The FPV just like the F1 racing car in the drone, which uses the first person view to control. In the process of flight, through the specified arches, high-speed turns sideways, all-around flips to control the flight. Then, when beginners to play FPV, how to fly it and what to attention?
The FPV hitting obstacles is inevitable with a high-speed flight in the air. So most of FPV have a anti-fall. But we should to pay more attention to the flight safety, avoiding to hurts somebody.
For the FPV racing, it just like the F1 racing car, there is a corresponding runway. For beginners, the FPV is suitable for flying in an open environment. Indoor or small-scale place is dangerous. And don' choose place that have many trees,people or other obstacles.
You can search for open site on the website to practice. When your skill have high level, you can set arch to practice operations, and also to plan the special flight routes to increase the difficulty..
The battery is also the key to experience the fun of flying FPV. At present, most of FPV battery flight time is about 10 to 20 minutes. So in order to flight more long time you can prepare more FPV batteries or choose the best lipo battery brand .
For the battery, I recommend the Tattu FPV batteries, they have a strong burst, high capacity and long flight time. At present, a lot of FPV drone pilots are using their batteries,such as 1300mAh lipo,1050mah lipo and 1800mah lipo battery, and they made outstanding achievements. So, the Tattu battery is worth to recommend and trust.
For beginners, it is very necessary to have a FPV image transmission display device. It is very helpful to determine the flight path, especially the direction control. Visual flight is a kind of training method for masters. So, the video display device is necessary, and the best choice to have high definition VR glasses.
In the FPV drone, the aircraft wheel base is usually used to distinguish the FPV. In addition to the difference in size, the flexibility, speed control, battery capacity and other aspects are different. When the size of wheelbase is large, the load bearing can also be increased, and the battery ,the beginners, the balanced 250 series which has the stable GPS is more suitable, and it is easier to control, so as not to burst.
FPV is a very interesting type of aerial UAV. With goggle glasses, Have a fun of flying FPV.
For RC FPV drone pilots, a good batteries are more important. Today, we will recommend the 4 best deals for FPV battery to you.
These high C rated batteries are useful for Nemesis 240 Mini, Skylark M4-FPV250, Mini Shredder 200, INDY250 PLUS, MOJO 280, HOVERSHIP MHQ2(270),ZMR 250,QAV250, QAV180/210, Emax Nighthawk 250, drone and FPV etc.
1. Stable automatic stacking technology enables single cell capacities of 1300mAh.
3. Superior Japan and Korea Lithium Polymer raw materials.
Tattu batteries provide high quality, reliable power for Nemesis 240 Min, Skylark M4-FPV250,Mini Shredder 200,INDY250 PLUS, MOJO 280, HOVERSHIP MHQ2(270), ZMR 250, QAV250, QAV180/210, Emax Nighthawk 250, drone and FPV etc.
Tattu batteries provide high quality, reliable power for Nemesis 240 Min, Skylark M4-FPV250,Mini Shredder 200,INDY250 PLUS, HOVERSHIP MHQ2(270):,Mini H,QAV250, QAV180/210, Danaus, Vortex 285, Mini H, FLIP FPV FRAME, Emax Nighthawk 250, ZMR 250, HOVERSHIP MHQ2, MOJO 280, drone and FPV etc.
TATTU 1550mAh 4S1P 75C lipo battery packs Max Burst Discharge: Perfectly suited to Vortex, LRC Freestyle V1(270-296) DRONE AND FPV ETC.
1. Stable automatic stacking technology enables single cell capacities of 1550mAh.
FPV battery deals starts on August 19th and ends on August 22nd, and Enjoy up to $50 off FPV Batteries plus $5.00 off on purchase over $98.00, $15.00 off to purchase over $198.00, $30.00 off on purchase over $298.00.
The RC LiPo batteries are Lithium polymer batteries that can be recharged and be re-used in the RC electric components. These batteries can be successfully used in RC planes, RC helicopters, UAV's, and multi-rotor.
The Tattu 12000 mAh battery pack is a very powerful RC LiPo battery which can power electric motors demanding high capacities. It is powered by 12000Mah and is packed with fireproof and vibration-proof materials.
The Tattu battery packs are powered by a stable stacking Automatic cell technology that has a capacity of 12000mAh. It requires a voltage of 22.2 V. The batteries are equipped with over voltage and under voltage alerts. This battery has a much higher capacity than the other contemporary models.
The Tattu LiPo batteries are manufactured under strict industrial quality control measures and are made up of superior quality products. These LiPo batteries have high energy density as per the capacity and weight. This makes the batteries adaptable to different UAV's, and RC helicopters, cars, and boats. Unlike other battery systems, this product has 'no memory effect'.
The batteries have a self-balancing function and a self-discharge mechanism at 100% SOC storage. These batteries are stably discharged simultaneously.
This product from Gens ace and its' partner concerns meets are safety and regulatory standards. They meet the ISO9001, ISO14001, standards and come in secure packages that are fire-proof and vibration-proof.
The LiPo Tattu batteries come with a JST-XH industry standard plug. The plug is compatible with the LiPo chargers for multi copters like DJI S800, S1000, Onyx Star FOX-C8-HD, and Gryphon X8.
The LiPo Tattu batteries are equipped with a computer system battery cell matching process and an automatic procedure. This ensures the products high-quality and stability. These batteries have been specially developed for the UAV and UAS market. They are fully secured battery systems with immense power. The power capacity of this Tattu battery is much higher than the other battery packs of the same size. Their capacity matches the requirements of many mainstream devices like the like DJI S800, S1000, OnyxStar FOX-C8-HD, and Gryphon X.
The LiPo batteries supply uninterrupted power to UAVs and other high-capacity RC electric motors. They are used in applications like social security, video mapping, and aerial photography and GIS services.
Shipping is quick and after sales services are provided in the USA. The product comes with a 90-day warranty.
The Tattu RC LiPo batteries have been developed by Gens Ace. they works on two principles- less is more. 'Less' means low weight, less hassle, and simple designs. 'More' pertains to better quality, battery life and better satisfaction and output. They have brought out the best of their services in this battery pack. It is a professionally designed battery pack for UAVs and other RC long flight planes.
Trust the battery that consistently delivers the dependability and high performance, the Gens ace 50c 2s 5000mah lipo battery has a high-capacity, high-discharge rate that gives you the power and run-time you expect from all Gens ace lipo batteries.
Gens Ace 2S 50C 5000mAh Hardcase LiPo Battery Pack, with a factory installed Deans connector, and it is ideal for all 1/10 scales & 1/8 RC car, etc.
1.Stable automatic stacking technology enables single cell capacities of 5000mAh.
2.The most strict single cell capacity, voltage, resistance, discharge curve matching process.
Thoroughly tested and rated at a continuous 50C, the all-new Gens Ace 5000mah 50C LiPo Hard Pack is perfect for the rigors of on and off road racing. It features improved internal materials, heavy gauge silicon wires, burst of 100C and applies to almost all 1/10 racing with a fast charging of 5C.
I attend competitive racing occasionally, this is a pretty nice battery for the high burst rate, faster and stronger. And also I running on the loose dirt and indoor clay,it has better performing,long lasting battery. I recommend to anyone who wants to reliable battery.
I like this Gens ace battery,it gives me fun, and the Gens ace lipo battery is more and more drivers to widely used . Anyone who wants to have a high-discharge rate battery pack , without hesitation. In other words, whether you need to choose Gens ace lipo battery or not depends on yourself. And finally,wish you have fun.
How to extend battery life and why use frequently can keep the battery best performance?
If the traditional Ni battery is charged for too long, the liquid inside would crystallize. In the way, to maximize the performance, the full charge and discharge are required. However, for the 2 cell Lipo battery, we can charge it whenever we are convenient.
It is a false about the lifespan of lipo battery that we should replace the lipo battery after charged for 300-500 times.
Instead, the factor influenced the lifespan is the charging cycle, and the times of charging will not directly influence the lifespan.
A charging cycle refers to the period from full power to the completely empty power and then fully charged. That does not mean charging for one time, as the following picture shows.
According to the picture, the battery is charged for 20% after the first time 40%. Then, after consumed some power, it is charged by 30% and 20% separately. In the half of this 20% (at the time of 10%), a charging cycle has been finished. And then, the next cycle begins.
For example, the first day, we charge the battery after consumed half of the power, and the second day, we repeat that process. This is just one charging cycle rather than two. Therefore, a cycle may be finished by several times of charging. Every single charging cycle will reduce the power slightly. However, a superior battery can maintain 80% power after many charging cycles. That is why some lipo battery can use normally after two or three years. Certainly, it is also needed that we replace the lipo battery if the lifespan has ended.
The lifespan of lipo battery is commonly 300-500 charging cycle. We set the Q as the power provided by one-time fully discharging. Ignoring the reduction of every charging cycle, the lipo battery can power 300Q-500Q through its lifespan. Accordingly, if we charge the battery after consuming ? power, the battery could be charged for 600-1000 times. (if we charge the battery after consuming 1/3 power, the battery could be charged for 900-1500 times.) we cannot tell the exact number of charging times if we charge randomly. In a word, the total power 300Q-500Q is constant. Therefore, the lifespan is related to the total charging power rather than the charging times. Besides, the difference between the influence of deep charging and discharging and the influence of light charging and discharging to lipo's lifespan is similar.
In fact, light charging and light discharging benefit more to the RC lipo battery. Only when the lipo battery is calibrated by the product has the need to charge and discharge battery deeply. Therefore, we can use the lipo battery for convenience and do not have to concern about the lifespan.
If the lipo battery is used above the regulated temperature (over 35 degree centigrade), the power will continuously decrease, which means the flight time would not be so long. If charged under the high temperature, the battery would be further damaged. It is unavoidable that storing under the high temperature will hurt the battery's quality.
If using below the 4 degree centigrade, you would also find the flight time of the battery has been reduced, and even some original lipo batteries of mobile phones cannot be charged. But, this situation is just temporary. Differ from using in the high temperature, once the temperature gets higher and the molecules inside the battery are heated, the battery would recover to the normal energy.
