SlideIn2D: 2D Sliding Mechanisms

• SlideIn2D is a cross-domain label uniting diverse 2D sliding phenomena by elevating constrained motion to a primary state variable.
• It spans applications in ferroelectric bilayers, planar mechanics, robotic pursuit–evasion, atomistic friction, and immersive video interfaces.
• Studies of SlideIn2D provide practical insights into mechanisms like curvature-induced polarization, sliding vector algebra, and dynamic motion planning.

“SlideIn2D” is not a single standardized term in the arXiv literature. In the cited corpus, it functions as a cross-domain label for technically distinct 2D sliding-centered constructs: curvature-induced polarization control in van der Waals bilayers, planar sliding vectors and line bivectors in mechanics, sliding-robot pursuit–evasion in orthogonal polygons, atomistic and coarse-grained models of 2D frictional sliding, and a desktop interaction technique for comparing immersive videos (He et al., 2024, Faris, 2021, Ghodsi et al., 2016, Teruzzi et al., 2017, Wang et al., 2023, Wang et al., 22 Feb 2026). The common denominator is the elevation of sliding from a kinematic detail to a primary state variable, but the underlying objects range from interlayer registry and ferroelectric domain walls to force lines of action, guarded visibility strips, moiré solitons, and viewport allocations.

1. Terminological scope

In the cited works, “SlideIn2D” is best understood as a family resemblance rather than a unified formalism. Each usage specializes “slide” and “2D” differently.

Domain	Core object	Representative paper
vdW electromechanics	Curvature-induced interlayer sliding and stacking transitions	(He et al., 2024)
Planar mechanics	Sliding vectors $P \wedge u$ and line bivectors	(Faris, 2021)
Computational geometry and robotics	Robots constrained to orthogonal sliding segments	(Ghodsi et al., 2016)
Friction and coarse-graining	2D sliding islands, moiré dynamics, MSM reduction	(Teruzzi et al., 2017, Wang et al., 2023)
Immersive media interfaces	Slider-based 2D comparison of two 360° videos	(Wang et al., 22 Feb 2026)

This range matters because superficially similar language masks different ontologies. In one setting, sliding is an interlayer translation vector that acts as a ferroelectric order parameter; in another, it is an equivalence class of bound forces along a line; elsewhere, it is a constrained robot trajectory, a tribological collective variable, or an interface technique that reallocates screen space between two immersive videos. A plausible implication is that “SlideIn2D” is most useful as an indexing label for 2D sliding-mediated behavior, not as a domain-independent theorem or architecture.

2. Sliding ferroelectric bilayers and “sliding flexoelectricity”

In two-dimensional sliding ferroelectrics, out-of-plane polarization does not arise from ionic off-centering but from interlayer charge transfer controlled by stacking. For bilayer h-BN and 3R-MoS$_2$, AB and BA stackings are energetically favorable and carry opposite out-of-plane polarization $P_z$; SP is polar with in-plane polarization only, and AA is centrosymmetric and non-polar. In parallel bilayer h-BN, the lattice constant is $a = 2.51$ Å, the interlayer distance is $D \approx 3.25$ Å, $P_z \approx +1.46\ \mathrm{pC/m}$ for AB and $P_z \approx -1.46\ \mathrm{pC/m}$ for BA, while SP has purely in-plane polarization $\approx 1.53\ \mathrm{pC/m}$ and AA has $P = 0$. Bending is modeled under the constraint of nearly fixed interlayer distance and in-plane lattice constants, so the geometry necessarily induces relative sliding with

$\Delta d = \theta \times D,$

where $_2$0 is in radians. Under these conditions, bent bilayers do not remain smoothly arced beyond threshold angles; they relax into kinks that contain ferroelectric domain walls (He et al., 2024).

For bilayer h-BN nanoribbons, the relaxed morphology is piecewise. When $_2$1, the system returns to a flat AB configuration with $_2$2. For $_2$3, a single $_2$4 kink forms, with stacking sequence AB $_2$5 SP $_2$6 BA. For $_2$7, two kinks form, with relaxed angles $_2$8 and $_2$9, corresponding to domain walls crossing SP and AA stackings. The $P_z$0 kink is a Néel-type wall: $P_z$1 rotates through an in-plane-polar SP core. The $P_z$2 kink is an Ising-type wall: $P_z$3 reverses through a non-polar AA core. Comparable behavior appears in 3R-MoS$P_z$4, with kink angles approximately $P_z$5 and $P_z$6, reflecting its larger interlayer distance $P_z$7 Å and larger bending modulus $P_z$8.

