arXiv subjects

Yuan Yu

Publications and source records attributed to Yuan Yu.

At least 19 recordsLinked to original sources

arXiv2026

Equilibrium-energy-scaled quantum lattice Boltzmann method for variable-velocity linear advection--diffusion equations

We develop a quantum lattice Boltzmann method for linear advection--diffusion equations with prescribed space- and time-dependent velocities. Direct block-encoding can accumulate normalization factors that suppress success probability exponentially, even when the classical propagator remains bounded. We control this loss by scaling each distribution component by the inverse square root of its local equilibrium weight. For uniformly positive weights and dimensionless relaxation times $τ^*\geq 1/2$, this equilibrium energy scaling gives the Bhatnagar--Gross--Krook collision operator unit spectral norm while preserving the discrete dynamics. Streaming normalization depends on weight ratios at the departure and arrival positions and times of each step; these ratios equal one for uniform steady advection. For periodic streaming, cumulative normalization stays bounded under mesh refinement at fixed physical time if logarithmic derivatives of the weights along streaming trajectories are bounded uniformly in space, time, and mesh resolution. A single-step block-encoding with two flag qubits supports coherent propagation of the full kinetic distribution without intermediate measurements. We compare oracle query bounds for time marching with those for a history-state linear system built from the same scaled operator, under specified assumptions on initial-state preparation and coefficient access. Tests in one and two dimensions and noiseless circuit simulations verify the construction. In a controlled comparison after 50 steps, scaling increases the probability of preparing the quantum state encoding the terminal distribution by approximately $450\times$. Classical refinement diagnostics up to $N_t=16{,}384$ steps confirm bounded cumulative normalization. The scaling controls additional normalization losses while retaining physical diffusive attenuation.

math-ph↗

arXiv2026

A hybrid quantum-classical lattice kinetic scheme with tensor-train feedback for incompressible flows

Nonlinear lattice kinetic simulation requires each updated distribution to supply the velocity and gradients that determine the next step. In a quantum-classical solver, reading out the full distribution incurs work proportional to the lattice size. We construct a tensor-train (TT) interface that retains reusable classical cores at the physical amplitude scale for a full-relaxation lattice kinetic scheme. The cores supply nonlinear coefficients and prepare each quantum input. Energy-scaled propagation and coordinate recovery encode the updated distribution, and alternating least-squares reconstruction converts signed Hadamard-test overlaps into output cores by restoring a known normalization factor. The next step starts from accepted cores without replaying previous quantum evolution. Under positive, unit-sum reference coefficients, positive lower and finite upper density bounds, and Lipschitz equilibrium sensitivity, perturbation bounds relate local defects to feedback errors. Resource bounds account for classical operations, circuit execution, sampling, and verification. Classical diagnostics expose why distribution accuracy alone is insufficient: in 80-step feedback on a $16\times16$ grid, rank cap 4 nearly eliminates the vortex despite a final distribution error below $1\%$, whereas rank cap 12 gives relative velocity error $1.03\times10^{-3}$. Four-step binomial readout simulations show that tightening core sampling tolerance threefold raises the prescribed sufficient budget from $5.97\times10^{12}$ to $5.37\times10^{13}$ shots as the result approaches the fixed-rank, fixed-sweep exact-overlap trajectory. The interface therefore provides a way to connect quantum propagation to nonlinear feedback and to assess the separate demands of compression, velocity accuracy, and readout precision.

math-ph↗

arXiv2026

Residual correction for accelerating dual-time-stepping lattice Boltzmann methods

For lattice Boltzmann simulations of unsteady flows at low Reynolds numbers, dual-time stepping decouples the physical time step from lattice streaming, yet conserved-moment iteration errors decay slowly at large steps. We develop a residual correction method based on the conserved-moment structure of the collision operator. With fixed step histories and both relaxation rates equal to unity, post-collision populations depend on incoming populations only through reconstructed conserved moments, so one collision eliminates local perturbations with zero conserved moments. Periodic rest-state linearization shows that, at large physical steps, the contraction factor of the uniform conserved mode approaches unity, while its moment residual scales inversely with the step relative to macroscopic error. On periodic domains, combining this scaling with linearized acoustic propagation and viscous diffusion yields a macroscopic auxiliary system driven by the conserved-moment residual and solved in Fourier space for low-wavenumber errors. For solid walls, reference-state linearization of the complete sweep, including executed bounce-back updates, yields a sparse kinetic correction. Both auxiliary systems compute increments from the full nonlinear residual, and we prove fixed-point equivalence with the original discrete system, preserving unsteady and nonlinear convective effects. Refining the time step on fixed grids verifies second-order temporal self-convergence of slowly varying periodic velocity fields in two and three dimensions. Under fixed physical steps and tolerances, mean inner sweeps per step drop from hundreds in three-dimensional periodic flow and thousands in a two-dimensional cavity to a few.

