Anisotropic Conductivity Research Articles

Spatially resolved lock-in micro-thermography (SR-LIT): A tensor analysis-enhanced method for anisotropic thermal characterization

While high-throughput (HT) computations have streamlined the discovery of promising new materials, experimental characterization remains challenging and time-consuming. One significant bottleneck is the lack of an HT thermal characterization technique capable of analyzing advanced materials exhibiting varying surface roughness and in-plane anisotropy. To tackle these challenges, we introduce spatially resolved lock-in micro-thermography, an innovative technique enhanced by tensor analysis for optical thermal characterization. Our comprehensive analysis and experimental findings showcase notable advancements: We present a novel tensor-based methodology that surpasses the limitations of vector-based analysis prevalent in existing techniques, significantly enhancing the characterization of arbitrary in-plane anisotropic thermal conductivity tensors. On the instrumental side, we introduce a straightforward camera-based detection system that, when combined with the tensor-based methodology, enables HT thermal measurements. This technique requires minimal sample preparation and enables the determination of the entire in-plane thermal conductivity tensor with a single data acquisition lasting under 40 s, demonstrating a time efficiency over 90 times superior to state-of-the-art HT thermology. Additionally, our method accommodates millimeter-sized samples with poor surface finish, tolerating surface roughness up to 3.5 μm. These features highlight an innovative approach to realizing HT and accurate thermal characterization across various research areas and real-world applications.

Anisotropy Reversal of Thermal Conductivity in Silicon Nanowire Networks Driven by Quasi-Ballistic Phonon Transport.

Nanostructured semiconductors promise functional thermal management for microelectronics and thermoelectrics through a rich design capability. However, experimental studies on anisotropic in-plane thermal conduction remain limited, despite the demand for directional heat dissipation. Here, inspired by an oriental wave pattern, a periodic network of bent wires, we investigate anisotropic in-plane thermal conduction in nanoscale silicon phononic crystals with the thermally dead volume. We observed the anisotropy reversal of the material thermal conductivity from 1.2 at 300 K to 0.8 at 4 K, with the reversal temperature of 80 K mediated by the transition from a diffusive to a quasi-ballistic regime. Our Monte Carlo simulations revealed that the backflow of the directional phonons induces the anisotropy reversal, showing that the quasi-ballistic phonon transport introduces preferential thermal conduction channels with anomalous temperature dependence. Accordingly, the anisotropy of the effective thermal conductivity varied from 2.7 to 5.0 in the range of 4-300 K, indicating an anisotropic heat manipulation capability. Our findings demonstrate that the design of nanowire networks enables the directional thermal management of electronic devices.

Electrical anisotropy and its mitigation in conductive polymers printed by vat photopolymerization

In most additive manufacturing (AM) technologies, objects are realized layer by layer. This layer-by-layer construction leads to inherent anisotropic physical properties. Controlling, understanding and sometimes mitigating such anisotropy is a critical issue in the development of AM. Electrical anisotropy in conductive nanocomposites processed by Vat photopolymerization is demonstrated and quantified in the present work. In the used method, which enjoys high resolution and high speed, layers of an acrylate based resin, are successively cross-linked by UV irradiation of 2D patterns. Carbon nanotubes are used as conductive fillers for their low percolation threshold that allows realizing conductive and still sufficiently transparent materials for UV polymerization. Conductivity parallel to the layers of 3D objects is found to be much greater than conductivity perpendicular to the layers. This electrical anisotropy is explained by the high contact resistance between printed layers. High contact resistance results from the slow diffusion of carbon nanotubes from the uncured material towards the interface of the cured object. It is found that implementing a delay time before curing successive layers, or decreasing the matrix viscosity with temperature, to promote diffusion of the conductive particles allow substantial reduction of the contact resistance between layers. As a result, conductivity anisotropy can be reduced by almost two orders of magnitude. This control and mitigation of conductivity anisotropy allows reconciliation of the high resolution of the Vat photopolymerization technology with the possibility to realize uniform 3D materials.

