Energy Variance Research Articles

Effects of nonmagnetic disorder on the energy of Yu-Shiba-Rusinov states

We study the sensitivity of Yu-Shiba-Rusinov states, bound states that form around magnetic scatterers in superconductors, to the presence of nonmagnetic disorder in both two and three dimensional systems. We formulate a scattering approach to this problem and reduce the effects of disorder to two contributions: disorder-induced normal reflection and a random phase of the amplitude for Andreev reflection. We find that both of these are small even for moderate amounts of disorder. In the dirty limit in which the disorder-induced mean free path is smaller than the superconducting coherence length, the variance of the energy of the Yu-Shiba-Rusinov state remains small in the ratio of the Fermi wavelength and the mean free path. This effect is more pronounced in three dimensions, where only impurities within a few Fermi wavelengths of the magnetic scatterer contribute. In two dimensions the energy variance is larger by a logarithmic factor because impurities contribute up to a distance of the order of the superconducting coherence length.

Bioluminescence Tomography Based on Gaussian Weighted Laplace Prior Regularization for In Vivo Morphological Imaging of Glioma.

Bioluminescence tomography (BLT) is a powerful non-invasive molecular imaging tool for in vivo studies of glioma in mice. However, because of the light scattering and resulted ill-posed problems, it is challenging to develop a sufficient reconstruction method, which can accurately locate the tumor and define the tumor morphology in three-dimension. In this paper, we proposed a novel Gaussian weighted Laplace prior (GWLP) regularization method. It considered the variance of the bioluminescence energy between any two voxels inside an organ had a non-linear inverse relationship with their Gaussian distance to solve the over-smoothed tumor morphology in BLT reconstruction. We compared the GWLP with conventional Tikhonov and Laplace regularization methods through various numerical simulations and in vivo orthotopic glioma mouse model experiments. The in vivo magnetic resonance imaging and ex vivo green fluorescent protein images and hematoxylin-eosin stained images of whole head cryoslicing specimens were utilized as gold standards. The results demonstrated that GWLP achieved the highest accuracy in tumor localization and tumor morphology preservation. To the best of our knowledge, this is the first study that achieved such accurate BLT morphological reconstruction of orthotopic glioma without using any segmented tumor structure from any other structural imaging modalities as the prior for reconstruction guidance. This enabled BLT more suitable and practical for in vivo imaging of orthotopic glioma mouse models.

Autocorrelation-based noise subtraction method with smoothing, overestimation, energy, and cepstral mean and variance normalization for noisy speech recognition

Autocorrelation domain is a proper domain for clean speech signal and noise separation. In this paper, a method is proposed to decrease effects of noise on the clean speech signal, autocorrelation-based noise subtraction (ANS). Then to deal with the error introduced by assumption that noise and clean speech signal are uncorrelated, two methods are proposed. Also to improve recognition rate of speech recognition system, overestimation parameter is used. Finally, with the addition of energy and cepstral mean and variance normalization to features of speech, recognition rate has improved considerably in comparison to standard features and other correlation-based methods. The proposed methods are tested on the Aurora 2 database. Between different proposed methods, autocorrelation-based noise subtraction method with smoothing, overestimation, energy, and cepstral mean and variance normalization (ANSSOEMV) method has a best recognition rate improvement in average than MFCC features which is 64.91% on the Aurora 2 database.

Locally advanced rectal cancer: predicting non-responders to neoadjuvant chemoradiotherapy using apparent diffusion coefficient textures.

