Local Phase Research Articles

Estimation of the proximal temperature rise of an excited upconversion particle by detecting the wavefront of emission.

Monitoring the temperature distribution within a local environment at the micro and nanoscale is vital as many processes are solely thermal. Various thermometric techniques have been explored in the community, and out of these, fluorescent nano/micro particle-based mechanisms are accepted widely (fluorescence intensity ratio (FIR) techniques, where the ratio of populations in two consecutive energy levels is compared with Boltzmann distribution). We describe a new technique to account for the temperature rise near an illuminated upconverting particle (UCP) using wavefront imaging, which is more sensitive than the conventional thermometric techniques on the microscale. We rely on a thermo-optical phase microscopic technique by reconstructing the wavefront of emission from an upconverting particle using a Shack-Hartmann wavefront sensor. The wavefront maps the local phase distribution, which is an indicator of the surroundings' optical parameters, particularly the suspended medium's temperature-induced refractive index in the presence of convection currents. We describe how these extracted phase values can provide information about the optical heating due to the particle and hence its local environment along the direction of the emission. Our findings demonstrate the detection of a minimum temperature rise of 0.23 K, while the FIR methods indicate a minimum of 0.3 K rise. This technique is used to study the temperature increase in the backscattered direction for an upconverting particle illuminated on pump resonance. We also estimate the Soret coefficient for an upconverting particle optically trapped on pump resonance and experiencing anisotropic heating across the body.

Exploring the dynamics of finite-energy Airy beams: a trajectory analysis perspective.

In practice, Airy beams can only be reproduced in an approximate manner, with a limited spatial extension and hence a finite energy content. To this end, different procedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In order to investigate the effects generated by the truncation and hence the propagation properties displayed by the designed beams, here we resort to a new perspective based on a trajectory methodology, complementary to the density plots more commonly used to study the intensity distribution propagation. We consider three different aperture functions, which are convoluted with an ideal Airy beam. As it is shown, the corresponding trajectories reveals a deeper physical insight about the propagation dynamics exhibited by the beams analyzed due to their direct connection with the local phase variations undergone by the beams, which is in contrast with the global information provided by the usual standard tools. Furthermore, we introduce a new parameter, namely, the escape rate, which allow us to perform piecewise analyses of the intensity distribution without producing any change on it, e.g., determining unambiguously how much energy flux contributes to the leading maximum at each stage of the propagation, or for how long self-accelerating transverse propagation survives. The analysis presented in this work thus provides an insight into the behavior of finite-energy Airy beams, and therefore is expected to contribute to the design and applications exploiting this singular type of beams.

Magnetic resonance imaging of trickle flow

AbstractTrickle bed reactors (TBR) are widely used in the chemical industries. These reactors involve gas and liquid flow through a catalyst‐packed bed. For optimal TBR performance, it is crucial to achieve a uniform distribution of gas and liquid among the catalyst particles. However, in multitubular reactors with slender tubes, flow maldistribution near the tube walls is a common issue. Therefore, a comprehensive understanding of local phase and flow distribution is essential for designing and operating reactors with slender tubes. This article employs Magnetic Resonance Imaging (MRI) to characterize the three‐dimensional distribution of the two‐phase trickle flow within a slender tube. Three quantities are characterized: gas‐liquid‐solid distribution, particle wetting efficiency, and the flow field. Structure and flow MRI images are processed to calculate these quantities. Additionally, a novel postprocessing technique is introduced to determine the liquid distribution over individual particle surfaces. This distribution is determined at several axial and radial positions.

Unsupervised deep learning with convolutional neural networks for static parallel transmit design: A retrospective study.