physics.flu-dyn↗

arXiv2026

A deterministic Fokker--Planck/lattice-Boltzmann micro--macro solver for dilute Hookean polymer solutions

Deterministic micro--macro simulation of polymer solutions requires the coupled evolution and spatial transport of a configuration distribution, together with the conversion of its moments into macroscopic stress and feedback to the flow. We develop a Fokker--Planck/lattice-Boltzmann solver for this coupling in two-dimensional dilute Hookean polymer solutions. The solver represents the distribution on the unbounded configuration space by Hermite coefficient fields, advances local configuration dynamics and physical-space transport in separate steps, and recovers Kramers stress from the second moment to achieve two-way coupling with a purified two-relaxation-time lattice-Boltzmann flow solver. To assess whether this configuration description recovers the corresponding macroscopic response, we use the exact second-moment closure of the continuous Hookean model as a macroscopic reference for comparison with analytical and independently discretized macroscopic solutions. The calculations reproduce velocity overshoot and damped oscillations in start-up Poiseuille flow, with velocity profiles approaching the analytical start-up transient under grid refinement; in four-roll flow with spatially nonuniform extension and stress feedback, the maximum full-domain relative differences in velocity and polymer stress are approximately $0.0309\%$ and $3.84\%$, respectively, over the tested Weissenberg numbers at corresponding sampling times. These comparisons support the solver's ability to recover the Hookean macroscopic response from configuration-distribution evolution. Further calculations of wall-bounded recirculation and open cross-slot flow exhibit the corresponding conformation responses and symmetric and asymmetric flow states, extending this deterministic micro--macro method to viscoelastic flows under different boundary constraints.

physics.flu-dyn↗

arXiv2026

Maia 200: A Software Defined Dataflow System for Large-scale AI Acceleration

We introduce Maia 200, an advanced AI accelerator delivering high performance-10 145 Tflop/s FP4 and 5072 Tflop/s FP8 within a 750W TDP and 7 TB/s HBM bandwidth. Maia exemplifies a new class of Software Defined Locally Accessed Dataflow Architectures (SDLA), which explicitly program dataflow engines to orchestrate highly specialized memories and data movement engines. This approach shifts the focus from today's thread-centric to data-movement-centric architecture, improving efficiency and scalability. Our taxonomy of data management, inspired by Flynn's classification, highlights how SDLA addresses challenges in modern AI computing. Maia 200 achieves significant cost and energy savings while supporting massive parallelism for AI inference workloads, making it a compelling solution for next-generation high-performance computing systems.

cs.AR↗

arXiv2026

Loss of positive definiteness is a symptom, not the cause, of high-Weissenberg-number breakdown

Numerical breakdown at high Weissenberg number is often attributed to loss of symmetric positive definiteness (SPD) of the conformation tensor. That conclusion follows from Maxwell-type models without solvent viscosity. With solvent fraction $β>0$, the initial-value problem is locally well posed for arbitrary symmetric stress. We derive the missing quantitative theory for indefinite states and test its computational consequences. Frozen-coefficient analysis gives a growth rate uniformly bounded in wavenumber and the direction-resolved instability threshold $λ_{\min}(A)<-β/(1-β)$; stress diffusion supplies a closed-form cutoff, while the classical $σ\propto k$ catastrophe is recovered as solvent viscosity vanishes. A determinant identity shows that violations self-heal on the timescale $λ/2$, so persistent violations measure the truncation error that recreates them. Spectral and lattice Boltzmann tests reproduce the threshold, solvent-fraction reversal, and resolution independence. In four-roll-mill interventions, enforcing SPD delays blow-up by 15 convective times but reduces the stagnation-point Weissenberg number by 30%. Across five coupling schemes, a local second-moment stress source remains stable through the full budget at $\mathrm{Wi}=50$ while carrying $\det A\approx-8.5\times10^5$; the divergence-coupled variant fails at $t^*=47$. The surviving scheme matches published benchmarks within 0.05% and 0.18% at $\mathrm{Wi}=10$ and 20. Thus loss of positive definiteness is neither necessary nor sufficient for breakdown: the discrete coupling route decides, and the violation is a resolution gauge for which we provide run-time monitors.