To maximize the performance of lipo battery, we should use it more often and make the electron flow. If we cannot use the lipo battery frequently, please remember to make a charging cycle and calibrate it (charge and discharge deeply) every month.
Due to the good characteristics, the lipo battery is widely applied in mobile phones, cameras, laptops, cordless telephone, remote control, electronic toys and other electronic devices.
The cathode material of Lithium-ion battery is graphite crystal, and the anode material is Lithium superoxide (LiO2). In the charging process, Li-ion moves from anode to cathode and embeds in the graphite layer. In the discharging process, Li-ion separates from the cathode of graphite crystal and moves to anode. Apparently, Lithium is always appeared as Li-ion rather than Lithium metal in both charging and discharging process. Consequently, this kind of battery is called Li-ion battery, Lipo battery in short.
The advantages of Lipo batteries are small volume, huge capacity, light weight, non-pollution, high voltage of single cell, low self-discharging rate, more cycle times, but its price is comparatively high. Nickel – cadmium battery is gradually being replaced because of the low capacity, serious self-discharging and the pollution to the environment. NI-MH battery (nickel-metal hydride battery) is cost-efficient and eco-friendly, but since its single cell voltage is only 1.2V, it has some restrictions in the application.
1. higher weight-energy rate, volume-energy rate.
2. high voltage. The single cell voltage is 3.6V, which equals to 3 nickel-cadmium battery or NI-MH battery put in series.
4. no memory effect. Lipo battery does not have the so-called memory effect as Lithium-cadmium battery, so there is no need to discharge it before charging.
5. Long lifespan. In the common working condition, the cycle times of charging and discharging is more than 500.
6.charging quickly. 0.5 to 1 time of current can be applied to the charging process, and the charging time can be shortened to 1-2 hours.
8. It is the most advanced "green" battery of the world, because it does not threaten the environment and does not have the heavy metal element like cadmium, lead or mercury.
9. high cost. Compared with other kinds of batteries, the Lipo battery is more expensive.
The internal structure of Lipo battery.
Lipo battery is often divided into cylinder and rectangular.
The internal structure is spiral, which puts a very precise and highly permeable polyethylene film between cathode and anode as a partition. The anode consists of the Li-ion collector made in Lithium and CoO2 and the current collector made in aluminum film. The cathode consists of Li-ion collector made in Carbon sheet materials and current collector made in bronze film. The battery is filled with organic electrolyte solution. Besides, there are safety valve and PTC component protecting the battery in the abnormality or short out.
The voltage of single cell is 3.6V, which is not the infinite capacity. Therefore, it is common to put the single li battery in series or in parallel to meet any demands.
1. The charging of Li battery: according to the structural characteristics, the maximum charging voltage of li battery is 4.2V. Over charging is prohibited as the battery would be damaged if the Li-ion from anode is taken too much. The charging and discharging process are demanding, so we can use the professional constant current, constant voltage charger. When the battery's voltage reaches 4.2V in the constant current charging mode, the battery would be charged in the constant voltage mode. And when the current lowers the 100 mA, it should be stop charging.
There are protecting plates in the internal Lipo battery group, so just control the external charging and discharging current.
The protective circuit of two cells consists of the two field-effect tube and dedicated protective manifold block; overcharging control valve and over discharging control valve are in the circuit in series, which is supervised and controlled by the protective IC. When voltage reaches up to 4.2V, the overcharging protective tube stops and charging ends. To avoid mistakes, delayed capacitance is added to external circuit. In the discharging process, when the voltage becomes 2.55V, over discharging control valve stops charging the load. Over-current protection is that stops discharging the load when large current flows across the load, which aims at protecting battery and field-effect tube. Over-current test is to use the on resistance of field-effect tube as the test resistance and supervise the voltage drop, stopping charging when exceed the set value. There is delayed circuit in the circuit to differ the surge current and short-circuit current. That circuit has complete function, reliable performance. It is professional and the manifold block cannot be purchased easily, so the amateurs are hard to fabricate.
Lipo batteries often refer to the polymer lithium batteries. According to the electrolyte materials, Li-ion battery is divided into liquid lithium ion battery and polymer lithium battery or plastic lithium battery. Do you know what are the difference between li-ion and li-polymer battery? Let us review these common senses with Gens Ace.
1. It would not leak the electrolyte, since it uses the colloidal solid rather than the liquid electrolyte.
2. It can be made into thin battery. For example, a 3.6V 400mAh 15C battery can have the thickness of 0.5mm.
3. It can be designed into multiple shapes.
4. The battery can distort and be flexible. The macromolecule battery can distort up to 900 around.
5. It can be made into single high voltage: the battery with liquid electrolyte can only acquire the high voltage and macromolecule battery by putting several batteries in series.
6. Because the battery itself does not have liquid, it is possible to obtain high voltage by making multi-layer combination inside the single battery.
7. The capacity is twice as that of the Li-ion battery.
The factor influenced the lifespan is the charging cycle, and the times of charging will not directly influence the lifespan.
The lifespan of lipo battery is commonly 300-500 charging cycle. We set the Q as the power provided by one-time fully discharging. Ignoring the reduction of every charging cycle, the lipo battery can power 300Q-500Q through its lifespan. Accordingly, if we charge the battery after consuming power, the battery could be charged for 600-1000 times. (if we charge the battery after consuming 1/3 power, the battery could be charged for 900-1500 times.) we cannot tell the exact number of charging times if we charge randomly. In a word, the total power 300Q-500Q is constant. Therefore, the lifespan is related to the total charging power rather than the charging times. Besides, the difference between the influence of deep charging and discharging and the influence of light charging and discharging to lipo's lifespan is similar.
In fact, light charging and light discharging benefit more to the lipo battery. Only when the lipo battery is calibrated by the product has the need to charge and discharge battery deeply. Therefore, we can use the lipo battery for convenience and do not have to concern about the lifespan.
If the 2 cell lipo battery is used above the regulated temperature (over 35 degree centigrade), the power will continuously decrease, which means the flight time would not be so long. If charged under the high temperature, the battery would be further damaged. It is unavoidable that storing under the high temperature will hurt the battery's quality.
Can't wait for Toppilot? Please check out the R-Line!
Good news! For those who can't wait to get through the process of applying a free Toppilot battery, please look forward to our R-Line professional FPV racing batteries.
R-Line is a brand new product line specifically designed for professional FPV racing competitions. It's the selling version of Toppilot batteries.It's also a subsidiary of the Tattu brand. It's got higher capacity, lower internal resistance and lower landing temperatures. They are remarkably more powerful than other graphene batteries. Generally, R-Line batteries have the same specs as our popular Toppilot batteries.
At the moment R-Line includes two items: the 1300mAh 4S 95C and the 1550mAh 4S 95C. R-Line is currently in version 1.0. In the future different versions will also be rolled out to meet the needs of different FPV racing competitions.
R-Line batteries are schedule to be on sale since late August. You will be able to order them from our official shop www.genstattu.com. Due to the high demand R-Line will possibly be available for pre-order. Please follow us on Facebook or Instagram and check back regularly.
1. To choose has "national exemption" "Chinese famous brand" marks of the battery products and local famous brand products, that have the quality guarantee. Such as Gens ace&Tattu RC lipo battery.
2. According to requirement of the electrical appliances, to choose the battery type and size, and also according to the size of the electrical appliances power consumption and characteristic, to purchase the fit battery.
3. Check the battery of the production date and shelf life, to choose the new battery, the new battery has better performance.
4. Check the battery of appearance, should to choose and buy the 15c battery of package exquisite,look neat and clean and no leakage.
5. Pay attention to the battery marks, shall identify the manufacturer name, polarity, type, nominal voltage, trademark and others on battery. On the sales packaging, shall have the address, production date and shelf life or indicate shelf life of deadline, execution of the standard number. When buying the ALKALINE zinc manganese battery should has the "ALKALINE" or "LR".
6. Due to mercury in battery is harmful to the environment, in order to protect the environment, when you purchase the battery should has trademark with "no mercury" "0% mercury" "no contain mercury".
1. Keep the clean between electrical and battery contact parts, wipe with wet cloth when necessity, after drying according to the polarity marked loaded correctly. It's very important things when install the battery should to see clearly the battery polarity, we should be according to the requirement of electrical appliances manual installation using the recommended battery; If not,maybe lead to failure, and damage the electrical appliance or battery.
2. Don't mix of the old and new batteries, should be replaced them at the same time. And don't mix the same type but different brand of batteries, or you will make a set of some batteries in the battery over discharge in use, thus increasing the battery of leakage possibility.
3. Don't heat or charge for disposable batteries, otherwise the possibly explosion.
4. Don't short circuit, to avoid the battery leakage and heat by damage to the insulating outer packing.
5. Remove the battery when you don't use the electrical appliances for a long time, and after used should turn off the power, lest make the batteries continue to discharge its internal battery adverse chemical reaction and lead to leaks.
6. Don't discarded the wasted battery, as far as possibly to separated with other rubbish.