To mitigate inhomogeneity at 7T for multi-channel transmit arrays using unsupervised deep learning with convolutional neural networks (CNNs). Deep learning parallel transmit (pTx) pulse design has received attention, but such methods have relied on supervised training and did not use CNNs for multi-channel maps. In this work, we introduce an alternative approach that facilitates the use of CNNs with multi-channel maps while performing unsupervised training. The multi-channel maps are concatenated along the spatial dimension to enable shift-equivariant processing amenable to CNNs. Training is performed in an unsupervised manner using a physics-driven loss function that minimizes the discrepancy of the Bloch simulation with the target magnetization, which eliminates the calculation of reference transmit RF weights. The training database comprises 3824 2D sagittal, multi-channel maps of the healthy human brain from 143 subjects. data were acquired at 7T using an 8Tx/32Rx head coil. The proposed method is compared to the unregularized magnitude least-squares (MLS) solution for the target magnetization in static pTx design. The proposed method outperformed the unregularized MLS solution for RMS error and coefficient-of-variation and had comparable energy consumption. Additionally, the proposed method did not show local phase singularities leading to distinct holes in the resulting magnetization unlike the unregularized MLS solution. Proposed unsupervised deep learning with CNNs performs better than unregularized MLS in static pTx for speed and robustness.

Evaluating the effectiveness of CFD-DEM and SPH-DEM for complex pipe flow simulations with and without particles

We investigate the effectiveness of two computational fluid dynamics (CFD) approaches: mesh-based CFD and meshfree particle-based smoothed particle hydrodynamics (SPH) for simulating pipe flows of varying complexity. The study covers laminar and turbulent flows, different fluid rheologies (Newtonian, power-law, Bingham plastic, Herschel-Bulkley), and different particle-laden scenarios, validated using experimental Lagrangian measurements obtained by positron emission particle tracking or available theoretical solutions, as appropriate. We assess these methods based on their ability to predict radial profiles of local phase velocity and concentration, as well as computational cost. In single-phase flows, CFD aligns well with experimental data and theoretical models. SPH exhibits boundary discrepancies due to no-slip condition approximations and limitations in turbulent flow simulation which need further development. Integrating the discrete element method (DEM) significantly enhances both techniques for particle-liquid flows. Mesh-based CFD is computationally efficient, while particle-based SPH can offer more insights into Lagrangian fluid dynamics.

Anomalous localization in a kicked quasicrystal

Quantum transport can distinguish between dynamical phases of matter. For instance, ballistic propagation characterizes the absence of disorder, whereas in many-body localized phases, particles do not propagate for exponentially long times. Additional possibilities include states of matter exhibiting anomalous transport in which particles propagate with a non-trivial exponent. Here we report the experimental observation of anomalous transport across a broad range of the phase diagram of a kicked quasicrystal. The Hamiltonian of our system has been predicted to exhibit a rich phase diagram, including not only fully localized and fully delocalized phases but also an extended region comprising a nested pattern of localized, delocalized and multifractal states, which gives rise to anomalous transport. Our cold-atom realization is enabled by new Floquet engineering techniques, which expand the accessible phase diagram by five orders of magnitude. Mapping transport properties throughout the phase diagram, we observe disorder-driven re-entrant delocalization and sub-ballistic transport, and we present a theoretical explanation of these phenomena based on eigenstate multifractality.

The 12 October 2021, MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W$$\\end{document}=6.4, Zakros, Crete earthquake