Comparison of preloading by fill surcharge and ground water lowering based on a case study

AbstractPreloading by fill surcharge is a widespread and rather simple ground improvement method for the anticipation of settlements brought on by additional loads from new constructions. The magnitude as well as the area of surcharge is adapted to the final construction, whereas in general about 120–140 % of the final load is applied as surcharge load. Both factors have an influence on the effective depth for which soil improvement and an anticipation of settlements is possible, respectively. In case of large construction areas with significant loads, for which a greater depth effect needs to be considered, a large earth volume for surcharge is necessary. It is a cost‐intensive and environmental‐relevant aspect, when earth material is not available in sufficient amount and near distance of the construction site. In order to avoid this, it was investigated whether lowering the in situ groundwater level and thus increasing the effective stresses over depth could be a possible alternative. Therefore, a case study was carried out to examine these two different types of preloading techniques and their efficacy based on known subsoil conditions. Furthermore, the influence of the possible anisotropy of hydraulic conductivity in the weak soil layer on the preloading process was investigated.

A molecular dynamics simulation study of thermal transport in hydrazinium cyclo-pentazolate

Cyclo-pentazolate salts (CPSs) as a new type of high-energy-density materials (HEDMs) with high nitrogen content have attracted considerable research attention. In contrast to the extensive studies on their energy properties, the thermal transport process in CPSs has been less studied which relates closely to the thermal safety of this material. Concerning the hydrazinium cyclo-pentazolate (HCP), we conduct a computational study to estimate the thermal conductivity of HCP by means of the non-equilibrium molecular dynamics (NEMD) simulation. To achieve that, we have customized interaction parameters based on the default OPLS force field for the HCP, as benchmarked by its crystal structure. Our simulations have revealed surprisingly anisotropic thermal conductivity for the HCP, while the thermal conductivity becomes highest roughly in the direction perpendicular to cyclo-N 5− with its value notably higher than common high explosives. By modulating the interaction parameters within the HCP molecule, we have further captured a dominant role of the interaction between cyclo-N 5− in regulating the thermal conductivity of the HCP. The attractive Lennard–Jones (LJ) potential may restrict the relative motion between cyclo-N 5− , which forms a long-range order thus enhances thermal transport in the direction perpendicular to cyclo-N 5− . Our simulations result on the effect of (cyclo-N 5− )-(cyclo-N 5− ) interaction provide insights to engineer thermal transport in CPSs at the molecular level.

Spreading resistance and conductance anisotropy in multilayer MoS2

The increasing interest in realizing the full potential of two-dimensional (2D) layered materials for developing electronic components strongly relies on quantitative understanding of their anisotropic electronic properties. Herein, we use conductive atomic force microscopy to study the anisotropic electrical conductance of multilayer MoS2 by measuring the spreading resistance of circular structures of different radii ranging from 150 to 400 nm. The observed inverse scaling of the spreading resistance with contact radius, with an effective resistivity of ρeff = 2.89 Ω cm, is compatible with a diffusive transport model. A successive etch of the MoS2 nanofilms was used to directly measure the out-of-plane resistivity, i.e., 29.43 ± 7.78 Ω cm. Based on the scaling theory for conduction in anisotropic materials, the model yields an in-plane resistivity of 0.28 ± 0.07 Ω cm and an anisotropy of ∼100 for the ratio between the in-plane and out-of-plane resistivities. The obtained anisotropy indicates that the probed surface area can extend up to 400 times the metal contact area, whereas the penetration depth is limited to roughly 20% of the contact radius. Hence, for contact radius less than 3 nm, the conduction will be limited to the surface. Our investigation offers important insight into the anisotropic transport behavior of MoS2, a pivotal factor enabling the design optimization of miniaturized devices based on 2D materials.

Mesoscopic combinatorial design of anisotropic graphitic carbon with ordered porous frameworks for thermoelectric conversion

The incorporation of carbon materials can effectively enhance the performance of thermoelectric materials. By optimizing the thermoelectric properties of the carbon scaffold, it is possible to further improve the thermoelectric performance of the prepared carbon-based composites. To elevate the thermoelectric performance of the carbon scaffold, this work introduces a novel mesoscopic design strategy, utilizing natural flake graphite to create a three-dimensional ordered porous framework. Highly controllable anisotropic conductivity and thermal conductivity of the porous graphite skeleton were achieved, by combining sizable sodium chlorine templates (37.5–250 μm) with a natural flake graphite matrix (50–150 μm). A porous graphite with high electrical conductivity and low thermal conductivity along the vertical axis was obtained by carefully regulating the parameters. The sample demonstrated exceptional thermoelectric conversion performance, achieving a thermoelectric power factor of 12.2 μW m−1 K−2 and a figure of merit value of 28.3 × 10−4. Furthermore, the thermoelectric property of the samples could be greatly improved by adding a small amount of ferric chloride, with a thermoelectric power factor reaching 41.9 × 10−4 and a thermoelectric figure of merit reaching 81.4 μW m−1 K−2. This work provides an effective scheme for the mesoscopic regulation of porous graphite carbon structures and offers a new strategy for enhancing the performance of thermoelectric generators.