The purpose of the study is to evaluate whether apparent diffusion coefficient (ADC) textures could identify patient with locally advanced rectal cancer (LARC) who would not respond to neoadjuvant chemoradiotherapy (NCRT). Twenty-six patients who underwent MRI including diffusion-weighted imaging at a 3.0T system before NCRT were enrolled. Texture analysis of pre-therapy ADC mapping was carried out, and a total of 133 ADC textures as well as routine mean ADC value of the primary tumor were extracted for each patient. Texture parameters and mean ADC were compared between responsive group and non-responsive group. Logistic regression was used to determine the independent predictors for non-responders. Receiver operating characteristic curve (ROC) was performed to evaluate the predictive performance of the significant parameters. Eighteen of the 133 texture parameters significantly differed between responsive and non-responsive groups (p<0.05). Further, energy variance and SdGa47 were identified as independent predictors for non-responders to NCRT; this logistic model achieved an area under the curve (AUC) of 0.908. Texture analysis based on pre-therapy ADC mapping could potentially be helpful to identify patients with LARC who would not respond to NCRT.

Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.

On the Definition of Diversity Order Based on Renyi Entropy for Frequency Selective Fading Channels

Outage probabilities are important measures of the performance of wireless communication systems, but to obtain outage probabilities it is necessary to first determine detailed system parameters, followed by complicated calculations. When there are multiple candidates of diversity techniques applicable for a system, the diversity order can be used to roughly but quickly compare the techniques for a wide range of operating environments. For a system transmitting over frequency selective fading channels, the diversity order can be defined as the number of multi-paths if multi-paths have all equal energy. However, diversity order may not be adequately defined when the energy values are different. In order to obtain a rough value of diversity order, one may use the number of multi-paths or the reciprocal value of the multi-path energy variance. Such definitions are not very useful for evaluating the performance of diversity techniques since the former is meaningful only when the target outage probability is extremely small, while the latter is reasonable when the target outage probability is very large. In this paper, we propose a new definition of diversity order for frequency selective fading channels. The proposed scheme is based on Renyi entropy, which is widely used in biology and many other fields. We provide various simulation results to show that the diversity order using the proposed definition is tightly correlated with the corresponding outage probability, and thus the proposed scheme can be used for quickly selecting the best diversity technique among multiple candidates.

Structural and Functional Characterization of Electron Transfer Complex Between Cytochrome C and Cytochrome C Oxidase

The electron transfer (ET) reactions in mitochondrial and bacterial respiratory chains are essential processes for energy transduction in cells. In the respiratory chain of mitochondria, the electrons to reduce molecular oxygen at cytochrome c oxidase (CcO) are donated from a small hemoprotein, cytochrome c (Cyt c), and Cyt c is thought to form an ET complex with CcO to promote the ET reaction from the heme iron in Cyt c to the CuA site in CcO. While the reduction of molecular oxygen to water molecules requires four electrons, Cyt c can carry only one electron, implying that Cyt c repetitively associates with and dissociates from CcO and suggesting that the specific interprotein interactions between Cyt c and CcO regulate the binding affinity and the ET rate from Cyt c to CcO. By using NMR spectroscopy, we have successfully determined the interaction site of Cyt c to CcO and found that the hydrophobic interactions are crucial for the complex formation between Cyt c and CcO1. To confirm the energetic contribution of the hydrophobic interaction to the complex formation, we determined the numbers and sites of the dehydrated water molecules associated with formation of the ES (E: CcO, S: reduced Cyt c) complex by the osmotic pressure analysis, presenting the critical contribution of the dehydration to the entropy increase for the ES complex formation. Based on the osmotic pressure dependence of kinetics for the ET from Cyt c to CcO, about 20 water molecules were found to be dehydrated in the complex formation under turnover conditions, and the systematic mutations in the interaction site of Cyt c for CcO revealed that nearly half of the dehydrated water molecules were located around Ile81, one of the hydrophobic amino acid residues near the exposed heme periphery of Cyt c. Such a specific dehydration from the hydrophobic residue, dominantly compensating for the entropy decrease due to the association of Cyt c with CcO, forms a structure blocking water access from the bulk water phase (a “molecular breakwater”) surrounding the ET pathway across the Cyt c – CcO interface in the ES complex to protect the ET pathway from the leak of electrons to the bulk water phase. To get further insights into the ET pathway from Cyt c to CcO, we determined the structure of the electron transfer complex between Cyt c and CcO under turnover conditions by considering the mutational effects on the steady state kinetics of the electron transfer reaction and our NMR analysis of the interaction site, and energetically characterized the interactions essential for complex formation2. The complex structures predicted by the protein docking simulation were computationally selected and validated by the experimental kinetic data for mutant Cyt c in the electron transfer reaction to CcO. The interaction analysis using the selected Cyt c – CcO complex structure revealed the electrostatic and hydrophobic contributions of each amino acid residue to the free energy required for complex formation. Several charged residues showed large unfavorable (desolvation) electrostatic interactions which were almost cancelled out by large favorable (Columbic) electrostatic interactions, but resulting in the destabilization of the complex. The residual destabilizing free energy is compensated by the van der Waals interactions mediated by hydrophobic amino acid residues to give the stabilized complex. Thus, hydrophobic interactions are the primary factors that promote complex formation between Cyt c and CcO under turnover conditions, while the change in the electrostatic destabilization free energy provides the variance of the binding free energy in the mutants. The distribution of favorable and unfavorable electrostatic interactions in the interaction site determines the orientation of the binding of Cyt c on CcO. Based on the simulated complex structure between Cyt c and CcO, we examined the contribution of hydrophobic interactions to the ET rate. The replacement of Ile81 in Cyt c, a key hydrophobic amino acid residue constituting the hydrophobic region in the protein interface between Cyt c and CcO in the ET complex, with Ser reduced the ET rate and the Marcus theory suggested that the significant decrease of electronic coupling constant (H DA), corresponding to the perturbations in the ET pathway from Cyt c to CcO. The dehydration of Ile81, therefore, facilitates the ET reaction from Cyt c to CcO by constituting the interprotein hydrophobic region as well as entropically promotes the ET complex formation. 1. Sakamoto, K. et al., Proc. Natl. Acad. Sci. USA 108, 12271-12276, (2011). 2. Sato, W. et al., J. Biol. Chem. 291, 15320-15331, (2016).