The paper explicitly distinguishes this mechanism from conventional strain-gradient flexoelectricity. The polarization change is mediated not by vertical ionic displacement within a monolayer but by curvature-induced interlayer sliding, stacking reconstruction, and domain-wall formation. The authors term this “sliding flexoelectricity.” This suggests a non-linear electromechanical coupling in which curvature controls interlayer registry, registry controls local polarization, and threshold crossing produces discrete domain rearrangements rather than a single linear flexoelectric coefficient.

3. Planar sliding vectors, line bivectors, and statics

In planar mechanics, the relevant “slide” is not interlayer registry but the freedom of a non-zero vector to move along its line of action. A sliding vector is a pair $P_z$9, where $a = 2.51$0 is a line in an affine Euclidean space and $a = 2.51$1 is a vector parallel to that line. The paper writes this object as $a = 2.51$2, meaning the equivalence class of bound vectors $a = 2.51$3 with $a = 2.51$4 anywhere on the line parallel to $a = 2.51$5. Formally, $a = 2.51$6 iff $a = 2.51$7 and $a = 2.51$8 is collinear with $a = 2.51$9. In two dimensions, the set of sliding vectors has dimension $D \approx 3.25$0, and the ambient line-bivector space $D \approx 3.25$1 also has dimension $D \approx 3.25$2 (Faris, 2021).

The central algebraic statement is that every line bivector can be written as

$D \approx 3.25$3

with $D \approx 3.25$4 and $D \approx 3.25$5. In 2D, $D \approx 3.25$6 is one-dimensional, so $D \approx 3.25$7 is a pure couple or scalar moment. Accordingly, every planar line bivector is either a sliding vector or a pure couple. The associated moment function is

$D \approx 3.25$8

which is an affine map from points in the plane to bivectors. In coordinates, if a force $D \approx 3.25$9 acts at $P_z \approx +1.46\ \mathrm{pC/m}$0, its scalar moment about the origin is

$P_z \approx +1.46\ \mathrm{pC/m}$1

This formulation clarifies several classical facts of planar statics. A force can be slid along its line of action without changing the sliding vector. Two equal and opposite parallel forces at different points produce a pure couple rather than a single resultant sliding vector. Any planar force system therefore reduces to a resultant force plus a scalar torque. The significance of the paper is not a new planar mechanics law but a precise Grassmann-algebraic and projective-geometric restatement of familiar statics, including the 2D degeneration of 3D screw theory.

4. Sliding robots in orthogonal polygons

In pursuit–evasion geometry, “SlideIn2D” refers to robots constrained to move back and forth along fixed orthogonal segments inside a simple orthogonal polygon $P_z \approx +1.46\ \mathrm{pC/m}$2. A point $P_z \approx +1.46\ \mathrm{pC/m}$3 is covered by a sliding robot moving on a segment $P_z \approx +1.46\ \mathrm{pC/m}$4 if there exists $P_z \approx +1.46\ \mathrm{pC/m}$5 such that $P_z \approx +1.46\ \mathrm{pC/m}$6 is perpendicular to $P_z \approx +1.46\ \mathrm{pC/m}$7 and lies entirely within $P_z \approx +1.46\ \mathrm{pC/m}$8. The sliding visibility polygon is therefore

$P_z \approx +1.46\ \mathrm{pC/m}$9

The paper assumes a set $P_z \approx -1.46\ \mathrm{pC/m}$0 such that $P_z \approx -1.46\ \mathrm{pC/m}$1, and it considers evaders that are mobile, adversarial, invisible except when seen, and have unbounded speed (Ghodsi et al., 2016).

