Phase space formulation: Difference between revisions
en>Teply mNo edit summary |
en>Cuzkatzimhut m copyediting |
||
| Line 1: | Line 1: | ||
'''Teledeltos paper''' is an electrically [[conductive]] paper. It is formed by a coating of [[carbon]] on one side of a sheet of [[paper]], giving one black and one white side. | |||
It has several uses within engineering, usually for modelling the distribution of [[electric field|electric]] and other [[scalar field]]s. | |||
== Use == | |||
Teledeltos provides a sheet of a uniform resistor, with [[isotropic]] [[resistivity]] in each direction. As it is cheap<ref >{{Cite web | |||
|title=Teledeltos conductive paper sheets | |||
|url=http://www.timstar.co.uk/Search/1/12/0/teledeltos/NA/Best.html | |||
}}</ref> and easily cut to shape, it may be used to make one-off resistors of any shape needed. The paper backing also forms a convenient insulator from the bench. These are usually made to represent or model some real-world example of a two-dimensional [[scalar field]], where is it is necessary to study the field's distribution. This field may be an electric field, or some other field following the same linear distribution rules. | |||
The resistivity of Teledeltos is around 6 kilohms / square.<ref name="Baxter" /><ref group="note" >Note that the [[sheet resistance|resistivity units for a two-dimensional sheet]] are ohms / square (<math>\Omega/\Box</math>), not the [[mho]]s or [[Siemens (unit)|Siemens]] that would be used for a bulk resistor.</ref> This is low enough that it may be used with safe low voltages, yet high enough that the currents remain low, avoiding problems with [[contact resistance]]. | |||
Connections are made to the paper by painting on areas of silver-loaded [[conductive paint]] and attaching wires to these, usually with spring clips.<ref name="Baxter" /><ref name="Aston" >{{Cite web | |||
|title=Field Plotting Using Teledeltos Paper | |||
|publisher=Department of Electronic Engineering and Applied Physics, Aston University | |||
|url=http://www-users.aston.ac.uk/~pearcecg/Teaching/PDF/TELDELT.PDF | |||
|format=pdf | |||
}}</ref> Each painted area has a low resistivity (relative to the carbon) and so may be assumed to be at a constant voltage. With the voltages applied, the current flow through the sheet will emulate the field distribution. Voltages may be measured within the sheet by applying a voltmeter probe (relative to one of the known electrodes) or current flows may be measured. As the sheet's resistivity is constant, the simplest way to measure a current flow is to use a small two-probe voltmeter to measure the voltage difference between the probes. As their spacing is known, and the resistivity, the resistance between them and (by [[Ohm's law]]) the current flow can be easily determined. | |||
An assumption in some cases is that the surrounding field is 'infinite', this would also require an infinite sheet of Teledeltos. Provided that the sheet is merely 'large' in comparison to the experimental area, a sheet of finite size is sufficient for most experimental practice.<ref name="Aston" /> | |||
== Field plotting == | |||
The basic technique for plotting a field is to first construct a model of the [[independent variable]]s, then to use voltage meter probes to measure the [[dependent variable]]s. Typically this means applying known voltages at certain points, then measuring voltages and currents within the model. The two basic approaches are to either applying electrodes and a voltage at known points within a large sheet of Teledeltos (modelling an infinite field) or else to cut a shape from Teledeltos and then apply voltages to its edges (modelling a bounded field).<ref name="Baxter" /><ref name="Aston" /> There is a common practical association that electrical field models are usually infinite and thermal models are usually bounded. | |||
== Modelling fields by analogy == | |||
Although the modelling of electric fields is itself directly useful in some fields such as [[thermionic valve]] design,<ref name="Pease" >{{Cite web | |||
|title=What's All This Teledeltos Stuff, Anyway? | |||
|url=http://electronicdesign.com/article/analog-and-mixed-signal/what-s-all-this-teledeltos-stuff-anyway-12594 | |||
|date=30 May, 1994 | |||
|author=Bob Pease | |||
}}</ref> the main practical use of the broader technique is for modelling fields of other quantities. This technique may be applied to ''any'' field that follows the same linear rules as Ohm's law for bulk resistivity. This includes heat flow, some optics and some aspects of Newtonian mechanics. It is not usually applicable to fluid dynamics, owing to viscosity and compressibility effects, or to high-intensity optics where [[non-linear optics|non-linear effects]] become apparent. It may be applicable to some mechanical problems involving homogeneous and isotropic materials such as metals, but not to composites. | |||