physics.comp-ph↗

arXiv2026

Static compliance and directional instability in indefinite conformation states

A conformation tensor is positive definite for every physically realizable polymer microstructural state. Numerical discretization can move the conformation tensor outside the positive-definite domain. This raises a question: can the least eigenvalue alone identify the first unstable direction? We answer it by linearizing Oldroyd-B, equilibrium-normalized FENE-P and Giesekus models about uniform frozen states. All include solvent viscosity and stress diffusion. We examine every non-zero planar Fourier mode, assuming each model's uncoupled constitutive tangent is strictly stable. The margin $1+rχ$ measures the balance between solvent damping and the zero-frequency polymer response. The complete velocity--conformation system is stable if and only if this margin is positive. At zero margin, a simple stationary root appears; finite inertia changes growth rates but not the neutral boundary. At fixed wavenumber and other parameters, decreasing $λ_1$ identifies the first neutral direction. Oldroyd-B and equilibrium-normalized FENE-P first become neutral along principal directions; Giesekus mobility can instead make an oblique direction neutral first. For the reference case, onset is $λ_{1,c}=-1.933$ at $θ_c=23.94^\circ$, before the principal-axis prediction. Along this family, the all-direction threshold approaches $-2.319$ as the other principal stretch grows, whereas the formal principal-axis extrapolation tends to negative infinity. A rational-parameter counterexample, matrix spectra and uniform forced-base calculations test the neutral boundary and both sides. These results concern one linear, uniform, planar Fourier mode, not nonlinear or inhomogeneous-flow stability. Within this scope, onset depends not on indefiniteness alone but also on constitutive-tangent geometry and wavevector direction.

cond-mat.soft↗

arXiv2026

Smooth-Curvature Bend Design Guided by Variational Analysis for Adiabatic Multimode Integrated Photonics

Multimode photonic integrated circuits enable ultralow-loss on-chip optical interconnects and microwave-photonic processing, yet waveguide bends dominate both chip footprint and excess loss. A high-performance multimode waveguide bend (MWB) must transmit the working mode with low loss while suppressing intermodal coupling, forcing a trade-off among bending radius, operating bandwidth, and fabrication tolerance. Here we formulate constant-width MWB design as a curvature-dependent variational problem. By constructing a figure of merit that incorporates higher-order-mode excitation, fundamental-mode mismatch, and sidewall field intensity, we derive a necessary condition for adiabatic optimality: the curvature profile must approach infinite differentiability throughout the bend, including its junctions with the input and output straight waveguides. This condition explains the limitations of circular and Euler bends and motivates a smooth polynomial curvature (SPC) family with a closed-form beta-function representation. We further introduce an optimized SPC hybrid (SPCh) bend that balances junction smoothness and the interior curvature gradient. On the 220 nm silicon-on-insulator platform, SPCh bends achieve a mode extinction ratio below $-37$ dB from 1500-1600 nm at an effective radius of $16\,μ\mathrm{m}$, providing more than 22 dB stronger mode suppression than a representative Euler bend at the same radius. The simulated response remains robust to $\pm 60$ nm waveguide-width deviations. Fabricated SPCh-based microring resonators reach an intrinsic quality factor of up to $7.53 \times 10^6$ and a free spectral range of up to 100 GHz through a standard silicon foundry process. The resulting design strategy provides compact, broadband, and fabrication-tolerant multimode bends for high-density optical interconnects and microwave-photonic systems.

physics.optics↗

arXiv2026

Purified Two-Relaxation-Time Lattice Boltzmann Method: Removing Ghost Modes from TRT for Enhanced Stability