We study the strong 12 October 2021, MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W$$\\end{document}=6.4, offshore Zakros, Crete earthquake, and its seismotectonic implications. We obtain a robust location (azimuthal gap equal to 17∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}) for the mainshock by combining all freely available local, regional and teleseismic phase arrivals (direct and depth phase arrivals). Based on our location and the spatial distribution of the poor aftershock sequence we parameterise the fault area as a 30 km ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document} 20 km planar surface, and using three-component strong motion data we calculate slip models for both earthquake nodal planes. Our preferred solution shows a simple, single slip episode on a NE-SW oriented, NW shallow-dipping fault plane, instead of a N-S oriented, almost vertical nodal plane. An anti-correlation of the aftershocks spatial distribution versus the maximum slip (∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document} 27 cm) of our model further supports this, although the accuracy of the aftershock hypocentral locations could be somewhat questionable. Coulomb stress changes calculated for both kinematic models do not show substantial differences, as the aftershock seismicity within the first 3 months after the mainshock is distributed along the stress shadow zone and over the stress enhanced areas developed at the southern fault edge, induced by the mainshock. The Kasos island tide gauge record analysis shows a small signal after the earthquake, but it can hardly demonstrate the existence of tsunami waves due to the low signal-to-noise ratio. Tsunami simulations computed for the two nodal planes do not yield conclusive evidence to highlight whether the causative fault plane is NE-SW oriented, NW shallow-dipping plane, or the N-S oriented plane, nevertheless, the power spectrum analysis of the NW shallow-dipping nodal plane matches the spectral peak at 8 s period and is overall closer to the spectrum of the tide gauge record. A USGS Shakemap was also produced with all available local strong motion data and EMSC testimonies. This was also investigated in an effort to document the responsible fault. The overall analysis in this study, slightly suggests a rather westward, shallow-dipping offshore fault zone, being antithetic to the main Zakros almost vertical normal fault which shapes the coast of eastern Crete and is perpendicular to the direction of Ptolemy Trench in this area. This result agrees with seismotectonic and bathymetric evidence which support the existence of approximately N-S trending grabens, east and northeast of Crete.

Anatomy of the eigenstates distribution: A quest for a genuine multifractality

Motivated by a series of recent works, an interest in multifractal phases has risen as they are believed to be present in the Many-Body Localized (MBL) phase and are of high demand in quantum annealing and machine learning. Inspired by the success of the Rosenzweig-Porter (RP) model with Gaussian-distributed hopping elements, several RP-like ensembles with the fat-tailed distributed hopping terms have been proposed, with claims that they host the desired multifractal phase. In the present work, we develop a general (graphical) approach allowing a self-consistent analytical calculation of fractal dimensions for a generic RP model and investigate what features of the RP Hamiltonians can be responsible for the multifractal phase emergence. We conclude that the only feature contributing to a genuine multifractality is the on-site energies’ distribution, meaning that no random matrix model with a statistically homogeneous distribution of diagonal disorder and uncorrelated off-diagonal terms can host a multifractal phase.

Phase unwrapping for phase imaging using the plug-and-play proximal algorithm.

Phase unwrapping (PU) is essential for various scientific optical applications. This process aims to estimate continuous phase values from acquired wrapped values, which are limited to the interval (-π,π]. However, the PU process can be challenging due to factors such as insufficient sampling, measurement errors, and inadequate equipment calibration, which can introduce excessive noise and unexpected phase discontinuities. This paper presents a robust iterative method based on the plug-and-play (PnP) proximal algorithm to unwrap two-dimensional phase values while simultaneously removing noise at each iteration. Using a least-squares formulation based on local phase differences and reformulating it as a partially differentiable equation, it is possible to employ the fast cosine transform to obtain a closed-form solution for one of the subproblems within the PnP framework. As a result, reliable phase reconstruction can be achieved even in scenarios with extremely high noise levels.

Homogeneous heterophase junction based on cubic/orthomorphic SnS for chemiresistive room temperature trace-ethanol sensor

