Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

We consider the antimaximum principle for the p-Laplacian in the exterior domain: {-Δpu=λK(x)|u|p-2u+h(x)in B1c,u=0on ∂B1, where Δp is the p-Laplace operator with p&gt;1,λ is the spectral parameter and B1c is the exterior of the closed unit ball in RN with N ≥ 1. The function h is assumed to be nonnegative and nonzero, however the weight function K is allowed to change its sign. For K in a certain weighted Lebesgue space, we prove that the antimaximum principle holds locally. A global antimaximum principle is obtained for h with compact support. For a compactly supported K, with N=1 and p=2, we provide a necessary and sufficient condition on h for the global antimaximum principle. In the course of proving our results we also establish the boundary regularity of solutions of certain boundary value problems. © 2015 Elsevier Ltd.}, author_keywords={Exterior domains; Local and global antimaximum; p-Laplacian; Positive eigenfunctions; principle; Regularity results}, keywords={Boundary value problems; Eigenvalues and eigenfunctions; Laplace transforms, Exterior domain; Local and global antimaximum; P-Laplacian; principle; Regularity results, Nonlinear equations}, funding_details={Grantová Agentura České RepublikyGrantová Agentura České Republiky, GA ČR, 13-00863S}, funding_details={European Social FundEuropean Social Fund, ESF}, funding_text_1={The second author was supported by the Grant Agency of Czech Republic, Project No. 13-00863S.}, funding_text_2={The first, third and fourth authors work is funded by the project EXLIZ-CZ.1.07/2.3.00/30.0013, which is co-financed by the European Social Fund and the state budget of the Czech Republic.}, references={Allegretto, W., Huang, Y.X., A Picone's identity for the p-Laplacian and applications (1998) Nonlinear Anal., 32 (7), pp. 819-830; Anoop, T.V., Drábek, P., Sasi, S., Weighted quasilinear eigenvalue problems in exterior domains (2015) Calc. Var. Partial Differential Equations, 53 (3-4), pp. 961-975; Birindelli, I., Hopf's lemma and anti-maximum principle in general domains (1995) J. Differential Equations, 119 (2), pp. 450-472; Clément, P., Peletier, L.A., An anti-maximum principle for second-order elliptic operators (1979) J. Differential Equations, 34 (2), pp. 218-229; Drábek, P., Huang, Y.X., Bifurcation problems for the p-Laplacian in RN (1997) Trans. Amer. Math. Soc., 349 (1), pp. 171-188; Fleckinger-Pellé, J., Gossez, J.-P., De Thélin, F., Antimaximum principle in RN: Local versus global (2004) J. Differential Equations, 196 (1), pp. 119-133; Fučík, S., Nečas, J., Souček, J., Souček, V., (1973) Spectral Analysis of Nonlinear Operators, 346. , Lecture Notes in Mathematics Springer-Verlag Berlin, New York; Godoy, T., Gossez, J.-P., Paczka, S., On the antimaximum principle for the p-Laplacian with indefinite weight (2002) Nonlinear Anal., 51 (3), pp. 449-467; Hess, P., An anti-maximum principle for linear elliptic equations with an indefinite weight function (1981) J. Differential Equations, 41 (3), pp. 369-374; Hörmander, L., Lions, J.L., Sur la complétion par rapport à une intégrale de Dirichlet (1956) Math. Scand., 4, pp. 259-270; Lieberman, G.M., Boundary regularity for solutions of degenerate elliptic equations (1988) Nonlinear Anal., 12 (11), pp. 1203-1219; Serrin, J., Local behavior of solutions of quasi-linear equations (1964) Acta Math., 111, pp. 247-302; Shi, J., A new proof of anti-maximum principle via a bifurcation approach (2005) Results Math., 48 (1-2), pp. 162-167; Stavrakakis, N.M., De Thélin, F., Principal eigenvalues and anti-maximum principle for some quasilinear elliptic equations on RN (2000) Math. Nachr., 212, pp. 155-171; Tolksdorf, P., Regularity for a more general class of quasilinear elliptic equations (1984) J. Differential Equations, 51 (1), pp. 126-150; Vázquez, J.L., A strong maximum principle for some quasilinear elliptic equations (1984) Appl. Math. Optim., 12 (3), pp. 191-202; Ziemer, W.P., Sobolev spaces and functions of bounded variation (1989) Weakly Differentiable Functions, 120. , Graduate Texts in Mathematics Springer-Verlag New York}, correspondence_address1={Drábek, P.; Department of Mathematics and NTIS, Univerzitní 22, Czech Republic}, publisher={Elsevier Ltd}, issn={0362546X}, coden={NOAND}, language={English}, abbrev_source_title={Nonlinear Anal Theory Methods Appl}, document_type={Article}, source={Scopus},