Before the use of Teledeltos, a similar technique had been used for modelling gas flows, where a shallow tray of [[copper sulphate]] solution was used as the medium, with copper electrodes at each side. Barriers within the model could be sculpted from wax. Being a liquid, this was far less convenient. [[Stanley Hooker]] describes its use pre-war, although he also notes that [[compressibility]] effects could be modelled in this way, by sculpting the base of the tank to give additional depth and thus conductivity locally.<ref >{{Cite book | |||
|last=Hooker |first=Stanley |authorlink=Stanley Hooker | |||
|title=Not much of an engineer. An autobiography | |||
|publisher=Airlife Publ. |location=Shrewsbury | |||
|year=2002 | |||
|isbn=1-85310-285-7 | |||
|ref=harv | |||
|pages=9–10 | |||
}}</ref> | |||
One of the most important applications is for thermal modelling. Voltage is the analog of temperature and current flow that of [[heat flow]]. If the boundaries of a [[heatsink]] model are both painted with conductive paint to form two separate electrodes, each may be held at a voltage to represent the temperatures of some internal heat source (such as a microprocessor chip) and the external ambient temperature. Potentials within the heatsink represent internal temperatures and current flows represent heat flow. In many cases the internal heat source may be modelled with a [[constant current source]], rather than a voltage, giving a better analogy of power loss as heat, rather than assuming a simple constant temperature. If the external airflow is restricted, the 'ambient' electrode may be subdivided and each section connected to a common voltage supply through a resistor or current limiter, representing the proportionate or maximum heatflow capacity of that airstream. | |||
As heatsinks are commonly manufactured from [[aluminium extrusion|extruded aluminium section]]s, the two-dimensional paper is not usually a serious limitation. In some cases, such as pistons for internal combustion engines, three dimensional modelling may be required. This has been performed, in a manner analogous to Teledeltos paper, by using volume tanks of a conductive electrolyte.<ref >{{Cite journal | |||
|title=The Napier Deltic Diesel Engine in Main-line Locomotives | |||
|journal=Proc. Inst. Mech. Engrs. | |||
|last=Chamberlin | |||
|first=R.H. | |||
|year=1963–1964 | |||
|volume=178 | |||
|issue=3 | |||
|ref={{harvid|Chamberlin}} | |||
|page=66 | |||
|url=http://pcp.sagepub.com/content/178/11/53.full.pdf+html | |||
}}</ref> | |||
This thermal modelling technique is useful in many branches of [[mechanical engineering]] such as heatsink or [[radiator]] design and [[die casting]].<ref name="jorstad" >{{Cite journal | |||
|last = John L. |first = Jorstad | |||
|title = Aluminum Future Technology in Die Casting | |||
|pages = 19 | |||
|url = http://www.wpi.edu/Images/CMS/MPI/Jorstad.pdf | |||
|journal = Die Casting Engineering | |||
|year = 2006 |month = September | |||
|archiveurl = http://www.webcitation.org/5uBp7JOJZ |archivedate = 11-12-2010 | |||
}}</ref> | |||
The development of [[computational modelling]] and [[finite element analysis]] has reduced the use of Teledeltos, such that the technique is now obscure and the materials can be hard to obtain.<ref name="Baxter" /> Its use is still highly valuable in teaching, as the technique gives a very obvious method for measuring fields and offers immediate feedback as the shape of an experimental setup is changed, encouraging a more fundamental understanding.<ref name="Aston" /><ref name="Pease" /> | |||
== Sensors == | |||
Teledeltos can also be used to make [[sensor]]s, either directly as an embedded resistive element or indirectly, as part of their design process. | |||
=== Resistive sensors === | |||
A piece of Teledeltos with conductive electrodes at each end makes a simple [[resistor]]. Its resistance is slightly sensitive to applied mechanical [[strain (mechanics)|strain]] by bending or compression, but the paper substrate is not robust enough to make a reliable sensor for long-term use. | |||
A more common resistive sensor is in the form of a [[potentiometer]]. A long, thin resistor with an applied voltage may have a conductive probe slid along its surface. The voltage at the probe depends on its position between the two end contacts. Such a sensor may form the keyboard for a simple electronic musical instrument like a [[Tannerin]] or [[Stylophone]]. | |||
