NDLI: Accurate Prediction of Transient Thermal Behavior of Electronic Systems With State-Space Models

Please wait, while we are loading the content...

ANES/ASME Joint National Solar Energy Week

ASME Citrus Engineering Symposium

ASME India Oil and Gas Pipeline Conference

ASME International Mechanical Engineering Congress and Exposition

ASME 2002 International Mechanical Engineering Congress and Exposition(IMECE2002)

ASME 2003 International Mechanical Engineering Congress and Exposition(IMECE2003)

ASME 2004 International Mechanical Engineering Congress and Exposition(IMECE2004)

ASME 2005 International Mechanical Engineering Congress and Exposition(IMECE2005)

ASME 2006 International Mechanical Engineering Congress and Exposition(IMECE2006)

ASME 2007 International Mechanical Engineering Congress and Exposition(IMECE2007)

ASME 2008 International Mechanical Engineering Congress and Exposition(IMECE2008)

ASME 2009 International Mechanical Engineering Congress and Exposition(IMECE2009)

ASME 2010 International Mechanical Engineering Congress and Exposition(IMECE2010)

ASME 2011 International Mechanical Engineering Congress and Exposition(IMECE2011)

Volume 3: Design and Manufacturing

Volume 5: Engineering Education and Professional Development

Volume 6: Fluids and Thermal Systems; Advances for Process Industries, Parts A and B

Comparison of Experimental Results to CFD Models for Blending in a Tank Using Dual Opposing Jets

Blending Time and Velocity Variations During Blending in a Tank Using Dual Opposing Jets

A Numerical Investigation of the Effects of Flow Pulsations on the Vortex Shedding, Drag and Lift Forces Over a Cylinder

Dynamic Response of Underwater Structures Subject to Impact Loads

Effects of High Initial Engine Start Up Speeds in Isothermal Fluid Flow and Piston Skirts EHL

Investigation of Low Reynolds Number Experiment and Numerical Simulation on Compressor Cascade

Ring-Shaped Sessile Droplet

Measurement of Hydrodynamic Frictional Drag on Superhydrophobic Flat Plates in High Reynolds Number Flows

Dynamics of Wake Behind a Low Aspect Ratio Pitching Plate

Experimental Study of Entrainment Ratio of the Near Exit Region of High-Speed Jets

CFD Assisted Design Optimization of a Flow Distributor for Uniform Fluid Distribution

Promoting or Suppressing Transition to Weak Turbulence in Porous Media Convection via Feedback Control

Modeling of Deformations and Stresses During Glass Tempering

Early-Stage Evolution of Electrons Emitted From Metal Target Surface During Ultrashort Laser Ablation in Vacuum

The Effect of External Magnetic Field on the Plasma Induced by Laser Ablation in Vacuum

A Model to Predict Contact Resistance During Contact Solidification in Ribbon Growth on Substrate Process

Normal-Mode and Lumped Mass Assessment of Acoustic Degassing of Liquid Metals in an Inductively Heated Cylindrical Furnace

Graetz Problem in Ducts of Circular and Some Non-Circular Cross-Sections With Viscoelastic Fluids

Numerical Simulations of Non-Newtonian Geophysical Flows Using Smoothed Particle Hydrodynamics (SPH) Method: A Rheological Analysis

A Variant Algorithm for Solving Eigenvalue Equation in Linear Stability Problems

Modeling of Laminar Viscous Flow in a Semi-Porous Channel Under Uniform Magnetic Field

Water-Hydrocarbon Emulsion Flow in Microchannels

Application of Viscoelastic Fluids in Industrial Dampers

Stress Analysis of Pseudo-Plastic Flow Between Rotating Cylinders

Flow Field Around Dimpled Pin-Fins in a Staggered Array

Conduit Flow Control Through Magnetorheology

Analysis of Plug Zones in Steady Flow in Undulating Channels

Anomalous Rheological Behavior of Complex Fluids (Nanofluids)

Rheological Properties of “Dry Water”