Unleashing the Potential of Boron Nitride Spheres for High‐Performance Thermal Management

AbstractHighly integrated and miniaturized electronic devices require advanced thermal management techniques to improve reliability and performance. Thanks to their high thermal conductivity and electrical insulation, boron nitride nanosheets (BNNSs) are commomly used as fillers to construct thermally conductive polymer composites for heat dissipation. However, the BNNS reinforced composites exhibit anisotropic thermal conductivity due to the anisotropic structure of BNNSs. Micro‐sized boron nitride spheres (BNSs) with isotropic thermal conductivity are considered one of the best solutions. Nevertheless, precisely measuring the thermal conductivity of BNSs remains a challenge, limiting the understanding of the thermal transport mechanism. Herein, we have successfully estimated the thermal conductivity of BNSs using the laser flash method. Factors influencing BNSs’ thermal conductivity, including precursor, polymer binder and sintering temperature, are also investigated. Under optimized conditions, BNSs exhibit high, isotropic thermal conductivity of 37.2±2.5 W/(m ⋅ K), and the BNS pellet outperforms its h‐BN counterpart in heat dissipation for an LED light. This superiority is attributed to outstanding heat transfer performance in the cross‐plane direction, in addition to high in‐plane thermal conductivity. This study provides a feasible method to estimate the thermal conductivity of spherical materials and highlights promising boron nitride materials with isotropic thermal conductivity for heat dissipation in advanced electronics.

Group III (In/Ga)-V (P/As)-VI (S/Se) Monolayers: A New Class of Auxetic Semiconductors with Highly Anisotropic Electronic/Optical/Mechanical/Thermal Properties.

We present a theoretical design of a class of 2D semiconducting materials, namely, group III (In/Ga)-V (P/As)-VI (S/Se) monolayers, whose global-minimum structures are predicted based on the particle swarm optimization method. Electronic structure calculations suggest that all group III-V-VI monolayers exhibit quasi-direct semiconducting characteristics with desirable band gaps ranging from 1.76 to 2.86 eV (HSE06 functional). Moreover, most group III-V-VI monolayers possess highly anisotropic carrier mobilities with large anisotropic ratios (3.4-6 for electrons, 2.2-25 for holes). G0W0+BSE calculations suggest that these monolayers show high optical anisotropy and relatively large exciton binding energies (0.33-0.75 eV), comparable to that (0.5 eV) of MoS2 monolayer. In particular, the GaPS monolayer manifests strikingly anisotropic I-V curves with a large ON/OFF ratio of ∼105 (106 for the GaPS bilayer) and anisotropic lattice thermal conductivity. Furthermore, the GaPS monolayer is predicted to exhibit both in-plane and out-of-plane negative Poisson ratios (NPRs) and prominent anisotropic Young moduli.

Unraveling High Thermal Conductivity with In-Plane Anisotropy Observed in Suspended SiP2.

The anisotropic thermal transport properties of low-symmetry two-dimensional materials play an important role in understanding heat dissipation and optimizing thermal management in integrated devices. Examples of efficient energy dissipation and enhanced power sustainability have been demonstrated in nanodevices based on materials with anisotropic thermal transport properties. However, the exploration of materials with high thermal conductivity and strong in-plane anisotropy remains challenging. Herein, we demonstrate the observation of anisotropic in-plane thermal conductivities of few-layer SiP2 based on the micro-Raman thermometry method. For suspended SiP2 nanoflake, the thermal conductivity parallel to P-P chain direction (κ∥b) can reach 131 W m-1 K-1 and perpendicular to P-P chain direction (κ⊥b) is 89 W m-1 K-1 at room temperature, resulting in a significant anisotropic ratio (κ∥b/κ⊥b) of 1.47. Note that such a large anisotropic ratio mainly results from the higher phonon group velocity along the P-P chain direction. We also found that the thermal conductivity can be effectively modulated by increasing the SiP2 thickness, reaching a value as high as 202 W m-1 K-1 (120 W m-1 K-1) for κ∥b (κ⊥b) at 111 nm thickness, which is the highest among layered anisotropic phosphide materials. Notably, the anisotropic ratio always remains at a high level between 1.47 and 1.68, regardless of the variation of SiP2 thickness. Our observation provides a new platform to verify the fundamental theory of thermal transport and a crucial guidance for designing efficient thermal management schemes of anisotropic electronic devices.