Efficiently estimating some common geostatistical models by ‘energy–variance matching’ or its randomized ‘conditional–mean’ versions

We consider the problem of fitting an isotropic zero-mean stationary Gaussian field model to (possibly noisy) observations, when the model belongs to the Matérn family with known regularity index ν>0, or to the spherical family. For estimating the correlation range (also called “decorrelation length”) and the variance of the field, two simple estimating functions based on the so-called “conditional Gaussian Gibbs-energy mean” (CGEM) and the empirical variance (EV) were recently introduced. This article presents an extensive Monte Carlo simulation study for problems with around a thousand observations and settings including large, moderate, and even “small”, correlation ranges. The known observation sites are either on a 2D grid (including a case of “very non-uniform” grid spacings) or randomly uniformly distributed on a simple 2D region. Some experiments for a 256×256 grid with missing values are also analyzed.This study empirically demonstrates that, for all the (possibly random) uniform designs, the statistical efficiency of CGEM-EV compared to exact maximum likelihood (ML) is globally very satisfactory (except a degradation for the very extremal ranges in some contexts) provided the signal-to-noise ratio (SNR) is strong enough and ν is not too large, this SNR restriction being alleviated as ν decreases. For the “very non-uniform” design, a simple weighting of EV restores this efficiency. In the less favorable cases, the statistical loss remains in fact acceptable: e.g. for the largest considered index (ν=3/2) and a “not strong enough” SNR, it may happen (in fact only for large ranges) that CGEM-EV almost doubles the mean squared error for the range parameter or for the widely used combination of the two parameters known as microergodic-parameter. Furthermore an important conclusion for computational efficiency is that the use of the natural fast randomized-trace version of CGEM-EV does not significantly degrade this statistical efficiency.