A similar linear sensor uses two strips of Teledeltos, placed face to face. Pressure on the back of one (finger pressure is enough) presses the two conductive faces together to form a lower resistance contact. This may be used in similar potentiometric fashion to the conductive probe, but without requiring the special probe. This may be used as a classroom demonstration for another electronic musical instrument, with a [[ribbon controller]] keyboard, such as the [[Korg Monotron|Monotron]]. If crossed electrodes are used on each piece of Teledeltos, a two-dimensional [[Touchscreen#Resistive|resistive touchpad]] may be demonstrated. | |||
=== Capacitive sensors === | |||
Although Teledeltos is not used to manufacture capacitive sensors, its field modelling abilities also allow it to be used to determine the capacitance of arbitrarily shaped electrodes during sensor design.<ref name="Baxter" >{{Cite book | |||
|title=Capacitive Sensors: Design and Applications | |||
|author=Larry K. Baxter | |||
|publisher=John Wiley & Sons | |||
|year=1996 | |||
|isbn=078035351X | |||
|chapter=Analytical solutions | |||
|url=http://books.google.co.uk/books?id=Tjd2laRnO4wC&pg=PA25&lpg=PA25&dq=teledeltos&source=bl&ots=NvX2nlzD_5&sig=jqIuhkVu61vtNa-3NPvyK-SufJ8&hl=en&sa=X&ei=v_PRT9OdCOOr0QWEnLmdBA&redir_esc=y#v=onepage&q=teledeltos&f=false | |||
|page=25 | |||
}}</ref> | |||
== See also == | |||
* [[Finite element analysis]] | |||
* [[Hydraulic analogy]] | |||
== References == | |||
{{Reflist|group=note|liststyle=lower-roman}} | |||
{{Reflist|colwidth=35em}} | |||
[[Category:Analog computers]] | |||
[[Category:Electrical engineering]] | |||
[[Category:Sensors]] | |||
Revision as of 16:49, 20 November 2013
Teledeltos paper is an electrically conductive paper. It is formed by a coating of carbon on one side of a sheet of paper, giving one black and one white side.
It has several uses within engineering, usually for modelling the distribution of electric and other scalar fields.
Use
Teledeltos provides a sheet of a uniform resistor, with isotropic resistivity in each direction. As it is cheap[1] and easily cut to shape, it may be used to make one-off resistors of any shape needed. The paper backing also forms a convenient insulator from the bench. These are usually made to represent or model some real-world example of a two-dimensional scalar field, where is it is necessary to study the field's distribution. This field may be an electric field, or some other field following the same linear distribution rules.
The resistivity of Teledeltos is around 6 kilohms / square.[2][note 1] This is low enough that it may be used with safe low voltages, yet high enough that the currents remain low, avoiding problems with contact resistance.
Connections are made to the paper by painting on areas of silver-loaded conductive paint and attaching wires to these, usually with spring clips.[2][3] Each painted area has a low resistivity (relative to the carbon) and so may be assumed to be at a constant voltage. With the voltages applied, the current flow through the sheet will emulate the field distribution. Voltages may be measured within the sheet by applying a voltmeter probe (relative to one of the known electrodes) or current flows may be measured. As the sheet's resistivity is constant, the simplest way to measure a current flow is to use a small two-probe voltmeter to measure the voltage difference between the probes. As their spacing is known, and the resistivity, the resistance between them and (by Ohm's law) the current flow can be easily determined.
An assumption in some cases is that the surrounding field is 'infinite', this would also require an infinite sheet of Teledeltos. Provided that the sheet is merely 'large' in comparison to the experimental area, a sheet of finite size is sufficient for most experimental practice.[3]
Field plotting
The basic technique for plotting a field is to first construct a model of the independent variables, then to use voltage meter probes to measure the dependent variables. Typically this means applying known voltages at certain points, then measuring voltages and currents within the model. The two basic approaches are to either applying electrodes and a voltage at known points within a large sheet of Teledeltos (modelling an infinite field) or else to cut a shape from Teledeltos and then apply voltages to its edges (modelling a bounded field).[2][3] There is a common practical association that electrical field models are usually infinite and thermal models are usually bounded.