Herein, we developed a homogeneous heterophase structure based on the stereochemically-active cubic/orthorhombic SnS (CUB/ORT-SnS) by chemical precipitation and vacuum annealing. By precisely adjusting the annealing temperature, spherical cubic-SnS partially transformed into block-like orthorhombic phase. In the constructed heterophase structure, abundant junction interfaces which directly exposed in the atmosphere, serve as high-active adsorption centers, effectively hoisting the ethanol adsorption capability of SnS. The experimental results show that CUB/ORT-SnS sensor exhibits a response of 184% towards 5 ppm ethanol with rapid response-recovery process at room temperature (RT). Moreover, in order to improve the selectivity of the sensor to ethanol vapor, principal component analysis (PCA) was adopted to realize the specific identification towards ethanol and isopropanol. Further investigations based on DFT calculations and band alignment indicate that local cubic phase SnS of the heterophase structure is the strong electron trap, and forms effective conductive path with ethanol molecules. Benefiting from the enrichment of the interface adsorption sites and the enhancement of carrier transport and diffusion, the heterophase junction of SnS obtains remarkably boosted ethanol-sensing performance. This work constructs a homogeneous heterophase structure for sensing ethanol at RT, which provides a new design strategy for developing high-performance VOCs gas sensors.

A compressible solver for two phase-flows with phase change for bubble cavitation

The present work describes the development of a novel fully compressible solver for two-phase flows with liquid-vapour phase change. Phase change phenomena in compressible two-phase flows are driving mechanisms for a multitude of phenomena including cavitation, droplet evaporation in acoustic fields, phase change in closed environments. Those are fundamental for a large number of technological applications including combustion chambers, propellant management in space and submarine engine design. The accurate simulation of phase change phenomena in compressible flows requires a direct numerical solver thermodynamically consistent and able to describe the smallest driving scales and to handle capillary effects. The present solver has these characteristics. It solves the full system of conservation equations for real fluid compressible flows of single species written in primitive variables using a semi-implicit pressure based solver. It leads to the energy equation being a Screened Poisson equation for the pressure that can be solved as a linear system. For the sake of thermodynamic consistency, several cubic equations of state are proposed to describe liquid and vapour phases as well as evolving saturation conditions at the interface. The proposed solver can be considered as an extension of classical incompressible solvers for nucleate boiling based on sharp interface approaches towards configurations with temporally and spatially evolving saturation conditions at the interface. It enables a complete coupling between local liquid-vapour phase change at the interface and pressure variations due to local flow features or time evolving thermodynamic conditions. Its interest is demonstrated with several benchmarks of increasing complexity with an ultimate configuration involving bubble cavitation due to the pressure drop in a convergent pipe.

Surface effect on the phase separation in thin liquid crystal film as seen from a mean-field approach

The effect of the interplay between attractive nonlocal surface interactions and attractive pair long-range intermolecular couplings on molecular structures of liquid crystals confined in thin cells with flat solid surfaces has been studied. It has been shown, in the framework of the extended McMillan′s mean field theory, that in the confined LC system a complex orientational and translational ordering of molecules can be induced. Several scenarios of the formation of local smectic A, nematic, and isotropic phases have been shown to coexist in a certain temperature range. Due to the nonlocality of the surface interaction, an unexpected complexity of the spatial arrangement of these local phases along the direction of the normal to the surface may exhibit itself.

Dissolution of Large‐Sized Primary Carbides in 6Cr13 Continuous Casting Slabs during High‐Temperature Homogenization

The morphology of carbides, the distribution of alloying elements, and the dissolution of primary carbides in 6Cr13 continuous casting slabs during the high‐temperature homogenization process are studied herein. The results show that severe segregation of alloying elements exists at the center of the cast slabs, accompanied by large, interconnected primary carbides in the form of a network. Large‐sized reticulated primary carbides are difficult to completely dissolve and eliminate during homogenization treatments. Large‐sized primary carbides will dissolve along the contours and the joints between the carbides when the temperature of high‐temperature homogenization does not exceed 1250 °C and the time does not exceed 1 h. The carbides that had broken off will precipitate again along the original contour in the form of large‐sized brain‐like carbides beyond this temperature and time. In situ observation of the high‐temperature homogenization process reveals that when the slab is heated to 1200 °C, the local liquid phase starts to be generated around the carbide. Cr atoms diffuse into the matrix through the liquid–matrix interface; it will accelerate the high‐temperature homogenization process and improve the segregation of alloying elements around carbides.