Unveiling a novel silicene-like material: A DFT study on pentahexoctite-silicon and its optoelectronic characteristics

Silicon-based two-dimensional (2D) materials, including well-known silicene, have garnered considerable attention due to their potential in advanced optoelectronic applications. Here, we introduce a novel 2D silicon variant, pentahexoctite silicon (PH-Si), inspired by the unique structural attributes of pentahexoctite carbon. By using state-of-the-art density functional theory (DFT) calculations and ab initio molecular dynamics (AIMD) simulations, we investigated the fundamental optoelectronic and structural traits of PH-Si. Our findings reveal that PH-Si boasts promising electronic properties characterized by anisotropic conductance and metallic behavior along specific directions. We also examine its structural and dynamic stability through phonon calculations and AIMD simulations. PH-Si structural stability was also confirmed by its low formation energy of −3.62 eV and dynamical stability at 1000 K. The material exhibits optical absorption in visible (Vis) and ultraviolet (UV) spectral regions, positioning it as a potential Vis-UV detector and absorber. Additionally, we assess its crucial mechanical attributes, encompassing elastic stiffness constants, Young’s modulus (ranging from 5 to 40 GPa), and a Poisson ratio of 0.8, collectively offering valuable insights into its mechanical performance. The comprehensive exploration of PH-Si’s properties is a step towards diversifying silicon-based 2D materials, opening channels for innovative applications in the rapidly evolving field of flat electronics.

Thermally Conductive Polymer Composites with Hexagonal Boron Nitride for Medical Device Thermal Management

Polymer composites with hexagonal boron nitride (hBN) have the potential to meet the heat dissipation and electrical insulation requirements of electronic and medical devices. In this study, hBN/polymer composites were fabricated with thermoplastic polyurethane (TPU) and epoxy as matrix materials. Three hBN powder types (BN1, BN2, BN3) with different platelet sizes and degrees of agglomeration were used. BN1 (with average size of 1 μm) and BN2 (with average size of 12 μm) mainly contained hBN platelets, while BN3 (with average size of 20 μm) contained both platelets and agglomerates of platelets. BN2 gave the highest thermal conductivity, while BN1 gave the lowest thermal conductivity. Thermal simulations were performed for a medical device with a limit for the maximum surface temperature. For the encapsulation of this device, several material combinations were simulated, using anisotropic thermal conductivity data. This included encapsulations with inner layers of commercial thermally and electrically conductive materials and an outer layer of the best thermally conductive (and electrically insulating) hBN/TPU composite fabricated by the authors.

Propagating surface plasmon polaritons in graphene under applied uniform strain

In this work, we theoretically investigate the propagation length of plasmon waves in graphene layer under uniform strain surrounded by two dielectric media of dielectric constants ε1 and ε2, respectively. The plasmon losses (plasmon damping), plasmon propagation length and the penetration depth of the electric field associates with the charge fluctuations can be controlled by varying the direction and the strength of the applied strain and the direction of the plasmon wave propagation with respect to the direction of the applied strain. Because strain induces anisotropy in graphene optical conductivity, the strain-dependent orientation plays an important role to manipulate the direction and variations of the graphene plasmon energy, which may be useful to tune graphene properties in plasmonic devices to enhance light-matter interaction.