Strain engineering of H/transition metal systems

The effects of both compressive and tensile surface strain on the hydrogenated low-index faces of Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt and Au has been investigated using density functional theory (DFT). Changes in the preferred H binding site have been observed on the Pd, Ir and Pt surfaces when the surface lattice constant is strained by up to 2%, and on Fe, Rh, Ag and Os surfaces for larger strains of up to 5%. A complete discussion of the variance of the hydrogen binding energy, charge, density of states and local geometry with strain is presented. The exchange-correlation, electrostatic and kinetic contributions to the binding energy are delineated and their respective contributions are discussed. The mechanism which determines the preferred binding site for each system under strain is shown to be complex.

Optimal welding parameters for small-scale resistance spot welding with response surface methodology

In this study, Ti–1Al–1Mn thin foils with thickness of 0.05 mm were welded by small-scale resistance spot welding. Welding current, electrode force and welding time have been changed while other welding parameters remained constant. The welded joints were subjected to tensile shear tests for determining the values of shear force and absorption energy. A quadratic model of response surface methodology based on Box–Behnken design was employed in establishing regression equations between input variables (current, electrode force and time) and output variables (shear force, absorption energy, variance of shear force and variance of absorption energy). The models were satisfied in optimising the welding parameters. Besides, the microstructure analysis on the typical spot welds was also conducted.

Comparison between passive scalar and velocity fields in a turbulent cylinder wake

This work compares the enstrophy with the scalar dissipation rate, as well as the passive scalar variance with the turbulent kinetic energy, in the presence of coherent Kármán vortices in the intermediate wake of a circular cylinder. Measurements are made at$x/d=10$, 20 and 40, where$x$is the streamwise distance from the cylinder axis and$d$is the cylinder diameter, with a Reynolds number of$2.5\times 10^{3}$based on the cylinder diameter and the free-stream velocity. A probe consisting of eight hot wires (four X-wires) and four cold wires is used to measure simultaneously the three components of the fluctuating velocity and vorticity vectors, as well as the fluctuating temperature gradient vector at nominally the same point in the plane of the mean shear. It is found that the enstrophy and scalar dissipation spectra collapse approximately at all wavenumbers except around the Kármán vortex street wavenumber for$x/d\geqslant 20$. The spectral similarity between the streamwise velocity fluctuation$u$and the passive scalar$\unicode[STIX]{x1D703}$is better than that between the velocity fluctuation vector$\boldsymbol{q}$and$\unicode[STIX]{x1D703}$. This is closely related to the highly organized lateral velocity fluctuation$v$in this flow. The present observations are fully consistent with the expectation that small scales of the velocity and temperature fields are more likely to exhibit a close relationship than scales associated with the bulk of the turbulent energy or scalar variance. The variation across the wake of the time scale ratio between scalar and velocity fields is significantly smaller than that of the turbulent Prandtl number.

A Distributed and Energy-Efficient Algorithm for Event K-Coverage in Underwater Sensor Networks.

For event dynamic K-coverage algorithms, each management node selects its assistant node by using a greedy algorithm without considering the residual energy and situations in which a node is selected by several events. This approach affects network energy consumption and balance. Therefore, this study proposes a distributed and energy-efficient event K-coverage algorithm (DEEKA). After the network achieves 1-coverage, the nodes that detect the same event compete for the event management node with the number of candidate nodes and the average residual energy, as well as the distance to the event. Second, each management node estimates the probability of its neighbor nodes’ being selected by the event it manages with the distance level, the residual energy level, and the number of dynamic coverage event of these nodes. Third, each management node establishes an optimization model that uses expectation energy consumption and the residual energy variance of its neighbor nodes and detects the performance of the events it manages as targets. Finally, each management node uses a constrained non-dominated sorting genetic algorithm (NSGA-II) to obtain the Pareto set of the model and the best strategy via technique for order preference by similarity to an ideal solution (TOPSIS). The algorithm first considers the effect of harsh underwater environments on information collection and transmission. It also considers the residual energy of a node and a situation in which the node is selected by several other events. Simulation results show that, unlike the on-demand variable sensing K-coverage algorithm, DEEKA balances and reduces network energy consumption, thereby prolonging the network’s best service quality and lifetime.