Application of metric space method in quantum information in quasi-periodic systems

Due to the rapid advancement of quantum information theory, some concepts such as fidelity and entanglement entropy have been introduced into the study of quantum phase transitions, which can be used not only to identify novel matter phases but also to detect the critical point and describe the critical behavior of the quantum phase transitions. From the point of view of the metric space, these physical quantities can be understood as the distance between the two functions in the metric space. In this work, we study a class of quasi-periodic system represented by the generalized Aubry-André-Harper (AAH) model, by using the distance between various wavefunctions or density distribution functions in real space. The generalized AAH model, an ideal platform to understand Anderson localization and other novel quantum phenomena, provides rich phase diagrams including extended, localized, even critical (multifractal) phases and can be realized in a variety of experimental platforms. In the standard AAH model, we find that the extended and localized phases can be identified. In addition, there exists a one-to-one correspondence between two distinct distances. We are able to precisely identify the critical point and compute the critical exponent by fitting the numerical results of different system sizes. In the off-diagonal AAH model, a complete phase diagram including extended phase, localized phase, and critical phase is obtained and the distance of critical phases is intermediate between the localized phase and extended phase. Meanwhile, we apply the metric space method to the wave packet propagation and discover that depending on the phase, the distance between wave functions or density functions exhibits varying dynamical evolution behavior, which is characterized by the exponent of the power-law relationship varying with time. Finally, the distance between the state density distribution functions is proposed, and it effectively identifies distinct matter phases and critical points. The critical phase which displays a multifractal structure, when compared with the other two phases, has the large state density distribution function distance. In a word, by defining the distances of a function under different parameters, we provide not only a physical quantity to identify familiar phase transitions but also an intuitive way to identify different matter phases of unknown systems, phase transition points, and their critical behaviors.

Localization transition in non-Hermitian coupled chain

In this paper, we study the properties of a coupled chain modulated by the quasiperiodic complex potential. It is found that as the disorder strength increases, the system undergoes a localization transition from a fully extended phase to an intermediate phase, and then to a fully localized phase. The numerical solving of order parameters such as the average inverse participation ratio and the average normalized participation ratio, demonstrate that the fully extended phase, the intermediate phase with mobility edges, and the fully localized phase are all existent during the transition. The scalar analysis of the normalized participation ratio, confirms the stable existence of three different localization phases in the system. Moreover, the analytical derivation, shows that the localization transition from the extended phase to the intermediate phase and from the intermediate phase to the localized phase can be precisely determined. In addition, the local phase diagram of the system is also obtained by numerical calculation, as shown in Fig. (a). The regions for the extended, intermediate and localized phases are denoted by I-a (I-b), II, and III, respectively. The three black solid lines represent the localization transition points determined by the analytical results. One can see that the analytical results match the numerical results. Moreover, we discuss that the relationship between the real-complex spectrum transition and the localization transition. It is found that the energy spectrum of the system can undergo two real-to-complex transitions. Specifically, during the transition from the fully extended phase to the intermediate phase, the first real-complex transition occurs, where part of the energy spectrum changes from the real spectrum to the complex spectrum, while another part spectrum remains real. When the system transitions from the intermediate phase to the fully localized phase, the energy spectrum completely transforms into a complex spectrum. These research results provide a reference for the study of localization transitions and real-complex transitions in one-dimensional coupled chain systems, and also offer a new perspective for the study of localization.