This article examines the relationship between monuments and publics, using Karin Barber's model of how texts interact with publics, which draws on the Bakhtinian notion of addressivity. Two monuments associated with the Yezidi community, Armenia's largest minority, are considered here. Both are of recent construction – one sacred, the shrine at Shamiram, and the other secular, the monument to Cahangir Agha, a hero of the battle of Sardarabad. These are set in the context of former Soviet and Armenian discourses; responses to them vary considerably between different constituencies. Barber's approach highlights the monuments' role in processes of convocation and interpellation which highlight the interplay of speech and non-verbal genres within discourses of memory in general.


Tremendous Motif - George Perez Crafted with support from Edward Turner, Frank Miller, Dennis Collins, Gregory Collins, Paul Turner, Donald Jackson, Anthony Hall, Kevin Clark, Stephen Jackson, Nicholas Clark, Andrew Wright, Andrew Jones, Jeffrey Parker, Andrew Anderson, Joseph Lopez, Stephen Allen, Dennis Martin, Alexander Parker, Daniel Martin, George Carter.
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Gas pressure regulators with filter.
The R... type products are pressure regulators for gaseous media, suitable for all types of gas consuming systems.
RF is a regulator with an integrated 30-micron filtering element.
All models are equipped with compensation diaphragm to assure high accuracy and are designed to perform lock-up function.