World University root node

Department of Mathematics

Nonlinear Analysis, Theory, Methods and Applications

Antimaximum principle in exterior domains

Landslide is a geological phenomenon which gets triggered by factors such as rainfall, earthquake and human activities such as deforestation, excavation, blasting etc. India is a country which has witnessed the deleterious effect of many disastrous landslides. North eastern parts (Himalayan Region) and Western Ghats of India are more prone to landslides every year mainly due to heavy rainfall and thus resulting in large casualties and huge economic loss. Therefore there is a need to precisely assess and manage this landslide hazards. In the present study, a methodology has been implemented to analyze rain induced slope failures by taking a landslide prone area in Western Ghats, Kerala as a case study. Many previous landslides are reported in this region due to heavy rainfall during monsoon and steep slopes of the area. A combined hydrological geotechnical model has been set up to evaluate rain induced slope failures in a deterministic framework using Microsoft Excel and it is used to back evaluate a slope failure which occurred in the study area during 2007 monsoon. Rainfall data, hydrologic properties and geotechnical properties of the study area is collected. Rainfall data and the infiltration capacity at the site is an important input to the model.Initial moisture content distribution, saturated moisture content, residual moisture content and saturated conductivity of the soil deposits are used to obtain soil water characteristic curves (SWCC). Pore water pressure and hydraulic conductivity of soil is estimated from SWCC for the initial state of stability. An implicit finite difference backward solution is used to solve partial differential equation for variably saturated flow and change in pore water pressure and moisture content as a result of a rainfall event is obtained. Top boundary condition is either flux controlled or head controlled. At each time step, top compartment of soil is checked for its saturation. If it is saturated, suction or pressure head is taken as zero and it is head controlled. If it is not saturated then potential infiltration rate is compared with infiltration capacity of soil at each time step and minimum of these two values is taken as actual flux and top boundary is flux controlled. Bottom boundary is controlled by water table. If water table is of shallow depth, model depth is taken as depth up to water table and suction is zero at this bottom boundary. If water table is deep, suction is assumed based on capillary forces and type of soil. As a result of rainfall, suction in soil is either reduced or eliminated. A reduction in suction can also initiate landslide. Thu change in pore water pressure (negative and positive) with respect to time and depth is obtained and this result from hydrological model is given to geotechnical (stability model) in the same spreadsheet.&nbsp;

Department of Civil Engineering

50th Indian Geotechnical Conference (IGC-2010)

ANALYSIS OF RAIN INDUCED SLOPE FAILURES USING COMBINED HYDROLOGICAL GEOTECHNICAL MODEL

Band structure Lab uses the sp3s*d5 tight binding method to compute E(k) for bulk, planar, and nanowire semiconductors. Using this tool, you can quickly compute and visualize the band structures of bulk semiconductors, thin films, and nanowires for various materials, growth orientations, and strain conditions. Physical parameters such as the bandgap and effective mass can also be obtained from the computed E(k). The bandedges and effective masses of the bulk materials and the nanostructures structures can be analyzed as a function of various strain conditions.

Department of Electrical Engineering

Band Structure Lab

A pair of free homotopy classes of closed curves in an orientable surface $F$ with negative Euler characteristic are said to be length equivalent if for any hyperbolic structure on $F$, the length of the geodesic representative of one class is equal to the length of the geodesic representative of the other class. Given an orientable hyperbolic surface $F$ with negative Euler characteristic, any self intersecting geodesic $\alpha$ on $F$ and any self-intersection point $P$ of $\alpha$, we construct infinitely many pairs of length equivalent curves in $F$. We also relate these examples with the terms of Goldman bracket.

arXiv

Construction of length equivalent curves from self-intersecting geodesic in a hyperbolic surface

This paper demonstrates light-load instability in a 100-kW open-loop induction motor drive on account of inverter deadtime. An improved small-signal model of an inverter-fed induction motor is proposed. This improved model is derived by linearizing the nonlinear dynamic equations of the motor, which include the inverter deadtime effect. Stability analysis is carried out on the 100-kW 415-V three-phase induction motor considering no load. The analysis brings out the region of instability of this motor drive on the voltage versus frequency (V-f) plane. This region of light-load instability is found to expand with increase in inverter deadtime. Subharmonic oscillations of significant amplitude are observed in the steady-state simulated and measured current waveforms, at numerous operating points in the unstable region predicted, confirming the validity of the stability analysis. Furthermore, simulation and experimental results demonstrate that the proposed model is more accurate than an existing small-signal model in predicting the region of instability.