Localized Phase for the Erdős–Rényi Graph

We analyse the eigenvectors of the adjacency matrix of the Erdős–Rényi graph G(N,d/N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {G}}(N,d/N)$$\\end{document} for logN≪d≲logN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\\log N} \\ll d \\lesssim \\log N$$\\end{document}. We show the existence of a localized phase, where each eigenvector is exponentially localized around a single vertex of the graph. This complements the completely delocalized phase previously established in Alt et al. (Commun Math Phys 388(1):507–579, 2021). For large enough d, we establish a mobility edge by showing that the localized phase extends up to the boundary of the delocalized phase. We derive explicit asymptotics for the localization length up to the mobility edge and characterize its divergence near the phase boundary. The proof is based on a rigorous verification of Mott’s criterion for localization, comparing the tunnelling amplitude between localization centres with the eigenvalue spacing. The first main ingredient is a new family of global approximate eigenvectors, for which sharp enough estimates on the tunnelling amplitude can be established. The second main ingredient is a lower bound on the spacing of approximate eigenvalues. It follows from an anticoncentration result for these discrete random variables, obtained by a recursive application of a self-improving anticoncentration estimate due to Kesten.

Improving electron mobility in MoS2 field-effect transistors by optimizing the interface contact and enhancing the channel conductance through local structural phase transition

A structural phase incorporation strategy was proposed to improve the electron mobility of MoS2 FETs up to 237 cm2 V−1 s−1.

CO<sub>2</sub>-mediated conversion of physical pressure into chemical pressure to realize lattice strain

<p>Lattice strains often lead to novel phenomena, and they are used in a variety of applications, such as thermoelectricity, ferroelectricity, ferromagnetic, skyrmion and superconductivity. In this paper, we briefly summarize the novel phenomena brought about by lattice strain. An efficient method to realize lattice strain using supercritical CO<sub>2</sub> (SC CO<sub>2</sub>) is proposed. When CO<sub>2</sub> molecules shuttle through the confined space of the crystal structure, it can generate huge energy subsequently. Specifically, CO<sub>2</sub> carries MPa-level external physical pressure inside the crystal structure, forming localized defects or phase transitions. This alters the original chemical coordination environment and generates internal chemical pressures up to the GPa level. The crystal is stripped from three-dimensional to two-dimensional under high pressure, and lattice strain is realized at the same time. This work will provide new insights into the realization of lattice strain and give valuable guidance to broaden its application.</p>

Investigation of local structure and phase recovery in an irradiated Nd2Zr2O7 pyrochlore

SHI irradiation-induced order–disorder transition in an Nd2Zr2O7 pyrochlore is observed by XRD and XAS measurements. The recrystallization of the irradiated phase was observed as a result of thermal annealing.

Resonant Raman scattering on graphene: SERS and gap-mode TERS.

Nanoscale deformations and corrugations occur in graphene-like two-dimensional materials during their incorporation into hybrid structures and real devices, such as sensors based on surface-enhanced Raman scattering (SERS-based sensors). The structural features mentioned above are known to affect the electronic properties of graphene, thus highly sensitive and high-resolution techniques are required to reveal and characterize arising local defects, mechanical deformations, and phase transformations. In this study, we demonstrate that gap-mode tip-enhanced Raman Scattering (gm-TERS), which offers the benefits of structural and chemical analytical methods, allows variations in the structure and mechanical state of a two-dimensional material to be probed with nanoscale spatial resolution. In this work, we demonstrate locally enhanced gm-TERS on a monolayer graphene film placed on a plasmonic substrate with specific diameter gold nanodisks. SERS measurements are employed to determine the optimal disk diameter and excitation wavelength for further realization of gm-TERS. A significant local plasmonic enhancement of the main vibrational modes in graphene by a factor of 100 and a high spatial resolution of 10 nm are achieved in the gm-TERS experiment, making gm-TERS chemical mapping possible. By analyzing the gm-TERS spectra of the graphene film in the local area of a nanodisk, the local tensile mechanical strain in graphene was detected, resulting in a split of the G mode into two components, G+ and G-. Using the frequency split in the positions of G+ and G- modes in the TERS spectra, the stress was estimated to be up to 1.5%. The results demonstrate that gap-mode TERS mapping allows rapid and precise characterization of local structural defects in two-dimensional materials on the nanoscale.