text:
Q: Ensuring access to an include.php file in all enviroments This question is about using PHP 'include' files in development and production environments.
Assume that the development system root folder is www.development.com/myprogram . Also assume that there is an 'inc' subfolder that contains an include.php  file (it would be in www.development.com/myprogram/inc ). There are pages in the development site like www.development.com/myprogram/index.php and www.development.com/myprogram/subfolder1/thispage.php.
All pages, not matter where their location, need to 'include' the /inc/include.php file.
And, the production site root folder is www.production.com . So a page on www.development.com/myprogram/subfolder1/thispage.php on the development site will correspond to www.production.com/subfolder1/thispage.php .
How best to ensure that the inc/include.php file is available to all pages, on the www.development.com and www.production.com sites? Assume that  the app might be installed anywhere, not just in the root folder of a site.

A: Simply use relative file paths with __DIR__ magic constant:
In index.php:
include __DIR__ . '/inc/include.php';

In subfolder1/thispage.php:
include __DIR__ . '/../inc/include.php';

redpajama_set_name: RedPajamaStackExchange


text:
Around Washington
Everything Bigfoot
Statehouse Gifts
Home Books Rosa Franklin: A life in Health Care, Public Service and Social Justice
Rosa Franklin: A life in Health Care, Public Service and Social Justice
Rosa Franklin was the first Black woman elected to the Washington State Senate. She served one term in the House of Representatives from 1991-1993. She was appointed to the Senate in 1993 and was subsequently re-elected by the people of the 29th District. She served in the Senate until 2011. During this time, she also served as President Pro Tempore of the Senate. A long-time resident of Tacoma, Ms. Franklin made her living as a registered nurse before being elected to the Legislature. This oral history explores the life and career of a local trailblazer. By Tamiko Nimura.
Weekends and Holidays: 11 am to 4 pm
Native American Heritage Day
(the Friday after Thanksgiving)
Southeast corner of the Legislative Building
416 Sid Snyder Ave. SW #106
Map Of Capitol Campus
Parking and driving directions
Copyright © 2021 Legislative Gift Center.

redpajama_set_name: RedPajamaCommonCrawl


Welcome to the New Bridgeport Apostolic website. Lots of good and powerful changes are right around the corner.
They say, "If you don't stand for something, you'll fall for anything."
We're not all about "cannots", we are about the "can-dos".
Find out what we DO believe!
Helpful links to some favorite links.