Modelling fields by analogy
Although the modelling of electric fields is itself directly useful in some fields such as thermionic valve design,[4] the main practical use of the broader technique is for modelling fields of other quantities. This technique may be applied to any field that follows the same linear rules as Ohm's law for bulk resistivity. This includes heat flow, some optics and some aspects of Newtonian mechanics. It is not usually applicable to fluid dynamics, owing to viscosity and compressibility effects, or to high-intensity optics where non-linear effects become apparent. It may be applicable to some mechanical problems involving homogeneous and isotropic materials such as metals, but not to composites.
Before the use of Teledeltos, a similar technique had been used for modelling gas flows, where a shallow tray of copper sulphate solution was used as the medium, with copper electrodes at each side. Barriers within the model could be sculpted from wax. Being a liquid, this was far less convenient. Stanley Hooker describes its use pre-war, although he also notes that compressibility effects could be modelled in this way, by sculpting the base of the tank to give additional depth and thus conductivity locally.[5]
One of the most important applications is for thermal modelling. Voltage is the analog of temperature and current flow that of heat flow. If the boundaries of a heatsink model are both painted with conductive paint to form two separate electrodes, each may be held at a voltage to represent the temperatures of some internal heat source (such as a microprocessor chip) and the external ambient temperature. Potentials within the heatsink represent internal temperatures and current flows represent heat flow. In many cases the internal heat source may be modelled with a constant current source, rather than a voltage, giving a better analogy of power loss as heat, rather than assuming a simple constant temperature. If the external airflow is restricted, the 'ambient' electrode may be subdivided and each section connected to a common voltage supply through a resistor or current limiter, representing the proportionate or maximum heatflow capacity of that airstream.
As heatsinks are commonly manufactured from extruded aluminium sections, the two-dimensional paper is not usually a serious limitation. In some cases, such as pistons for internal combustion engines, three dimensional modelling may be required. This has been performed, in a manner analogous to Teledeltos paper, by using volume tanks of a conductive electrolyte.[6]
This thermal modelling technique is useful in many branches of mechanical engineering such as heatsink or radiator design and die casting.[7]
The development of computational modelling and finite element analysis has reduced the use of Teledeltos, such that the technique is now obscure and the materials can be hard to obtain.[2] Its use is still highly valuable in teaching, as the technique gives a very obvious method for measuring fields and offers immediate feedback as the shape of an experimental setup is changed, encouraging a more fundamental understanding.[3][4]
Sensors
Teledeltos can also be used to make sensors, either directly as an embedded resistive element or indirectly, as part of their design process.
Resistive sensors
A piece of Teledeltos with conductive electrodes at each end makes a simple resistor. Its resistance is slightly sensitive to applied mechanical strain by bending or compression, but the paper substrate is not robust enough to make a reliable sensor for long-term use.
A more common resistive sensor is in the form of a potentiometer. A long, thin resistor with an applied voltage may have a conductive probe slid along its surface. The voltage at the probe depends on its position between the two end contacts. Such a sensor may form the keyboard for a simple electronic musical instrument like a Tannerin or Stylophone.
A similar linear sensor uses two strips of Teledeltos, placed face to face. Pressure on the back of one (finger pressure is enough) presses the two conductive faces together to form a lower resistance contact. This may be used in similar potentiometric fashion to the conductive probe, but without requiring the special probe. This may be used as a classroom demonstration for another electronic musical instrument, with a ribbon controller keyboard, such as the Monotron. If crossed electrodes are used on each piece of Teledeltos, a two-dimensional resistive touchpad may be demonstrated.
Capacitive sensors
Although Teledeltos is not used to manufacture capacitive sensors, its field modelling abilities also allow it to be used to determine the capacitance of arbitrarily shaped electrodes during sensor design.[2]
See also
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
- ↑ Template:Cite web
- ↑ 2.0 2.1 2.2 2.3 2.4 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 3.0 3.1 3.2 3.3 Template:Cite web
- ↑ 4.0 4.1 Template:Cite web
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
Cite error: <ref> tags exist for a group named "note", but no corresponding <references group="note"/> tag was found