The two-relaxation-time (TRT) lattice Boltzmann model is widely adopted for its simplicity and tunable boundary accuracy. However, its collision operator relaxes the full symmetric non-equilibrium component, implicitly retaining non-hydrodynamic ghost modes that degrade stability at high Reynolds numbers. In this work, we establish a rigorous connection between ghost-mode filtering and regularization within the TRT framework. By decomposing the discrete velocity space into hydrodynamic and non-hydrodynamic subspaces, we prove that the TRT-regularized lattice Boltzmann (TRT-RLB) model is mathematically equivalent to the standard TRT model with ghost modes explicitly removed. This equivalence holds exactly for D2Q9 and D3Q19 lattices, where the symmetric and antisymmetric subspaces are completely spanned by the physically relevant Hermite modes and identifiable ghost modes. Based on this finding, we propose the Purified TRT (P-TRT) model, which achieves regularization-level stability through simple algebraic ghost-mode subtraction rather than expensive tensor projections. For D2Q9, the non-equilibrium collision cost is reduced from 180 to 52 floating-point operations per node, a 71% reduction. Linear stability analysis in moment space further reveals that the P-TRT operator annihilates the ghost eigenvalue, proving its spectral radius is bounded above by that of standard TRT and that stability is governed exclusively by hydrodynamic modes. Benchmarks including the double shear layer at Re up to 10^7, Taylor--Green vortex decay, force-driven Poiseuille flow, and creeping flow past a square cylinder confirm that P-TRT preserves the stability, second-order accuracy, and zero-slip boundary properties of TRT-RLB while retaining the simplicity of the TRT family.

physics.flu-dyn↗

arXiv2025

Intelligent Configuration of Integrated Microwave Photonic Filter Featuring Self-Stabilization and Programmable Response

Integrated microwave photonic filters (IMPFs) emerge as promising candidates for advanced microwave systems owing to their distinctive combination of wide operational bandwidth, flexibility, and compact size. Nevertheless, the complex and time-consuming manual manipulation of IMPFs remains a significant impediment to their widespread applications. Here, to the best of the knowledge, the first intelligent configuration of IMPF is experimentally demonstrated, featuring wideband center frequency tunability, flexible bandwidth reconfigurability, self-stabilization, and excellent channel equalization simultaneously. The configuration is enabled by our proposed universal hybrid collaboration strategy, which fully unleashes the hardware potential of the optical device, thus enabling comprehensive synergy of multiple properties. Results show that the center frequency of IMPF is tuned from 2 to 48 GHz, covering microwave S band to Ka band, and the bandwidth is reconfigured from 0.66 to 4.15 GHz, with a rejection ratio of up to 37.67 dB. The roll-off rate and shape factor reach as high as 17.50 dB GHz-1 and 0.78, respectively. Meanwhile, the maximum center frequency drift of IMPF over 3 h is reduced from 11.950 to 0.051 GHz even without a thermo-electric cooler, indicating that the center frequency stability is enhanced by 234 times. The passband shape of the IMPF is dynamically adjusted to equalize frequency-dependent fading, achieving up to 2.42 dB of intra-channel fading compensation. This work highlights the potential of IMPFs based on intelligent configuration, unlocking new avenues for practical applications of microwave photonic signal processing.

physics.optics↗

arXiv2025

An improved lattice Boltzmann method with a novel conservative boundary scheme for viscoelastic fluid flows

The high Weissenberg number problem has been a persistent challenge in the numerical simulation of viscoelastic fluid flows. This paper presents an improved lattice Boltzmann method for solving viscoelastic flow problems at high Weissenberg numbers. The proposed approach employs two independent two-relaxation-time regularized lattice Boltzmann models to solve the hydrodynamic field and conformation tensor field of viscoelastic fluid flows, respectively. The viscoelastic stress computed from the conformation tensor is directly embedded into the hydrodynamic field using a newly proposed local velocity discretization scheme, thereby avoiding spatial gradient calculations. The constitutive equations are treated as convection-diffusion equations and solved using an improved convection-diffusion model specifically designed for this purpose, incorporating a novel auxiliary source term that eliminates the need for spatial and temporal derivative computations. Additionally, a conservative non-equilibrium bounce-back (CNEBB) scheme is proposed for implementing solid wall boundary conditions in the constitutive equations. The robustness of the present algorithm is validated through a series of benchmark problems. The simplified four-roll mill problem demonstrates that the method effectively improves numerical accuracy and stability in bulk regions containing stress singularities. The Poiseuille flow problem validates the accuracy of the current algorithm with the CNEBB boundary scheme at extremely high Weissenberg numbers (tested up to Wi = 10,000). The flow past a circular cylinder problem confirms the superior stability and applicability of the algorithm for complex curved boundary problems compared to other existing common schemes.