Fast algorithm for hybrid region‐based active contours optimisation

Active contours are usually based on the optimisation of energy functionals that are built to attract the curve towards the objects' boundaries. This study describes a hybrid region-based active contours technique that uses global means to define the global fitting energy and local means and variances to define the local fitting energy. The optimisation of the functional is performed by applying a sweeping-principle algorithm, which avoids solving any partial differential equation and removes the need for any stability conditions. Furthermore, sweeping-principle algorithm is not based on the computation of derivatives, which allows using a binary level set function during the minimisation process instead of the signed distance function, consequently this removes the need for the distance regularisation term, avoiding its subtle side effects and speeding up the optimisation process. Successful and accurate segmentation results are obtained on synthetic and real images with a significant gain in the CPU execution time when compared with the minimisation via the commonly used gradient descent method.

Energy Efficient Reverse Path Routing Protocol for Asymmetric Links in Wireless Sensor Networks

Recent research has revealed that substantial percentage of the links in realistic Heterogeneous Wireless Sensor Networks (HWSNs) are asymmetric. Discovering and exploiting asymmetric links efficiently pose subsequent challenges in designing the wireless sensor networks routing protocols. In this paper we propose ERPPro, an Energy Efficient Reverse Path Routing Protocol scheme to discover and exploit asymmetric links in WSNs. ERPPro performs an intelligent computing by analyzing the unequal proportionate link state to select the best energy efficient reverse route among multiple paths. It applies the exponential upper bound value for calculating the average mean and variance of residual energy along with link quality of forwarding nodes to select a legitimate reverse route. Simulations were conducted to verify ERPPro's performance. From the simulation results it is observed that the proposed scheme is able to achieve higher delivery ratio reducing significant number of duplicated packets. Moreover, the mechanism was able to find more asymmetric links and maintain them with minimal overhead. Overall when energy reduces across sensors, performance of ERPPro degrades more slowly consuming only moderate energy resulting in prolonged network lifetime.

Evaluation of genome similarities using the non-decimated wavelet transform.

The wavelets have become increasingly popular in the field of bioinformatics due to their capacity in multiresolution analysis and space-frequency localization; the latter particularity is acquired due to a moving window that runs through the analyzed space. As a feature, they have a better ability to capture hidden components of biological data and an efficient link between biological systems and the mathematical objects used to describe them. The decomposition of signals/sequences at different levels of resolution allows obtaining distinct characteristics in each level. The energy (variance) obtained at each level provides a new set of information that can be used to search similarities between sequences. We show that the behavior of GC-content sequence can be succinctly described regarding the non-decimated wavelet transform, and we indicate how this characterization can be used to improve clustering of the similar strains of the genome of the Mycobacterium tuberculosis, having a very efficient level of detail. The clustering analysis using the energy obtained at each level of the analyzed sequences was essential to verify the dissimilarity of the sequences.

Clustering Based Energy Efficient and Communication Protocol for Multiple Mix-Zones Over Road Networks

The collection of information is one of the most crucial processes in many internet-enabled applications for multiple mix-zones over road networks. It is essential to use road networks for prolonged time duration in an energy efficient manner. However, network life time increases in response of reducing the stability period (i.e. time required before first node dies).The stability period reduces due to the high energy variance of nodes. In this paper, we present a protocol named as clustering based energy efficient and communication protocol (CEECP) for multiple mix-zones over road networks, which is proposed to reduce the loop holes of prevailing clustering protocols. Additionally, we present a novel CEECP for chain scenario to connect with the road side units for gaining benefits of V2V as well as, V2I communication for Cooperative Traffic Information Systems. The stability period is responsible to preserve coverage properties of the network. It analysis that as the stability period increases, the trustworthiness of the network increases. Hence, it is indispensable to articulate a clustering protocol that shall be energy efficient, low energy variant and of high stability. It has been proved that our scheme outperforms SEECP and VBN as well as, includes its variants with respect to stability period and energy variance.