Steady and Dynamic Rheological Properties of Dense Slurries of Chlorella vulgaris

Dispersion of Particles on Liquid Surfaces

Modeling of Blood Flow in the Human Brain

Rheological Study of Y2O3 Nanofluids

The Effects of Operating Conditions on the Design of Radial Spiral Mandrel Dies

Numerical Investigation of Slider Bearings With Limited Corrugation and Power-Law Lubricant

Performance of a Multiple Stage EHD Gas Pump in a Square Channel

Dynamic Simulation of a HRSG System for a Given Start-Up/Shut Down Curve

Hydrodynamic Added Mass and Damping of the Kaplan Turbine

Developing the Color Full-Scale Schlieren Technique for Flow Visualization

Large Eddy Simulation of the Flow Around a Diffuser-Equipped Bluff Body in Ground Effect

Computational Study of Slurry Flow in Pipes to Determine Profiles Sensed in Near Infrared Slurry Measurements

Effect of a Symmetric Contraction on the Concentration Profiles of a Particle-Laden Slurry

Numerical Investigation of an Impingement Flow due to a Free Surface Axisymmetric Long Water Jet

Simulation of Heat Transfer in a Counterflow Porous Bed Reactor With a Thermal Non-Equilibrium Model

Reduction Effects of Suspended Particulate Matters in Air by Thermal Moisture Swing Method

Hydraulic Accumulator as Energy Storage

Assessment of Prototypic and Closed Loop Operation During Pulse Jet Mixer Tests With Non-Cohesive Solids to Develop Scale-Up Relationships

Continuing Towards the Optimization of a Pulsatile Three-Stream Coaxial Airblast Injector

Cavitation at Sharp Edge Multi-Hole Baffle Plates

A Mechanistic Model of Two-Phase Pressure Drop in Microchannels

Two-Phase Flow Simulations of Protective Gas Layer for Spallation Neutron Source Target

Computational Fluid Dynamics Using Graphics Processing Units: Challenges and Opportunities

Large Eddy Simulations of Film-Cooling Flows With a Micro-Ramp Vortex Generator

Aerodynamic Bicycle Helmet Design Using a Truncated Airfoil With Trailing Edge Modifications

Prediction of Boiling and Critical Heat Flux Using an Eulerian Multiphase Boiling Model

Initial Impact of Liquid Jets and Entrainment of Air Bubbles: A Numerical Study

Development of Surface Tension Model Using Inter-Particle Force in Particle Method Based on Continuum Dynamics

Determination of Minimum Fluidization Velocity for Gas-Solid Beds by Experimental Data and Numerical Simulations

Simulation of Effects of the Saffman Force and the Magnus Force on Sand Saltation in Turbulent Flow

CFD Analyses of the Mixing Characteristics in Bubble Columns and Airlift Reactors

Simulation of Two-Phase Flow and Heat Transfer for Practical Design of Mini- and Micro-Channel Heat Exchangers

Analysis of Taylor Flow in Microchannels by the Phase Field Method

Numerical Simulation of Melting/Solidification Phenomena Using a Multi–Fluid Modeling Approach

Investigation of Convective Heat Transfer of Aqueous Nanofluids in Microchannels Integrated With Temperature Nanosensors

Numerical Modeling and Validation of Supersonic Two-Phase Flow of CO2 in Converging-Diverging Nozzles

Particle Resuspension From Carpeted Floorings in Indoor Environment in Turbulent Flows

Transport and Deposition of Elongated Particles in the Upper Airways

Simulation of Laminar Liquid Jets in Gaseous Crossflow Before the Onset of Primary Breakup

Effect of Indoor Air Ventilation on Particulate Pollutant Concentration Distribution, Including Nucleation, Coagulation and Surface Growth

Particle Effects on Gas-Liquid-Solid Flows

Detection of Elliptical Cylindrical Inclusions by Magnetic Sensing

Separation of Magnetic Beads in a Microfluidic Device: Modeling and Experimentation