A new random walk method for simulating heat flow and temperature distribution in three-dimensional discontinuous systems

Numerical methods for analyzing diffusion phenomena involving strong discontinuities and complicated interfaces are of great scientific and technical importance. In this paper, we extend the existing step-balanced random walk, which overcomes the problem of detailed balance of a random walker in three-dimensional (3D), diffusion-tensor discontinuous systems, to particle density (ρ) discontinuous systems, and introduce volumetric heat capacity C and temperature T by considering ρ as heat density, i.e., ρ=CT, to apply it to thermal problems. Two types of thermophysical simulations are demonstrated: one is steady-state heat flow due to a temperature difference at the end surfaces on a two-phase slab model unit cell with periodic boundary conditions; the other is the time variation of temperature distribution due to heat diffusion from a point heat source in a repeated two-phase slab model with no periodic boundary conditions. We see the correct behavior of heat and temperature expected in 3D discontinuous systems composed of two phases with anisotropic thermal conductivity. The applicability to problems other than pure diffusion and the limitations of the method are also discussed.

Distribution of gas hydrate in fractured reservoirs: implications from anisotropic elastic and electrical numerical simulations

SUMMARY Fractured hydrate-bearing reservoirs are extensively discovered worldwide and show notable anisotropic geophysical properties. Hydrate distribution in fractures significantly affects the anisotropic properties, and hence plays an important role in the accurate assessment of hydrate resources. However, the knowledge about how the hydrate distribution impacts the anisotropic geophysical properties of fractured reservoirs, which is the premise for the identification and quantification of hydrate in fractured reservoirs, is still poorly understood. To obtain such knowledge, we forward study the effects of various hydrate distribution (including floating, bridging and evolving hydrate distribution) in aligned fractures on the anisotropic elastic, electrical and joint elastic–electrical properties of a digital core using validated numerical methods. We show that for all the hydrate distribution, the anisotropic velocities increase, while the conductivities decrease with increasing hydrate saturation, with the effects of the floating and bridging distribution being the least and greatest, respectively. We also show that the anisotropic velocities and conductivities for the floating and bridging distribution vary approximately linearly with hydrate saturation, leading to linear correlations between the elastic and electrical properties. Further investigation illustrates that the difference in the slopes of the linear joint correlations between the two distribution is significantly greater than that of the individual properties as a function of hydrate saturation. The results have revealed the distinct effects of hydrate distribution on the anisotropic elastic and electrical properties of fractured reservoirs, and have confirmed the superiority of the joint elastic–electrical properties for the distinguishment of hydrate distribution in fractures over individual physical properties.

Experimental Investigation of the Anisotropic Thermal Conductivity of C/SiC Composite Thin Slab

Fiber-reinforced composites possess anisotropic mechanical and heat transfer properties due to their anisotropic fibers and structure distribution. In C/SiC composites, the out-of-plane thermal conductivity has mainly been studied, whereas the in-plane thermal conductivity has received less attention due to their limited thickness. In this study, the slab module of a transient plane source method is adopted to measure the in-plane thermal conductivity of a 2D plain woven C/SiC composite slab, and the test uncertainty is analyzed numerically. The numerical investigation proves that the slab module is reliable for measuring the isotropic and anisotropic slabs with in-plane thermal conductivity greater than 10 W⋅m−1⋅K−1. The anisotropic thermal conductivity of the 2D plain woven C/SiC composite slab is obtained within the temperature range of 20–900 °C by combining with a laser flash analysis method to measure the out-of-plane thermal conductivity. The results demonstrate that the out-of-plane thermal conductivity of C/SiC composite decreases with temperature, while its in-plane thermal conductivity first increases with temperature and then decreases, and the ratio of in-plane thermal conductivity to out-of-plane thermal conductivity is within 2.2–3.1.

Finite strain elastic visco-plastic consolidation model for layered soils with vertical drain considering self-weight loading and nonlinear creep

Prefabricated vertical drains (PVDs) combined with vacuum and/or surcharge loading have been widely adopted to improve the strength of soft soils. Precise consolidation analysis is the theoretical basis for the design of preloading method with PVD. Current consolidation theories for layered soils with PVD seldom consider the influence of large strain, nonlinear creep, and self-weight loading simultaneously. This paper, thus, presents a finite strain elastic visco-plastic consolidation model, called RCS-EVP, for radial consolidation of layered soils with PVD. RCS-EVP is developed based on the piecewise-linear method. It takes into account nonlinear creep with limit creep strain, variable boundary conditions, anisotropy of soil hydraulic conductivity, and variable compressibility and hydraulic conductivity during the consolidation under self-weight, time-dependent surcharge and/or vacuum loading. The performance of RCS-EVP is evaluated by comparing with the results from finite element simulations and a laboratory physical model test. The variations of settlement and pore pressure of a soft soil ground improved by vacuum preloading with PVD are estimated using RCS-EVP. The results indicate that RCS-EVP provides good estimates of long-term consolidation of layered soils with PVD under both laboratory and in-situ conditions.