The geometric core of the algorithm is a window decomposition induced by reflex vertices. Extending the incident edges of each reflex vertex inward yields windows that partition the polygon into orthogonal rectangles. The motion planner then maintains clearance information using four boolean flags $P_z \approx -1.46\ \mathrm{pC/m}$2 per reflex vertex and three per-robot storage sets $P_z \approx -1.46\ \mathrm{pC/m}$3, $P_z \approx -1.46\ \mathrm{pC/m}$4, and $P_z \approx -1.46\ \mathrm{pC/m}$5, representing, respectively, what has been cleared, what remains to be cleared, and what must be cleared before the robot can continue. Event points occur when a robot sees a reflex vertex, sees a waiting sliding robot, or reaches an endpoint of its segment.

The main theorem states that if $P_z \approx -1.46\ \mathrm{pC/m}$6 is a simple orthogonal polygon and $P_z \approx -1.46\ \mathrm{pC/m}$7 is a set of line segments whose sliding visibility polygons cover $P_z \approx -1.46\ \mathrm{pC/m}$8, then there is a motion-planning algorithm for sliding robots moving on the segments of $P_z \approx -1.46\ \mathrm{pC/m}$9 that finds all evaders while using at most $\approx 1.53\ \mathrm{pC/m}$0 robots. A corollary states that if $\approx 1.53\ \mathrm{pC/m}$1 is a minimum-cardinality sliding-camera guard set, then the clearing strategy uses the minimum number of sliding robots. A common misconception in this setting would be to equate static coverage with dynamic clearing. The paper’s contribution is precisely the additional scheduling machinery needed to prevent recontamination in the presence of arbitrarily fast evaders.

5. Atomistic sliding, moiré physics, and reduced models of 2D friction

In tribology and statistical physics, “SlideIn2D” centers on relative motion at atomically thin interfaces. One thread analyzes a 2D Frenkel–Kontorova-type model consisting of a hexagonal island of $\approx 1.53\ \mathrm{pC/m}$2 harmonically bound particles sliding over a rigid 2D triangular periodic potential with incommensurate lattice ratio $\approx 1.53\ \mathrm{pC/m}$3. The dynamics are overdamped Langevin, the driving spring constant is $\approx 1.53\ \mathrm{pC/m}$4, the external velocity is $\approx 1.53\ \mathrm{pC/m}$5, and trajectories of about $\approx 1.53\ \mathrm{pC/m}$6 timesteps are coarse-grained using non-equilibrium Markov State Modeling. Configurations are clustered with the Density Peak algorithm under a metric defined modulo substrate periodicity, and with lag time $\approx 1.53\ \mathrm{pC/m}$7 the transfer-matrix spectrum yields a very small number of slow variables sufficient to describe the sliding dynamics of the island (Teruzzi et al., 2017).

The physical interpretation of those slow variables connects directly to the broader theory of structurally lubric 2D interfaces. In the Colloquium on graphene and related interfaces, an ideal infinite defect-free incommensurate interface is “structurally superlubric,” with $\approx 1.53\ \mathrm{pC/m}$8. Real finite systems are “structurally lubric”: their interiors remain unpinned, but edges and defects produce nonzero static friction obeying

$\approx 1.53\ \mathrm{pC/m}$9

with $P = 0$0 reported for circular graphene islands at $P = 0$1. Kinetic friction separates into a bulk superlubric contribution, linear in area and velocity, and an edge-dominated stick–slip contribution that is also subextensive,

$P = 0$2

The moiré period for twisted or lattice-mismatched interfaces is

$P = 0$3

and moiré solitons, corrugation, island boundaries, velocity, temperature, load, and contaminants govern the crossover between smooth viscous sliding and pinned stick–slip behavior (Wang et al., 2023).

Taken together, these papers show two complementary reductions of 2D sliding. The MSM work reduces a high-dimensional non-equilibrium trajectory to a few slow modes; the structurally lubric framework reduces a broad class of interfaces to the competition among incommensurability, elasticity, moiré reconstruction, and defects. This suggests that, even in large 2D sliding systems, a small number of collective variables—center-of-mass advance, soliton rearrangement, work bursts, edge pinning—can dominate the observable dynamics.