physics.flu-dyn↗

arXiv2025

A fluctuating lattice Boltzmann method for viscoelastic fluid flows

This study introduces a novel fluctuating lattice Boltzmann (LB) method for simulating viscoelastic fluid flows governed by the Oldroyd-B model. In contrast to conventional LB approaches that explicitly compute the divergence of the polymer stress tensor using finite-difference schemes, the proposed method incorporates the polymer stress implicitly by introducing a polymer stress fluctuation term directly into the evolution equation. This treatment avoids the need for stress-gradient computations, and preserves the physical characteristics of viscoelastic fluid flows. The proposed method is validated against four classical benchmark problems: the simplified four-roll mill, planar Poiseuille flow, unsteady Womersley flow, and the three-dimensional Taylor-Green vortex. The numerical results show excellent agreement with analytical solutions and previous numerical results, confirming the method's reliability in viscoelastic fluid dynamics. Moreover, performance evaluations demonstrate that the present model reduces the memory occupancy and enhances computational efficiency, highlighting its potential for large-scale simulations of complex viscoelastic flows systems.

physics.flu-dyn↗

arXiv2025

Lattice Boltzmann simulation reveals supercritical bifurcation in flow mode transitions of power-law fluids in the four-roll mill

The four-roll mill has been traditionally viewed as a device generating simple extensional flow with a central stagnation point. Our systematic investigation using a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model reveals unexpected richness in the flow physics, identifying two previously unreported supercritical bifurcation modes: a quadrifoliate vortex mode featuring four symmetrical counter-rotating vortices, and a dumbbell-shaped quad-vortex mode where vortices detach from but remain symmetric about the stagnation point. The numerical framework, representing the first successful extension of TRT-RLB method to power-law fluid dynamics, enables comprehensive mapping of flow characteristics across Reynolds numbers ($1 \leq Re \leq 50$), power-law indices ($0.7 \leq n \leq 1.3$), and geometric configurations. The transition from quadrifoliate vortex mode exhibits distinct pathways depending on the power-law index: at relatively small $n$, the flow undergoes a direct supercritical bifurcation to simple extensional flow, while at relatively large $n$, it evolves through an intermediate dumbbell-shaped state. Among geometric parameters, the roller radius $r$ emerges as the dominant factor controlling bifurcation points and vortex dimensions, whereas the roller-container gap $δ$ exerts minimal influence on flow regimes. The transitions between flow modes can be precisely characterized through the evolution of vortex dimensions and velocity gradients at the stagnation point, providing quantitative criteria for flow regime identification. These findings enrich our fundamental understanding of bifurcation phenomena in extensional devices and provide quantitative guidelines for achieving desired flow patterns in four-roll mill applications.

physics.flu-dyn↗

arXiv2024

Structural and electrical properties of fiber textured and epitaxial molybdenum thin films prepared by magnetron sputter epitaxy

Molybdenum (Mo) due to its optimal structural, physical, and acoustic properties find application as electrode material in aluminum scandium nitride (AlScN) and aluminum nitride (AlN) based bulk acoustic wave (BAW) resonators. Epitaxial Mo thin films exhibiting low resistivity can improve the performance of the BAW resonator by enhancing both the electromechanical coupling coefficient and quality factor. In this study, we systematically vary the growth temperature of Mo grown on fiber-textured and epitaxial wurtzite-aluminum nitride (AlN) to study the changes in structural and electrical properties of the Mo films. Results show that Mo grown at 700°C on epitaxial AlN exhibit low surface roughness, large average grain diameter, low resistivity, and high crystal quality. XRD pole figure and phi-scan reveal that irrespective of the growth temperature, Mo is fiber textured on fiber-textured AlN, and has three rotational domains on epitaxial AlN. The study shows that the resistivity of Mo reduces with increasing growth temperature, which we relate to increasing average grain diameter. Additionally, we show that fiber-textured Mo has more high angle grain boundaries resulting in consistently higher resistivity than its epitaxial equivalent.

physics.app-ph↗

arXiv2024

Thermocapillary migration of a self-rewetting droplet on an inclined surface: A phase-field simulation