I have recently moved to Netherlands. So i would like to help with the CoinFest2017 as well.
Cool, there will probably be two events there, actually, and one in Arnhem. It's still a ways away, so the others aren't talking about it on the forum, yet.
Well i am currently living in Wageningen. So i can travel some distance for the events.
Would be awesome for you to come to CoinFestUK! You were instrumental in the amazing designs at the last event (and this time if you are free)!
Plans are coming along and when details are finalised I'll post updates here. We have signed some new speakers and sponsors which is great news.


This edition of Columbine by Norman Lindsay has a image size is 21.8×21.5cm. it was also sold as a Folio set with Your Fate.
Norman Lindsay's Columbine and Your Fate folio set of Facsimile Etchings were released in 2005. the original Etching of Columbine was published in 1920.
The Facsimile folio set contains as well as the two Facsimile Etchings, a brochure with details of the two books Colombine and The Etchings of Norman Lindsay in which the original etchings of Columbine and Your Fate are included and also the essay 'The Craft of Etching' by Norman Lindsay.


From the Eternal Flames™ collection a Pure White 18 karat Canadian Certified Gold princess cut Canadian diamond engagement ring with diamond shoulder.
The Eternal Flames™ collection. From that initial spark that you felt on your first date, to that roaring fire that rages in your heart now, the Eternal Flames Collection captures all those feelings. For fire in our Elements of Love series distinctive metal wires swerve upwards to hold the Canadian centre diamond.


Question on the WorkAngle Map, there are 16 sets which are for the changing air flows, is 1 the lowest or the highest air flow. The example curve has the greatest advance at air flow 1 and lowest at flow 16, note that I am setting the curve for a carb slide which is directly linked to the throttle and not a CV carb so at low revs if you open the throttle to WOT the air speed will drop, the mixture weakens and you risk pinking.
Also I can only seem to be able to edit one named table called tunable set, how do I get to edit all the named tables, if I go into 4 Functions and select different named tables for gasoline and gas when I then select edit tables it still only gives me the same table regardless and the Table set name reverts to the first one I renamed from tunable set. Got that sorted mostly, by going to Firmware data and reading Flash from Secu-3 I could then edit the tables for the 4 named tables and the names for the tables.
N1 is small "air flow". Used if engine conditions near to idle. Corresponds to small pressure in the intake manifold.
N16 is big "air flow". Used if you sharply open throttle. Corresponds to the maximum pressure in the intake manifold.
There are two parameters on the "4: Functions" tab. Upper and lower pressure. These two parametets map pressure range onto 1...16 "air flows".
Next. There are five sets of curves. First four can only be edited from "Firmware data" tab: read firmware, edit, write back. Also you can edit names here (click on set name in the list and it becomes editable).
Last (5-th) set can be edited in real time, it stored in the EEPROM.
That is fine, I know what to edit the tables too now, looks like I will need to play around with the low air flow settings, reading up it is normal to advance timing at low pressures but I will test the engine running at low revs and large throttle openings and see what the pressure reading is when its pinking and retard the timing accordingly and retest until I get rid of the pinking. I will start with the N16 being the current std timing curve and add advance as the number decreases and take it from there.
Yes, so, another words, pressure range is distributed between 16 curves in work ignition timing map. This is some kind of assigning axis values, and nothing else.


TOSS has the best systems, experience, and understanding of our needs. The process and communication was great, all TOSS employees continue to be extremely pleasant to work with.
The TOSS Cloud allows you to utilize the latest technologies, bringing service to your customers without worrying about IT.
I emailed TOSS at 11:34 PM on Saturday night. The issue was being resolved by 11:37 PM. You cannot ask for better service.


text:
\section{Introduction}

The van der Waals picture
\cite{widom, wca, hansen}
is a robust framework for liquids with nontrivial density correlations.
According to this treatment, the harshly repulsive interactions at short distances determine the average relative arrangements of components, and slowly varying long-ranged interactions play a minor role in the liquid structure.
One of well-known prescriptions for the potential separation is the systematic Weeks-Chandler-Andersen (WCA) method
\cite{wca, hansen}
which has been successful for the interaction potentials with minima such as the Lennard-Jones potential.

The WCA separation, however, is not applicable to the Coulomb interaction potential with neither minimum nor a characteristic length. A typical potential form due to the Coulomb interaction between one component charged particles
is given by $\gamma v(r)=\gamma(a/r)$, where $|{\bf r}|=r$, the coupling constant $\gamma=\beta(ze)^2/(4\pi\epsilon\,a)$ is defined by the inverse thermal energy $\beta$, the charge per particle $ze$, the dielectric permittivity $\epsilon$, and a reference length $a$ equal to the Wigner-Seitz radius \cite{review}: $a=(3/4\pi\rho)^{1/3}$ where the concentration of charged particles is given by $\rho=N/V$ with $N$ being the total number of particles and $V$ the system volume. A prototype of the Coulomb systems is the one-component plasma (OCP) \cite{review}, a uniform system of point ions in a neutralizing background, which we will consider here.
This model can in fact be regarded as a limiting case of real matter such as liquid metals, salt-free colloidal dispersions, and so on. The long-range Coulombic nature  of the OCP in the strong coupling (SC) regime satisfying that $\gamma>>1$ leads to the Wigner crystallization with large lattice constant comparable to the wavelength of visible light, which is an underlying cause of photonic crystal formation observed for salt-free colloidal dispersions \cite{warren}.