IEEE Transactions on Industry Applications

Small-Signal Stability Analysis of an Open-Loop Induction Motor Drive Including the Effect of Inverter Deadtime

Sound radiation from a rectangular, baffled and perforated piston vibrating harmonically is investigated in the two dimensional wavenumber domain. The perforations are in the form of an array of uniformly distributed circular holes. Perforation ratios in the piston and the baffle are independently chosen and this generalization is later used to represent a more practical case of a perforated piston fixed in an unperforated baffle. It is found that there exists a 'coupling' of the different wavenumbers of the spatially averaged fluid particle velocity field. Analytical expressions for the radiated power and the radiation efficiency are derived in an integral form. The results are presented and compared with those from a finite element solver (COMSOL). The COMSOL results are different due to dissimilar perforate impedance and flow continuity models adopted in their solver. The effect of the perforation ratio on the radiation efficiency of a perforated piston is also discussed.

Department of Mechanical Engineering

a 2-D Wavenumber Domain Formulation for the Radiation Efficiency of a Perforated Piston Fixed in a Baffle With an Arbitrary Perforation Ratioc

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted ℐ α ) were studied. Such minimizers were called forward ℐ α -projections. Here, a complementary class of minimization problems leading to the so-called reverse ℐ α -projections are studied. Reverse ℐ α -projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (α &gt; 1) and in constrained compression settings (α &lt;; 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse ℐ α -projection into a forward ℐ α -projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

Fulltext

IEEE Transactions on Information Theory

Minimization Problems Based on Relative α -Entropy II: Reverse Projection

Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subtle competition between different symmetry-broken phases, resulting from an interplay between the internal spin and valley degrees of freedom. The transition between different phases is often identified by an enhancement of the conductance. Here, we propose that the enhanced conductance at the transition is due to the appearance of robust conducting edge states at domain walls between the two phases. We formulate a criterion for the existence of such conducting edge states at the domain walls. For example, for a spontaneously layer polarized state at filling factor ν=2, domain walls between regions of opposite polarization carry conducting edge modes. A microscopic analysis shows that lattice-scale interactions can favor such a layer polarized state.

Department of Physics

covering condensed matter and materials physics

Spontaneous layer polarization and conducting domain walls in bilayer graphene

When a bridge engineer encounters a design or analysis problem concerning a bridge substructure, that structure will commonly have a mixture of member types, some slender, and some squat. Slender members are generally governed by flexure, and normal beam theory should suffice for analysis and design. Squat members can often be handled by beam theory too, although nowadays designers have a choice and may opt to use strut-and-tie (SAT) models. When the structure possesses a mixture of beam (B-) regions and deep or disturbed (D-) regions the dilemma facing the structural engineer is: What method should one use for structural analysis and design? The issue becomes even more murky when a structure already exists, but shows signs of damage and deterioration from the effects of Alkali Silica Reaction (ASR), Delayed Ettringite Formation (DEF), or other deterioration mechanisms. The engineer is faced with a second dilemma: How do deteriorated material properties get incorporated into the analysis?

Guidelines for analyzing the capacity of d-regions with premature concrete deterioration of ASR/DEF

The boxicity (cubicity) of a graph G is the minimum natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes (axis-parallel unit cubes) in Rk. In this article, we give estimates on the boxicity and the cubicity of Cartesian, strong and direct products of graphs in terms of invariants of the component graphs. In particular, we study the growth, as a function of d, of the boxicity and the cubicity of the dth power of a graph with respect to the three products. Among others, we show a surprising result that the boxicity and the cubicity of the dth Cartesian power of any given finite graph is, respectively, in O(log. d/log. log. d) and Θ (d/log. d). On the other hand, we show that there cannot exist any sublinear bound on the growth of the boxicity of powers of a general graph with respect to strong and direct products. © 2015 Elsevier Ltd.