Destruction of Water-in-Oil Emulsions in Electromagnetic Fields

Analytical Solution for Temperature Distribution in Microwave Heating of Rectangular Objects

Microscale Electrokinetics: Dielectrophoretic Manipulation of Particles

Effect of Brownian Motion and External Magnetic Field on the Effective Heat Capacity of Ferrofluids

Research and Practice on the In-Situ Calibration System for Flowrate of Pump-Test-Rig

SENARIET, A Water Hammer Software for Analyzing Hydraulic Transients in Complex Circuits

Electrokinetic Microscope for Imaging Three-Dimensional Surface Topography and Heterogeneity

Images Analysis of Horizontal Two-Phase Slug Flows

Cryogenic Temperature Stabilization of the Daikin 308 Cryocooler

Tracer Gas Mapping of a Beverage Cart Wake in a Twin Aisle Aircraft Cabin

Characterisation of Air-Water Two-Phase Flow Using a Wire-Mesh Sensor

Measuring Paint Droplet Size, Velocity, and Charge-to-Mass Ratio Distribution for Electrostatic Rotary Bell Spray Simulation

Optimal Parametric Model for Vortex Tube Using DOE

Can We Rescue Thermal Wall Shear Stress Sensing?

An Experimental Study of Natural Convection in a Rectangular Enclosure Using PIV Measurement Techniques

Turbulent Flow Over a Facing Step at Several Reynolds Numbers

Normalisation of Test Results in Air Screw Compressor Measurements as a Basis for Performance Estimation of Refrigeration and Process Gas Compressors

Flow Signal Characteristics of an Ultrasonic Transducer at a High Temperature

Cross Analysis of Metal Foam Design Parameters for Achieving Desired Fluid Flow

Influence of Pipe Roughness on the Performance of Ultrasonic Meters for Flow Rate Measurement

The Effect of Orifice Angle and Cavity Dimension on Rectangular Synthetic Jet Actuators

Gas Mass Flow Rate Measurement in T-Shaped Microchannels in Slip Flow Regime

A State Space Thermal Model for HEV/EV Non-Linear and Time-Varying Battery Thermal Systems

Numerical Simulation of Relationship Between Flow Pattern and Hydraulic Performance of Tubular Pump

An Unsteady Numerical Investigation on the Hysteresis Stall Loop of a Counter-Rotating Compressor

Gerotor Fuel Pump Performance and Leakage Study

Massively Parallel Computational Fluid Dynamics With Large Eddy Simulation in Complex Geometries

Mixing Performance of Sewage Treatment Mixer at Different Rotational Speed

Stability of Non-Newtonian Taylor-Couette With Axial Flow

Numerical Study of Ventilation Flow Through a Two Dimensional Room Fitted With a Windcatcher

The Direct Numerical Simulation of the Rising Gas Bubble With the Volume of Fluid (VOF) Method

Flow About an Oscillating Plate Used to Extract Sea-Wave Energy

Numerical Analysis of Erosion and Sediment Control Using Lake-Shore Extensions in Lake Charles

Proper Orthogonal Decomposition Analysis of JaVA Flows for Cross-Flow Conditions

CFD Analysis of Hydro Turbine Performance for Multi-Rotor Configurations

Modeling Guidelines for Large Telecom Rack CFD Models

Numerical Simulation of a PAK-B Airfoil Using Fully Turbulent and Transition-Sensitive RANS Models

Simulation of the Turbulent Dispersion of 10 Micron Particles in a Generic Half-Cabin Model

CFD Computation, Analysis and Design of a Two-Bladed Wastewater Pump

A Semi-Staggered Numerical Procedure for the Incompressible Navier-Stokes Equations on Curvilinear Grids

Computer Modeling of Time History of Velocity Field and Net Momentum Output of a Synthetic Jet Actuator

Closed-Loop Feedback Control Algorithms for Flow Control Over NACA 0015 Airfoil

Effects of Number of Stator Blades on the Performance of a Torque Converter

Validation and Optimization of Heat Transfer in the Electrical Submersible Pump Motor by CFD