When we separate the Coulomb potential $\gamma v$ into short- and long-ranged parts, $\gamma v_S$ and $\gamma v_L$, with $v_L$ supposed to have a finite value at zero separation, we have had a choice, as short-ranged contribution $\gamma v_S$, to use a hard core potential with an effective hard-core diameter, an adjustable parameter in the SC regime \cite{review}. In addition to the hard-core type division, there have been other various ad-hoc methods \cite{review, original, weeks_ocp, totsuji, onsager, rosenfeld_lb, brilliantov, frusawa_lb} of the potential separation. In the random phase approximation (RPA), the previous SC theories with various optimized forms of the long-ranged potentials $\gamma v_L$ have provided the internal correlation energy in excellent agreement with simulation results over a wide range of coupling constant $\gamma$ \cite{review, original, weeks_ocp, totsuji, onsager, rosenfeld_lb, brilliantov}.
Moreover, it has been recently demonstrated by use of local molecular field (LMF) theory \cite{weeks_ocp} that the structures of the OCP are related to those of a mimic system with only short-ranged interactions in an external field incorporating a mean-field average of the remaining long-ranged interaction system: the density-density correlation function in the mimic system resembles that of the full Coulomb system.
The successful predictions of previous SC theories for both thermodynamic and structural properties
implies the efficiency of the Coulomb potential separation along the van der Waals picture; however these treatments have not clarified both a criterion for the division of Coulomb potential and a functional-integral form validating the RPA in the SC regime.

In order to verify the van der Waals picture of the strongly coupled OCP, we must thus face the following fundamental questions: (i) What theory forms the basis of separating into two parts the Coulomb potential without characteristic length scales? (ii) Why is the RPA (or the saddle-point approximation), validated so far in the weak coupling regime \cite{samuel, brown, netz_strong}, relevant even to the strongly coupled systems? Our main aim is to provide a solution to these problems by developing a hybrid theory which combines both the liquid state theory and the statistical field theory; essential use is made of both lower bound variational principle, other than the well-known upper bound approach \cite{hansen, frusawa_lb} referred to as the thermodynamic perturbation theory, and strong coupling expansion around saddle-point which can actually be formulated via the standard field-theoretic method, contrary to the statements in the literature \cite{samuel, brown, netz_strong}. In the following, we first establish a variational principle to optimize the potential separation by maximizing the lower bound of the free energy.
Next we present a functional integral form to which the RPA is applicable in the SC regime. Our variational principle offers not only a framework for addressing the above fundamental problems, but also an alternative to deriving the lower bound of internal correlation energy evaluated so far in various ways \cite{review, totsuji, onsager, rosenfeld_lb, brilliantov, frusawa_lb, lieb}. Finally we compare our result of potential separation with that of the LMF theory
\cite{weeks_ocp}.

\section{Outline of the lower bound approach}

To answer the first question described in the introduction, we start with not the upper bound due to the Gibbs--Bogoliubov inequality
\cite{hansen, frusawa_lb},
but the lower bound \cite{hansen} of the true free energy $F\{v\}$ for the OCP with full Coulomb interactions. Taking the long-ranged potential $v_L$ as a reference system potential in the Coulomb separation of $\gamma v=\gamma v_S+\gamma v_L$, we have the inequality for the lower bound $\mathcal{L}\{v_L;h\}$ as a functional of both $v_L$ (or $v_S=v-v_L$) and the pair correlation function $h(r)$ of {\itshape not a reference but a full Coulomb system} \cite{hansen}:
   \begin{equation}
   \frac{\mathcal{L}\{v_L;h\}}{N}=
   \frac{\beta F\{v_L\}}{N}+
   \frac{\gamma\rho}{2}\int_{{\bf r}}h(r)v_S(r)\leq\frac{\beta F\{v\}}{N},
   \label{start}
   \end{equation}
where $F\{v_L\}$ is the free energy of a long-ranged interaction system, $\int_{{\bf r}}$ denotes the integral $\int d{\bf r}$.
Evaluating the free energy $F\{v_L\}$ in the RPA, it will be shown that {\itshape maximization} of the lower bound functional $\mathcal{L}$ with respect to $v_L$ yields
   \begin{equation}
   \fl\qquad\qquad
   \frac{\mathcal{L}_{\mathrm{max}}}{N}\equiv
   \frac{\mathcal{L}\{v_L^*;h\}}{N}=
   \frac{\beta F\{-c/\gamma\}}{N}
   +\frac{\rho}{2}\int_{{\bf r}}h(r)\left[\,
   \gamma v(r)+c(r)
   \,\right].
   \label{max}
   \end{equation}
This means that the optimum potentials, $v_L^*$ and $v_S^*$, are
   \begin{equation}
   \gamma v^*_L=-c;\qquad \gamma v^*_S=\gamma v + c=c_{sr},
   \label{optimum}
   \end{equation}
where $c$ denotes the direct correlation function and $c_{sr}$ corresponds to the so-called short-ranged direct correlation function \cite{evans}. In other words, the long-range part $\gamma v^*_L$ of Coulomb potential satisfies the Orstein-Zernike (OZ) integral equation \cite{hansen}:
   \begin{equation}
   h(r)=-\gamma v^*_L(r)-\rho\int_{{\bf r}'}
   \gamma v_L^*(|{\bf r}-{\bf r}'|)h(r').
   \label{oz}
   \end{equation}
Using diagrammatic analysis, the exact closure to the OZ equation is expressed as
   \begin{equation}
   g(r)=\exp\left[
   -\gamma v(r)+\gamma v_L(r)+h(r)-b(r)
   \right],
   \label{closure}
   \end{equation}
where the radial distribution function $g(r)$ is defined by $g=1+h$ and the bridge function $b(r)$ denotes the negative of the sum of elementary diagrams \cite{hansen}.

