, highlighting compliance as a design feature that can be exploited for robust movement in both homogeneous and heterogeneous environments.

cs.RO↗
arXiv2025

Robust control for multi-legged elongate robots in noisy environments

Modern two and four legged robots exhibit impressive mobility on complex terrain, largely attributed to advancement in learning algorithms. However, these systems often rely on high-bandwidth sensing and onboard computation to perceive/respond to terrain uncertainties. Further, current locomotion strategies typically require extensive robot-specific training, limiting their generalizability across platforms. Building on our prior research connecting robot-environment interaction and communication theory, we develop a new paradigm to construct robust and simply controlled multi-legged elongate robots (MERs) capable of operating effectively in cluttered, unstructured environments. In this framework, each leg-ground contact is thought of as a basic active contact (bac), akin to bits in signal transmission. Reliable locomotion can be achieved in open-loop on "noisy" landscapes via sufficient redundancy in bacs. In such situations, robustness is achieved through passive mechanical responses. We term such processes as those displaying mechanical intelligence (MI) and analogize these processes to forward error correction (FEC) in signal transmission. To augment MI, we develop feedback control schemes, which we refer to as computational intelligence (CI) and such processes analogize automatic repeat request (ARQ) in signal transmission. Integration of these analogies between locomotion and communication theory allow analysis, design, and prediction of embodied intelligence control schemes (integrating MI and CI) in MERs, showing effective and reliable performance (approximately half body lengths per cycle) on complex landscapes with terrain "noise" over twice the robot's height. Our work provides a foundation for systematic development of MER control, paving the way for terrain-agnostic, agile, and resilient robotic systems capable of operating in extreme environments.

cs.RO↗
arXiv2025

$\pi_1$-injective bounding and application to 3- and 4-manifolds

Suppose a closed oriented $n$-manifold $M$ bounds an oriented $(n+1)$-manifold. It is known that $M$ $\pi_1$-injectively bounds an oriented $(n+1)$-manifold $W$. We prove that $\pi_1(W)$ can be residually finite if $\pi_1(M)$ is, and $\pi_1(W)$ can be finite if $\pi_1(M)$ is. In particular, each closed 3-manifold $M$ $\pi_1$-injectively bounds a 4-manifold with residually finite $\pi_1$, and bounds a 4-manifold with finite $\pi_1$ if $\pi_1(M)$ is finite. Applications to 3- and 4-manifolds are given: (1) We study finite group actions on closed 4-manifolds and $\pi_1$-isomorphic cobordism of 3-dimensional lens spaces. Results including: (a) Two lens spaces are $\pi_1$-isomorphic cobordant if and only if there is a degree one map between them. (b) Each spherical 3-manifold $M\ne S^3$ can be realized as the unique non-free orbit type for a finite group action on a closed 4-manifold. (2) The minimal bounding index $O_b(M)$ for closed 3-manifolds $M$ are defined, %and bounding Euler charicteristic $\chi_b(M)$. the relations between finiteness of $O_b(M)$ and virtual achirality of aspherical (hyperbolic) $M$ are addressed. We calculate $O_b(M)$ for some lens spaces $M$. Each prime is realized as a minimal bounding index. (3) We also discuss some concrete examples:Surface bundle often bound surface bundles, and prime 3-manifolds often virtually bound surface bundles, $W$ bounded by some lens spaces realizing $O_b$ is constructed.

math.GT↗
arXiv2025

Dax invariants, light bulbs, and isotopies of symplectic structures

This paper addresses several isotopy problems on $4$-manifolds. First, we classify the isotopy classes of embeddings of $\Sigma$ in $\Sigma\times S^2$ that are geometrically dual to $\{\mbox{pt}\}\times S^2$, where $\Sigma$ is a closed oriented surface with a positive genus, and show that there exist infinitely many such embeddings that are homotopic to each other but mutually non-isotopic, thereby answering a question of Gabai. By combining this construction with techniques from symplectic topology, we also answer Problem 2(a) in McDuff-Salamon's problem list and a question of Cieliebak-Eliashberg-Mishachev, which concern the uniqueness and $h$-principle of symplectic structures on closed $4$-manifolds. We answer these questions by establishing the following results: (1) The space of symplectic forms on every irrational ruled surface homologous to a fixed symplectic form has infinitely many connected components; (2) There exist infinitely many symplectic forms on every irrational ruled surface that are formally homotopic, cohomologous, but not homotopic to each other. Both are the first such examples for closed $4$-manifolds. The proofs are based on a generalization of the Dax invariant to embedded closed surfaces. In the course of the proof, we obtain several properties of the smooth mapping class group of $\Sigma\times S^2$, which may be of independent interest. For example, we show that there exists a surjective homomorphism from $\pi_0\operatorname{Diff}(\Sigma\times S^2)$ to $\mathbb{Z}^\infty$, such that its restriction to the subgroup of elements pseudo-isotopic to the identity is of infinite rank.

math.GT↗
arXiv2025

On the mapping class groups of 4-manifolds with 1-handles

We develop a framework that generalizes Budney-Gabai's $W_3$ invariant on $\pi_0\textrm{Diff}(S^1\times D^3,\partial)$ to 4-manifolds with 1-handles. As applications, we show that if $M=(S^1\times D^3)\natural \hat M$ where $\hat M$ either has the form $I\times Y$ or is a punctured aspherical manifold, then the center of the mapping class group of $M$ is of infinite rank.

math.GT↗