Radial Impeller Design Optimization Matched for High Efficiency Fans

Three-Dimensional Scouring Analysis for Open Channel Pressure Flow Scour Under Flooded Bridge Decks

Effects of Guide Vanes in Transition Flow From a Round Pipe to a Rectangular Chamber

Optimization of a Centrifugal Fan Impeller Using Kriging Simulated Annealing

Modeling and Optimization of Micro-Channel Heat Sinks for the Cooling of 3D Stacked Integrated Circuits

Effect of Viscosity and Reynolds Number for Flow in Converging Microchannels

Investigation for Toroidal Microfluidic Vortices Generated by a Laser Illumination Application in an Uniform Electric Field

Non-Linear Behavior of Electrothermal Flows

The Effect of Nano-Structured Surfaces on Droplet Impingement Heat Transfer

Performance Characteristics of a Variable Density Pin Array Micro-Heat Exchanger

Capillary-Based Liquid Micro/Nano Deposition

Nanoparticle Deposition and Convective Transport in Microchannel Heat Exchanger Systems

Continuum/Nano-Scale Simulation of Surface Diffusion Process in Flow

Tracking of Capillary Interface in Microfluidic Channels

Study of Factors in Coffee-Ring Structure Formation Using PIV Methods

Experimental Investigations of Turbulent Gas Flow in a Micro-Channel

Simulation of Red Blood Cell Passing Through Constrictions Using Modified Moving Particle Semi-Implicit Method

Simulation of Red Blood Cell Deformation in Microvessels Using a New Rapid Modified Particle Method

Spectral Boundary Element Method for Liquid Bridge Dynamics Between Capillary and Substrate

Orthogonal Electrode Micropump Design Using DC and AC Electroosmosis

Numerical Study of Microchamber Filling in Centrifugal Microfluidics

Microfluidic Study of Drainage and Imbibition in Porous Media: Definition of Amott Indices

Numerical Simulation on Heat Transfer Characteristics of Turbulent Gas Flow in Micro-Tubes

Minimizing the Wick Thickness in a Planar Microscale Loop Heat Pipe Using Efficient Thermodynamic Design

Numerical Modeling and Experimental Investigation of Improved Mixing From Both Coriolis Effect and Go¨rtler Vortices in Rotating Zigzag Microchannel

Electrothermal Pumping With Thin Film Resistive Heaters

A Numerical Study of Unsteady Laminar Flow and Heat Transfer Through an Array of Rotating Rectangular Microchannels

Enhanced Capillarity in Microchannels Coated With Nanoscale Porous Titanium Dioxide

Acoustic Manipulation of Particles in Variously Shaped Liquid Droplets

Flow Visualization in Artificial Porous Media From Microfluidic PMMA Devices

Experimental Parametric Analysis of Water-Mist Sprays: An Investigation on Coalescence and Initial Dispersion

Study of Bubbly Flow Through a Packed Bed

Experimental Investigation of EHD Flow Regimes Map in an Electrostatic Air-Oil Droplets Separator

Far-Infrared Imaging Method for Non-Contact Monitoring of Ice Valve Array in Controlling Micro/Nano Fluidics

Effect of Airfoil Shape and Turning Angle on Turbine Airfoil Aerodynamic Performance at Transonic Conditions

Computational Investigation of Tower Shadow Effects on Wind Turbines

Investigation of Two Analytical Wake Models Using Data From Wind Farms

Integration of Computational Fluids Dynamics and Virtual Reality Visualization for Constructing the Wind Field

Controller Design to Reduce Mechanical Fatigue in Offshore Wind Turbines Affected by Ice and Tide

Longitudinal Flight Control for a Novel Airborne Wind Energy System: Robust MIMO Control Design Techniques

Studying the Effect of Number of Blades on the Aerodynamic Performance of a Venturi Effect Fluid Turbine (VEFT) by Numerical Simulation