6. SlideIn2D as a desktop technique for immersive video comparison

A distinct and explicit usage of the term is the interaction technique “SlideIn2D,” introduced for comparing two immersive 360° videos on a desktop display. The interface is web-based and contains a top toolbar, a central canvas, and bottom controls. Within the canvas, two 3D perspective viewports are stacked: a back-layer immersive video is always fully visible, while a top-layer immersive video appears as a movable partial overlay. Both videos are rendered as perspective projections of a monoscopic 360° sphere with fixed vertical field of view $P = 0$4, and horizontal field of view computed as

$P = 0$5

In the implementation, the maximum horizontal field of view is approximately $P = 0$6 (Wang et al., 22 Feb 2026).

The interaction model simplifies a broader sliding concept into desktop-specific operations. The top-layer viewport has a single draggable vertical slider attached to its right edge; moving this edge reallocates horizontal screen space, thereby hybridizing side-by-side and overlay comparison. A Swap button exchanges foreground and background roles. Pressing P activates a peek mode that temporarily reveals a $P = 0$7 patch of the back-layer video at the mouse position, corresponding to about $P = 0$8 field of view. The system also provides ROIs SxS and ROIs Overlay macros that automatically reorient cameras and adjust the slider so that tracked regions of interest appear either side-by-side or aligned in overlay. Each video has an azimuthal equidistant minimap showing the current footprint, an ROI marker, and a gradient-encoded ROI trajectory from red to green.

The paper evaluates SlideIn2D against SlideInVR, ToggleInVR, ToggleIn2D, and SideBySideIn2D in a within-subjects user study with $P = 0$9. SlideIn2D achieved mean accuracy $\Delta d = \theta \times D,$0 with SD $\Delta d = \theta \times D,$1 and $\Delta d = \theta \times D,$2, the highest numerical mean among the five techniques, although the mixed-effects logistic regression found no significant main effect of technique. Its mean UMUX-Lite score was $\Delta d = \theta \times D,$3. In overall ranking, SlideIn2D appeared in the top two for $\Delta d = \theta \times D,$4 of participants, and pairwise testing showed it was preferred to ToggleIn2D with $\Delta d = \theta \times D,$5. The technique’s significance lies in integrating side-by-side and overlay within a single 2D interface, rather than forcing a fixed comparison mode for immersive media.

7. Cross-cutting structure and recurring distinctions

A common misconception would be to read all of these usages as variants of one method. The cited literature instead shows a shared structural motif: a constrained sliding degree of freedom becomes the mechanism by which a 2D system changes state. In sliding ferroelectric bilayers, bending generates a stacking gradient and thereby polarization reversal (He et al., 2024). In planar mechanics, sliding along a line preserves the equivalence class $\Delta d = \theta \times D,$6 while changing the point of application (Faris, 2021). In orthogonal pursuit–evasion, the robot’s legal motion is restricted to a segment, and the induced perpendicular visibility defines what can be cleared (Ghodsi et al., 2016). In 2D tribology, relative sliding reorganizes moiré patterns, solitons, and defect-mediated barriers (Wang et al., 2023). In immersive media, a slider reallocates pixel visibility between two spherical-video projections (Wang et al., 22 Feb 2026).

Another recurring distinction is between idealized and realized sliding. The ferroelectric paper distinguishes sliding flexoelectricity from conventional strain-gradient flexoelectricity. The mechanics paper distinguishes a sliding vector from a pure couple. The robotics paper distinguishes static coverage from dynamic clearing. The tribology Colloquium distinguishes structural superlubricity, structural lubricity, and engineering superlubricity. The immersive-video paper distinguishes SlideIn2D from pure side-by-side and pure toggle comparison. These are not minor taxonomic refinements; they define what the sliding degree of freedom actually does in each system.

A plausible synthesis is that “SlideIn2D” marks a research pattern in which low-dimensional geometric constraints create high-leverage control variables. Whether the controlled quantity is $\Delta d = \theta \times D,$7, resultant moment, contamination status, frictional dissipation, or comparison layout, the underlying logic is similar: a 2D sliding coordinate mediates access to otherwise difficult state transitions. That recurring logic explains why the same label can plausibly index topics as far apart as van der Waals ferroelectrics, screw theory, orthogonal search, atomistic friction, and immersive-video interfaces.