The relations (\ref{start}) to (\ref{optimum}) state that the variational approach for the lower bound functional $\mathcal{L}\{v_L;h\}$ provides a first principle for separating the Coulomb potential. A question still remains whether the real density correlations represented by $h(r)$ are mimicked by the short-ranged system with the interaction potential $c_{sr}$. Let $F_{sr}=F\{v\}-F\{-c/\gamma\}$ and $F\{c_{sr}/\gamma\}$, respectively, the short-ranged contribution to the full free energy and the mimic free energy associated with short-ranged system. In the RPA of the long-ranged contribution, the mimic free energy $F\{c_{sr}/\gamma\}$ is identified with $F_{sr}$, giving
   \begin{equation}
   \frac{\beta F\{c_{sr}/\gamma\}}{N}=\frac{\beta F_{sr}}{N}\approx \frac{\rho}{2}\int_{{\bf r}}h(r)c_{sr}(r)
   \label{mimic}
   \end{equation}
in the approximation, $\beta F_{sr}\approx\mathcal{L}_{\mathrm{max}}-\beta F\{v_L\}$. Equation (\ref{mimic}) leads to
   \begin{equation}
   \frac{2}{N}
   \frac{\delta \beta F\{c_{sr}/\gamma\}}{\delta c_{sr}}
   =\rho h(r),
   \label{correlation_ocp}
   \end{equation}
indicating that the mimic system with only short-ranged interaction potential, $\gamma v^*_S$, can reproduce the pair correlation function $h(r)$ of full Coulomb system in line with the van der Waals picture.

\section{Strong Coupling Approximation of the OCP}

All of the discussions made in the previous section have relied on the RPA, though the RPA has not been verified in the SC regime: while previous field theories have formulated the RPA only in the weak coupling regime $\gamma<<1$
\cite{samuel, brown, netz_strong},
strong coupling theories have successfully used the RPA without the field-theoretic justification
\cite{review, totsuji, onsager, rosenfeld_lb, brilliantov}.
We then reveal below the underlying functional integral form behind the RPA in the SC regime.

For later convenience, we introduce the free energy functional $\mathcal{A}\{v_L\}$ including the self-energy via the expression:
   \begin{equation}
   \fl\qquad\qquad
   \beta F\{v_L\}=\beta\mathcal{A}\{v_L\}-\frac{\gamma v_L(0)}{2}
   \ln\left<
   e^n\right>
   =\beta\mathcal{A}\{v_L\}-
   \frac{\gamma v_L(0)}{2}N,
   \label{def_A}
   \end{equation}
with the bracket denoting the average as follows: $<\mathcal{O}>=\mathrm{Tr}\,\mathcal{O}e^{-\gamma U\{v_L\}}/\mathrm{Tr}\,e^{-\gamma U\{v_L\}}$, where $\mathrm{Tr}\equiv\sum_{n=0}^{\infty}(z^n/n!)\,\int_{{\bf r}_1\cdots{\bf r}_n}$, $z$ the activity, and the total electrostatic interaction energy $U\{v_L\}$ includes the self-energy of ions. In the last equality in eq. (\ref{def_A}), use has been made of the relation: $\left<\e^n\right>=e^{\left<n\right>}=e^N$. The interaction energy $\gamma U\{v_L\}$ is expressed as
   \begin{eqnarray}
   \gamma U\{v_L\}=\frac{\gamma}{2}\int_{{\bf r}_1{\bf r}_2}
   \delta\hat{\rho}_1\,v_L(r_{12})\,\delta\hat{\rho}_2
   \label{interaction},
   \end{eqnarray}
setting for abbreviation that $\delta\hat{\rho}({\bf r})=\hat{\rho}({\bf r})-\rho$, $\hat{\rho}({\bf r})=\sum_i\delta({\bf r}-{\bf r}_i)$, $\delta\hat{\rho}_1=\delta\hat{\rho}({\bf r}_1)$ and $r_{12}=|{\bf r}_1-{\bf r}_2|$. Along the Hubbard-Stratonovich transformation
\cite{samuel, brown, netz_strong}, we rewrite eq. (\ref{interaction}) as
   \begin{eqnarray}
   e^{-\gamma U\{v_L\}}&=&\frac{1}{\mathcal{N}}\int_{\phi}e^{-\gamma S_0\{\phi\}+\gamma\int_{{\bf r}}i\phi({\bf r})\left\{\hat{\rho}({\bf r})-\rho\right\}}\nonumber\\
   S_0\{\phi\}&=&\frac{1}{2}\int_{{\bf r}_1{\bf r}_2}
   \phi_1\,
   v_L^{-1}(r_{12})\,
   \phi_2
   \nonumber
   \end{eqnarray}
with $\mathcal{N}=\int_{\phi}e^{-S_0\{\phi\}}$. Consequently, we obtain the functional integral form of $\mathcal{A}\{v_L\}$:
   \begin{eqnarray}
   &&e^{-\beta \mathcal{A}\{v_L\}}=\frac{1}{\mathcal{N}}\int_{\phi}\exp\left(-\gamma S\{\phi\}\right)\nonumber\\
   &&\gamma S\{\phi\}=\gamma S_0\{\phi\}+\gamma\rho\int_{{\bf r}}i\phi({\bf r})
   -z\int_{{\bf r}}e^{\gamma i\phi({\bf r})}.
   \label{fieldstart}
   \end{eqnarray}
Since the action $\gamma S\{\phi\}$ is proportional to the coupling constant $\gamma$, our functional integral form verifies that the perturbation expansion around the saddle-point satisfying that $\delta S/\delta\phi|_{\phi=i\phi^*}=0$ is allowed to use in the SC regime.