Hybrid Foams based on Multi‐Walled Carbon Nanotubes and Cellulose Nanocrystals for Anisotropic Electromagnetic Shielding and Heat Transport

AbstractLightweight and mechanically robust hybrid foams based on cellulose nanocrystals (CNC) and multi‐walled carbon nanotubes (MWCNT) with an anisotropic structure are prepared by directional ice‐templating. The anisotropic hybrid CNC‐MWCNT foams displayed a combination of highly anisotropic thermal conductivity and an orientation‐dependent electromagnetic interference (EMI) shielding with a maximum EMI shielding efficiency (EMI‐SE) of 41–48 dB between 8 and 12 GHz for the hybrid foam with 22 wt% MWCNT. The EMI‐SE is dominated by absorption (SEA) which is important for microwave absorber applications. Modelling of the low radial thermal conductivity highlighted the importance of phonon scattering at the heterogeneous CNC‐MWCNT interfaces while the axial thermal conductivity is dominated by the solid conduction along the aligned rod‐like particles. The lightweight CNC‐MWCNT foams combination of an anisotropic thermal conductivity and EMI shielding efficiency is unusual and can be useful for directional heat transport and EMI shielding.

Highly tailorable thermomechanical properties of nanograined silicon: Importance of grain size and grain anisotropy

Nanocrystalline silicon can have unique thermal transport and mechanical properties governed by its constituent grain microstructure. Here, we use phonon ray-tracing and molecular dynamics simulations to demonstrate the largely tunable thermomechanical behaviors with varying grain sizes (a0) and aspect ratios (ξ). Our work shows that, by selectively increasing the grain size along the heat transfer direction while keeping the grain area constant, the in-plane lattice thermal conductivity (kx) increases more significantly than the cross-plane lattice thermal conductivity (ky) due to anisotropic phonon–grain boundary scattering. While kx generally increases with increasing ξ, a critical value exists for ξ at which kx reaches its maximum. Beyond this transition point, further increases in ξ result in a decrease in kx due to substantial scattering of low-frequency phonons with anisotropic grain boundaries. Moreover, we observe reductions in the elastic and shear modulus with decreasing grain size, and this lattice softening leads to significant reductions in phonon group velocity and thermal conductivity. By considering both thermal and mechanical size effects, we identify two distinct regimes of thermal transport, in which anisotropic phonon–grain boundary scattering becomes more appreciable at low temperatures and lattice softening becomes more pronounced at high temperatures. Through phonon spectral analysis, we attribute the significant thermal conductivity anisotropy in nanograined silicon to grain boundary scattering of low-frequency phonons and the softening-driven thermal conductivity reduction to Umklapp scattering of high-frequency phonons. These findings offer insights into the manipulation of thermomechanical properties of nanocrystalline silicon via microstructure engineering, carrying profound implications for the development of future nanomaterials.

Numerical MHD simulations of solar flares and their associated small-scale structures

ABSTRACT Using numerical simulations, we study the formation and dynamics of solar flares in a local region of the solar atmosphere. The magnetohydrodynamics (MHD) equations describe the dynamic evolution of flares, including space-dependent and anomalous magnetic resistivity and highly anisotropic thermal conduction on a 2.5 D slice. We adopt an initial solar atmospheric model in magnetohydrostatic equilibrium, with a magnetic configuration consisting of a vertical current sheet, which helps trigger the magnetic reconnection process. Specifically, we study three scenarios, two with only resistivity and the third with resistivity plus thermal conduction. The main results of the numerical simulations show differences in the global morphology of the flares, including the post-flare loops and the current sheet in three cases. In particular, localized resistivity produces more substructure around the post-flare loops that could be related to the Ritchmyer–Meshkov Instability (RMI). Furthermore, in the scenario of anomalous resistivity, we identify the formation of a plasmoid and a jet at coronal heights. On the other hand, in the scenario with resistivity plus thermal conduction, the post-flare loops are smooth, and no apparent substructures develop. Besides, in the z-component of the current density for the Res + TC case, we observe the development of multiple magnetic islands generated due to the Tearing instability in the non-linear regime.