arXiv subjects

Linjie Ma

Publications and source records attributed to Linjie Ma.

8 recordsLinked to original sources

arXiv2026

A simple proof for the insulated conductivity problem and application to flat boundaries

In high-contrast composites, the electric (or stress) field may exhibit significant amplification in the narrow region between inclusions. The behavior of the solution depends on the distance $\epsilon$ between the inclusions, which tends to $0$. The purpose of this paper is to provide a simple proof of optimal pointwise estimates for the insulated conductivity problem in any dimension, including the case of flat inclusions. Our approach is based on two fundamental tools: the maximum principle and the Hopf lemma. A key feature of this method is that it avoids the flattening techniques commonly used in the literature, such as those in \citet{dong2021optimal,dong2022gradient}, which require transforming the narrow region into an n-dimensional cuboid. We show that the solution of the insulated problem is $\alpha$-order ($\alpha\in[0,1)$) polynomial growth for $n\geq2$ near the origin. Moreover, when the boundaries near the origin are flat, we prove that the gradient of the solution remains uniformly bounded.

math.AP↗

arXiv2026

From Displacement to Angle: Diamond-Based 3D Rotation Sensing for High-Precision Cellular Force Measurement

Cellular traction forces are conventionally measured by tracking the displacement of beads or micropillars, an approach fundamentally limited by optical diffraction and the classical Euler-Bernoulli beam assumption, which is accurate only when the traction-induced deformation is relatively small while the aspect ratio of micropillars is large. Here we introduce an alternative approach: quantifying force through direct measurement of rotational angle, in addition of displacement of the micropillar, using fluorescent nanodiamonds as embedded 3D orientation markers. Specifically, by integrating optically detected magnetic resonance (ODMR) with laser polarization modulation (LPM), we determine the complete three-dimensional orientation of nanodiamonds attached to PDMS micropillars with sub-degree precision ($\sim$0.5$^\circ$). This angle-based measurement framework bypasses the resolution constraints of displacement tracking and remains valid for stocky beams or when large deformations occur. Finite-element simulations demonstrate that our method reduces force estimation errors by at least 10% compared to conventional displacement-based approaches. Moreover, we successfully capture multidimensional pillar deformations -- including bending and twisting -- that are inaccessible to conventional displacement-only method. Taken together, our work establishes diamond-based angular force microscopy as a high-precision platform for mechanobiology.

physics.optics↗

arXiv2026

Nanodiamond-Enabled Torsion Microscopy Uncovers Multidimensional Cell-Matrix Mechanical Interactions

Traditional cellular force-sensing techniques, such as traction force microscopy (TFM), are predominantly limited to measuring linear tractions, overlooking and technically unable to capture the nanoscale torsional forces that are critical in cell-matrix interactions. Here, we introduce a nanodiamond-enabled torsion microscopy (DTM) that integrates nitrogen-vacancy (NV) centers as orientation markers with micropillar arrays to decouple and quantify nanoscale rotational and translational motions induced by cells. This approach achieves high precision (~1.47 degree rotational accuracy and ~3.13*10-15 Nm torque sensitivity), enabling reconstruction of cellular torsional force fields and twisting energy distributions previously underestimated. Our findings reveal the widespread presence of torsional forces in cell-matrix interactions, introducing "cellular mechanical modes" where different adhesion patterns dictate the balance between traction- and torque- mediated mechanical energy transferred to the substrate. Notably, in immune cells like macrophages that generally exert low linear tractions, torque overwhelmingly dominates traction, highlighting a unique mechanical output for specific cellular functions. By uncovering these differential modes, DTM provides a versatile tool to advance biomechanical investigations, with potential applications in disease diagnostics and therapeutics.

physics.bio-ph↗

arXiv2025

Wafer-scale integration of single nanodiamonds via electrostatic-trapping

Nanodiamonds (NDs) are key materials for building nanoscale quantum sensing, imaging and communication devices. Scalable configuration of single NDs on heterogeneous platforms, forming photonic quantum source arrays, will be an essential solution towards realizing next-generation practical and industrial quantum devices. However, NDs are challenging to manipulate because their size, shape and surface chemistry vary substantially. Here, we show a simple method based on electrostatic-trapping to rapidly and reliably pattern single ND arrays on arbitrary substrates at scale. Our method, which uses carefully engineered microscale hole templates and electrostatic force, captures single NDs across 8-inch wafers with 82.5% yields within 5 min. Systematic experimental and theoretical studies show the number of deposited NDs primarily depends on the diameter of the hole trap. The method is compatible with mature CMOS technologies, enabling the mass production of scalable and integrable quantum devices. This advancement is expected to accelerate the commercialization and industrial adoption of ND-based technologies.