Design Considerations, Performance Enhancing Techniques, and Wind Tunnel Testing for Small-Scale, Low Reynolds Number Wind Turbines

Numerical Investigation of Pulsed Chemical Vapor Deposition of Aluminum Nitride to Reduce Particle Formation

Optimization of Ski Jumper’s Posture Considering Lift-to-Drag Ratio and Aerodynamic Stability in Pitch

Analyzing Compression and Buoyancy in Technical Swimming Suits

Experimental Investigation of Selective Withdrawal and Light Layer Entrainment of Stratified Immiscible Liquids

Phase Field Method for Simulation of Multiphase Flow

Simulation of 3D Multistage Axial Compressor Using a Fully Conservative Sliding Boundary Condition

A Product-Service System for Industrial Waste Heat Recovery Using Mobile Latent Heat Accumulators

Three Dimensional Numerical Simulation of the Natural Convection in an Annulus With an Internal Slotted Cylinder

Numerical Analysis on Thermal Deformation of Linear Motor in Chip Mounter

Aerodynamic Analysis in Lean Blade Effects in Centrifugal Compressor

The Ideal Control Curves of Low Stress Precision Cropping Experimental Study on Metal Bar

Effect of Supply Air Temperature on Rack Cooling in a High Density Raised Floor Data Center Facility

Computational Modeling of Anisotropic Thermal Conductivity and Joule Heating on Printed Circuit Boards

Accurate Prediction of Transient Thermal Behavior of Electronic Systems With State-Space Models

Enhanced Selective Non-Catalytic Reduction (SNCR) for Refinery Applications: Pilot-Scale Test Data With a Hydrogen Promoter

Flow Dynamic Effect in Cake Shape and Resistance in Membrane Filtration

Aqua-Ammonia as an Environmentally Acceptable Low Temperature Brine

Radial, Two-Phase Heat Transport Device Driven by Electrohydrodynamic Conduction Pumping

Numerical Studies of Thermoacoustic Convection in Near-Critical Fluids

Optimization of Heat Exchanger Networks

Electrohydrodynamic (EHD) Enhanced Separation of Fine Liquid Droplets From Gas Flows

Heat and Mass Transfer in Double-Filmwise Heat Exchanger for Industrial Food Processing Applications

Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, Uncertainty and Probability

Volume 1: Advances in Aerospace Technology; Energy Water Nexus; Globalization of Engineering; Posters

Volume 2: Biomedical and Biotechnology Engineering; Nanoengineering for Medicine and Biology

Volume 4: Energy Systems Analysis, Thermodynamics and Sustainability; Combustion Science and Engineering; Nanoengineering for Energy, Parts A and B

Volume 8: Mechanics of Solids, Structures and Fluids; Vibration, Acoustics and Wave Propagation

Volume 10: Heat and Mass Transport Processes, Parts A and B

Volume 7: Dynamic Systems and Control; Mechatronics and Intelligent Machines, Parts A and B

Volume 11: Nano and Micro Materials, Devices and Systems; Microsystems Integration

ASME 2012 International Mechanical Engineering Congress and Exposition(IMECE2012)

ASME 2013 International Mechanical Engineering Congress and Exposition(IMECE2013)

ASME 2014 International Mechanical Engineering Congress and Exposition(IMECE2014)

ASME 2015 International Mechanical Engineering Congress and Exposition(IMECE2015)

ASME 2016 International Mechanical Engineering Congress and Exposition(IMECE2016)

ASME 2017 International Mechanical Engineering Congress and Exposition(IMECE2017)

ASME 2018 International Mechanical Engineering Congress and Exposition(IMECE2018)