In this paper, we investigated the thermocapillary migration of a self-rewetting droplet on an inclined surface using a phase field based lattice Boltzmann method. Unlike the normal fluid whose surface tension decreases linearly with temperature, the self-rewetting fluid consider in the current work has a quadratic temperature dependence of surface tension with a well-defined minimum. we first explored the influence of the Marangoni number on droplet migration, and found that the droplet hardly deforms and migrates slowly when the Marangoni number is small. However, as the Marangoni number increases, the droplet begins to deform and elongate, and its migration speed increases. Subsequently, we studied the effect of surface wettability on droplet migration. The results show that the droplet migrate towards regions of higher surface energy on hydrophilic surfaces and in the opposite direction on hydrophobic surfaces. Furthermore, by varying the viscosity ratio and the inclination angle of the plate, we found that the droplet's migration speed decreases with an increase in the viscosity ratio. In particular, two vortices appear inside the droplet at a high viscosity ratio, whereas only one vortex is present at a low viscosity ratio.

physics.flu-dyn↗

arXiv2024

Towards establishing best practice in the analysis of hydrogen and deuterium by atom probe tomography

As hydrogen is touted as a key player in the decarbonization of modern society, it is critical to enable quantitative H analysis at high spatial resolution, if possible at the atomic scale. Indeed, H has a known deleterious impact on the mechanical properties (strength, ductility, toughness) of most materials that can hinder their use as part of the infrastructure of a hydrogen-based economy. Enabling H mapping, including local hydrogen concentration analyses at specific microstructural features, is essential for understanding the multiple ways that H affect the properties of materials, including for instance embrittlement mechanisms and their synergies, but also spatial mapping and quantification of hydrogen isotopes is essential to accurately predict tritium inventory of future fusion power plants, ensuring their safe and efficient operation for example. Atom probe tomography (APT) has the intrinsic capabilities for detecting hydrogen (H), and deuterium (D), and in principle the capacity for performing quantitative mapping of H within a material's microstructure. Yet the accuracy and precision of H analysis by APT remain affected by the influence of residual hydrogen from the ultra-high vacuum chamber that can obscure the signal of H from within the material, along with a complex field evaporation behavior. The present article reports the essence of discussions at a focused workshop held at the Max-Planck Institute for Sustainable Materials in April 2024. The workshop was organized to pave the way to establishing best practices in reporting APT data for the analysis of H. We first summarize the key aspects of the intricacies of H analysis by APT and propose a path for better reporting of the relevant data to support interpretation of APT-based H analysis in materials.

cond-mat.mtrl-sci↗

arXiv2024

Two-relaxation-time regularized lattice Boltzmann model for Navier-Stokes equations

In this paper, we propose a novel two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows. A free relaxation parameter, $τ_{s,2}$, is employed to relax the regularized non-equilibrium third-order terms. Chapman-Enskog analysis reveals that our model can accurately recover the Navier-Stokes equations (NSEs). Theoretical analysis of the Poiseuille flow problem demonstrates that the slip velocity magnitude in the proposed model is controlled by a magic parameter, which can be entirely eliminated under specific values, consistent with the classical TRT model. Our simulations of the double shear layer problem, Taylor-Green vortex flow, and force-driven Poiseuille flow confirm that the stability and accuracy of our model significantly surpass those of both the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models, even under super-high Reynolds numbers as $Re=10^7$. Concurrently, the TRT-RLB model exhibits superior performance in very high viscosity scenarios. The simulations of creeping flow around a square cylinder demonstrates the model's capability to accurately compute ultra-low Reynolds numbers as $Re=10^{-7}$. This study establishes the TRT-RLB model as a flexible and robust tool in computational fluid dynamics.

physics.flu-dyn↗

arXiv2024

Atom probe tomography: a local probe for chemical bonds in solids

Atom probe tomography is frequently employed to characterize the elemental distribution in solids with atomic resolution. Here we review and discuss the potential of this technique to locally probe chemical bonds. Two processes characterize the bond rupture in laser-assisted field emission, the probability of molecular ions, i.e. the probability that molecular ions (PMI) are evaporated instead of single (atomic) ions, and the probability of multiple events, i.e. the correlated field-evaporation of more than a single fragment (PME) upon laser- or voltage pulse excitation. Here we demonstrate that one can clearly distinguish solids with metallic, covalent, and metavalent bonds based on their bond rupture, i.e. their PME and PMI values. Differences in the field penetration depth can largely explain these differences in bond breaking. These findings open new avenues in understanding and designing advanced materials, since they allow a quantification of bonds in solids on a nanometer scale, as will be shown for several examples. These possibilities would even justify calling the present approach bonding probe tomography (BPT).

cond-mat.mtrl-sci↗