physics.optics↗

arXiv2024

A versatile method for nano-fabrication on diamond film: flexible diamond metasurfaces as a demonstration

Diamond exhibits superb performance across a wide range of applications due to its enormous outstanding properties in electronic, photonic and quantum fields. Yet heterogeneous integration of diamond for on-chip functionalities, like 2D materials, remains challenging due to the hard acquisition of scalable, transferable and ultrathin diamond samples. Recently, the edge-exposed exfoliation has been demonstrated as an effective way to produce wafer-scale, freestanding and ultrathin diamond films. However, the incompatibility of the newly developed diamond film with conventional nano-fabrication methods makes it difficult to fabricate diamond film into practical devices. Herein, we demonstrate the mask-transferring by sugar as a versatile method for pattern-definition on diamond films, which shows excellent geometrical resolution and accuracy comparing to conventional approaches. Additionally, based on this method, the flexible all-diamond metasurfaces functioning as structural colors have been achieved, which indicates its huge potential for fabricating more diamond-related devices.

physics.optics↗

arXiv2024

A diamond heater-thermometer microsensor for measuring localized thermal conductivity: a case study in gelatin hydrogel

Understanding the microscopic thermal effects of the hydrogel is important for its application in diverse fields, including thermal-related studies in tissue engineering and thermal management for flexible electronic devices. In recent decades, localized thermal properties, such as thermal conductivity, have often been overlooked due to technical limitations. To tackle this, we propose a new hybrid diamond microsensor that is capable of simultaneous temperature control and readout in a decoupled manner. Specifically, the sensor consists of a silicon pillar (heater) at about 10 microns in length, topped by a micron-sized diamond particle that contains silicon-vacancy (SiV) centers (thermometer) with 1.29 K*Hz^(-1/2) temperature measurement sensitivity. Combining this innovative, scalable sensor with a newly established simulation model that can transform heating-laser-induced temperature change into thermal conductivity, we introduced an all-optical decoupled method with about 0.05 W/(m* K) precision, which can reduce laser crosstalk. For the first time, we track the thermal conductivity change of hydrogels during the gelation process and demonstrate the existence of variation. We introduce a rapid, undisturbed technique for measuring microscale thermal conductivity, potentially serving as a valuable tool for cellular thermometry and highlight the idea that decoupling can reduce crosstalk from different lasers, which is helpful for quantum sensing.

physics.optics↗

arXiv2023

Quantum-Enhanced Diamond Molecular Tension Microscopy for Quantifying Cellular Forces

The constant interplay and information exchange between cells and their micro-environment are essential to their survival and ability to execute biological functions. To date, a few leading technologies such as traction force microscopy, have been broadly used in measuring cellular forces. However, the considerable limitations, regarding the sensitivity and ambiguities in data interpretation, are hindering our thorough understanding of mechanobiology. Herein, we propose an innovative approach, namely quantum-enhanced diamond molecular tension microscopy (QDMTM), to precisely quantify the integrin-based cell adhesive forces. Specifically, we construct a force sensing platform by conjugating the magnetic nanotags labeled, force-responsive polymer to the surface of diamond membrane containing nitrogen vacancy (NV) centers. Thus, the coupled mechanical information can be quantified through optical readout of spin relaxation of NV centers modulated by those magnetic nanotags. To validate QDMTM, we have carefully performed corresponding measurements both in control and real cell samples. Particularly, we have obtained the quantitative cellular adhesion force mapping by correlating the measurement with established theoretical model. We anticipate that our method can be routinely used in studying important issues like cell-cell or cell-material interactions and mechanotransduction.

q-bio.CB↗

arXiv2022

Optimal gradient estimates for the insulated conductivity problem with dimensions more than two

In high-contrast composite materials, the electric (or stress) field may blow up in the narrow region between inclusions. The gradient of solutions depend on $\epsilon$, the distance between the inclusions, where $\epsilon$ approaches to $0$. By using the maximum principle techniques, we give another proof of the Dong-Li-Yang estimates \cite{DLY} for any convex inclusions of arbitrary shape with $n\geq 3$. This result solves the problem raised by \cite{W}, where the spherical inclusions with $n\geq 4$ is considered. Moreover, we also generalize the above results with flatter boundaries near touching points.

math.AP↗