ASME International Pipeline Geotechnical Conference

ASME Power Conference

ASME Turbine Blade Tip Symposium

ASME/IEEE Joint Rail Conference

ASME/JSME Thermal Engineering Joint Conference

ASME/NRC Pump and Valve Symposium

ASME/USCG Workshop on Marine Technology and Standards

CANEUS: MNT for Aerospace Applications

Dynamic Systems and Control Conference

Energy Nanotechnology International Conference

Energy Sustainability

Engineering Systems Design and Analysis

Engineering Technology Conference on Energy

Fluid Power Systems Technology

Fluids Engineering Division Summer Meeting

Frontiers in Biomedical Devices

Gas Turbine India Conference

Global Congress on NanoEngineering for Medicine and Biology

Heat Transfer Summer Conference

High Temperature Reactor Technology

Information Storage and Processing Systems

Integrated Nanosystems: Design, Synthesis, and Applications

Internal Combustion Engine Division Fall Technical Conference

Internal Combustion Engine Division Spring Technical Conference

International Conference on Fluidized Bed Combustion

International Conference on Fuel Cell Science, Engineering and Technology

International Conference on Integration and Commercialization of Micro and Nanosystems

International Conference on Micro/Nanoscale Heat Transfer

International Conference on Nanochannels, Microchannels, and Minichannels

International Conference on Nuclear Engineering

International Conference on Offshore Mechanics and Arctic Engineering

International Conference on Radioactive Waste Management and Environmental Remediation

International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

International Electronic Packaging Technical Conference and Exhibition

International Heat Transfer Conference

International Joint Power Generation Conference

International Joint Tribology Conference

International Manufacturing Science and Engineering Conference

International Pipeline Conference

International Solar Energy Conference

International Symposium on Flexible Automation

Multifunctional Nanocomposites and Nanomaterials International Conference

Noise Control and Acoustics Division Conference

North American Waste-to-Energy Conference

Pressure Technology

Pressure Vessels and Piping Conference

Rail Transportation Division Conference

Small Modular Reactors Symposium

Smart Materials, Adaptive Structures and Intelligent Systems

Summer Bioengineering Conference

Turbo Expo: Power for Land, Sea, and Air

Verification and Validation

Water Quality, Drought, Human Health and Engineering Conference

Wind Energy Symposium

World Conference on Innovative Virtual Reality

World Tribology Congress

Accurate Prediction of Transient Thermal Behavior of Electronic Systems With State-Space Models

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Dogruoz, M. Baris Magargle, Ryan Shankaran, Gokul
Copyright Year	2011
Abstract	Accurate prediction of transient thermal behavior of electronic systems with the use of Computational Fluid Dynamics (CFD) requires large amount of CPU time. Even though steady state response of such systems is mostly of interest, transient thermal simulations with actual time dependent power cycles should be carried out to determine the steady-state behavior. Traditionally, power dissipation values are time-averaged to obtain steady-state characteristics, which may or may not be accurate. To overcome the large associated computational cost, several different approximate models were suggested and published in the literature. Among these models, Resistor-Capacitor (R-C) thermal network approaches have been popular in obtaining the transient response for the past few decades. These approaches require rigorous curve-fitting effort followed by an optimization process and are applicable to relatively simple systems. This study presents a state-space approach to determine transient and steady state behavior of electronic systems as accurately as possible without compromising the speed. This technique is applied to a sample graphics card system and the comparisons are made with the fully transient CFD model computations. It is shown that the temperature histories obtained from the state-space approach agree very well with those from the fully transient CFD simulations, where the CPU time for the former is radically (three to four orders of magnitude) smaller compared to that of the latter.
Starting Page	1389
Ending Page	1395
Page Count	7
File Format	PDF
ISBN	9780791854921
DOI	10.1115/IMECE2011-65628
Volume Number	Volume 6: Fluids and Thermal Systems; Advances for Process Industries, Parts A and B
Conference Proceedings	ASME 2011 International Mechanical Engineering Congress and Exposition
Language	English
Publisher Date	2011-11-11
Publisher Place	Denver, Colorado, USA
Access Restriction	Subscribed
Subject Keyword	Resistors Temperature Computational fluid dynamics Capacitors Thermodynamic power cycles Steady state Optimization Transients (dynamics) Electronic systems Simulation Computation Energy dissipation Engineering simulation Curve fitting
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in