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

Abstract Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number and predict a saturation of flux Richardson number () at sufficiently large . The CSB approach further predicts the value of and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

Adaptive robust control of Mecanum-wheeled mobile robot with uncertainties

This paper presents a novel implementation of an adaptive robust second-order sliding mode control (ARSSMC) on a mobile robot with four Mecanum wheels. Each wheel of the mobile robot is actuated by separate motors. It is the first time that higher-order sliding mode control method is implemented for the trajectory tracking control of Mecanum-wheeled mobile robot. Kinematic and dynamic modeling of the robot is done to derive an equation of motion in the presence of friction, external force disturbance, and uncertainties. In order to make the system robust, second-order sliding mode control law is derived. Further, adaptive laws are defined for adaptive estimation of switching gains. To check the tracking performance of the proposed controller, simulations are performed and comparisons of the obtained results are made with adaptive robust sliding mode control (ARSMC) and PID controller. In addition, a new and low-cost experimental approach is proposed to implement the proposed control law on a real robot. Experimental results prove that without compromising on the dynamics of the robot real-time implementation is possible in less computational time. The simulation and experimental results obtained confirms the superiority of ARSSMC over ARSMC and PID controller in terms of integral square error (ISE), integral absolute error (IAE), and integral time-weighted absolute error (ITAE), control energy and total variance (TV).

Three-dimensional vorticity, momentum and heat transport in a turbulent cylinder wake

The transport of momentum and heat in the turbulent intermediate wake of a circular cylinder is inherently three-dimensional (3-D). This work aims to gain new insight into the 3-D vorticity structure, momentum and heat transport in this flow. All three components of the velocity and vorticity vectors, along with the fluctuating temperature, are measured simultaneously, at nominally the same point in the flow, with a probe consisting of four X-wires and four cold wires. Measurements are made in the ($x$,$y$) or mean shear plane at$x/d=10$, 20 and 40 at a Reynolds number of$2.5\times 10^{3}$based on the cylinder diameter$d$and the free-stream velocity. A phase-averaging technique is developed to separate the large-scale coherent structures from the remainder of the flow. It is found that the effects of vorticity on heat transport at$x/d=10$and$x/d=20{-}40$are distinctly different. At$x/d=10$, both spanwise and streamwise vorticity components account significantly for the heat flux. At$x/d=20$and 40, the spanwise vortex rollers play a major role in inducing the coherent components of the heat flux vector, while the ribs are responsible for the small-scale heat diffusion out of the spanwise vortex rollers. The present data indicate that, if the spanwise-velocity-related terms are ignored, the estimated values of the production can have errors of approximately 22 % and 13 % respectively for the turbulent energy and temperature variance at$x/d=40$, and the errors are expected to further increase downstream. A conceptual model summarizing the 3-D features of the heat and momentum transports at$x/d=10$is proposed. Compared with the previous two-dimensional model of Matsumura &amp; Antonia (J. Fluid Mech., vol. 250, 1993, pp. 651–668) or MA, the new model provides a more detailed description of the role the rib-like structures undertake in transporting heat and momentum, and also underlines the importance of the upstream half of the spanwise vortex rollers, instead of only one quadrant of these rollers, as in the MA model, in diffusing heat out of the vortex.

Robust subwavelength focusing of surface plasmons on graphene

Graphene plays a substantial role in nano-scale optical engineering and miniature information signal processing systems gradually. In this letter, we propose a pipe-like substrate scheme to achieve the properly designed inhomogeneous, nonuniform conductivity distribution on a single sheet of graphene. The transverse-magnetic surface plasmon polariton wave supported by graphene will oscillate like water running in an inclined pipe and focus onto one point in a deep-subwavelength scale in the graphene sheet. Importantly, we find that this focusing behavior is robust and insensitive to the variance of background Fermi energy and incident frequency based on the analytic analysis. We verify our scheme by exploiting Hamiltonian optics and numerical calculation. This nano-scale optical manipulation will lead to the development of miniature optical system integration on a 1-atom-thick structure.