Before proceeding, let us compare the present action $\gamma S\{\phi\}$ with the previous one for the weak coupling regime \cite{netz_strong}: $\gamma^{-1}S'\{\psi\}=\gamma^{-1}S_0\{\psi\}-\rho\int_{{\bf r}}i\psi({\bf r})-ze^{\gamma v_L(0)/2}\int_{{\bf r}}e^{-i\psi({\bf r})}$ where $v_L$ should be replaced by $v$ and elimination of the self-energy is considered in the last exponent on the right hand side
\cite{netz_strong} other than our treatment in eq. (\ref{def_A}).
The comparison indicates that our statistical field theory has introduced a normalized field $\phi=-\psi/\gamma$ instead of the standard potential field $\psi$. Our selection of potential variable is indispensable for picking up inherent fluctuations from $\psi$ whose variations multiplied by $\gamma$ are amplified extremely in the SC regime.

The saddle-point equation, given by $\delta S/\delta\phi|_{\phi=i\phi^*}=0$, reads
   \begin{equation}
   \phi^*({\bf r}_1)=\int_{{\bf r}_2}v^*_L(r_{12})
   \left[
   ze^{-\gamma\phi^*({\bf r}_2)}-\rho
   \right].
   \label{mf_uniform}
   \end{equation}
The prefactor $\gamma$ appearing in the exponent leads to the exact solution in the SC limit: we obtain that $\lim_{\gamma\rightarrow\infty}\phi^*\equiv 0$ and $z=N/V=\rho$; otherwise there are no self-consistent solutions, because the above term, $e^{-\gamma\phi^*}$, goes to zero for $\phi>0$ and diverges for $\phi<0$ in the limit $\gamma\rightarrow\infty$. While eq. (\ref{mf_uniform}) holds in the SC regime $\gamma>>1$, the expression is identified with the Poisson-Boltzmann equation valid in the weak coupling regime $\gamma<<1$ \cite{netz_strong} if $\phi^*$ and $v_L^*$ are replaced by $\psi/\gamma$ and the full potential $v$, respectively. The availability of the saddle-point equation in both the strong and weak coupling regimes seems to be one of the reasons for the success so far of the RPA, or the saddle-point approximation, in the intermediate regime \cite{review, original, weeks_ocp, totsuji, onsager, rosenfeld_lb, brilliantov}.

Let us write $\phi=i\phi^*+\chi/\gamma$ to expand $S\{\phi\}$ around the saddle point $\phi^*=0$. In the RPA, we find from eqs. (\ref{def_A}) to (\ref{fieldstart}) that the long-ranged contribution $F\{v_L\}$ to the free energy is of the form:
   \begin{eqnarray}
   \beta F\{v_L\}=\gamma S\{i\phi^*=0\}-\ln
   \frac{1}{\mathcal{N}}
   \int_{\chi}
   \exp\left[-\Delta S\{\chi\}\right]-\frac{N\gamma}{2}v(0),
   \label{rpa}
   \end{eqnarray}
where the first term $\gamma S\{0\}$ on the right hand side corresponds to the mean-field free energy, and the quadratic action $\Delta S\{\chi\}$ in the second term is associated with the expansion for the last term on the right hand side of eq. (\ref{fieldstart}) such that $e^{\gamma i\phi}=e^{-\gamma\phi^*+i\chi}=e^{-\gamma\phi^*}(1+i\chi-\chi^2/2)$, giving
   \begin{equation}
   \Delta S\{\chi\}=\frac{1}{2\gamma}
   \int_{{\bf r}_1{\bf r}_2}\chi_1\left[v_L^{-1}(r_{12})+\gamma\rho \delta(r_{12})\right]\chi_2.
   \label{quadratic}
   \end{equation}
Combining eqs. (\ref{start}), (\ref{rpa}) and (\ref{quadratic}), we obtain
   \begin{equation}
   \fl\quad
   \frac{\mathcal{L}\{v_L;h\}}{N}
   =-\frac{\gamma v_L(0)}{2}-\frac{\rho\gamma}{2}\int_{{\bf r}}v_S(r)
   +\frac{\rho\gamma}{2}\int_{{\bf r}}g(r)v_S(r)
   +\frac{1}{2\rho}\int_{{\bf k}}\ln\left[1+\rho\gamma \tilde{v}_L(k)\right],
   \label{lower_functional}
   \end{equation}
where we have used the relation $h(r)=-1+g(r)$ and $\tilde{v}_L(k)$ denotes the Fourier transform of the interaction potential $v_L$. The maximum condition on the lower bound functional $\mathcal{L}$ is the functional differentiation of $\mathcal{L}\{v_L;h\}$ given by eq. (\ref{lower_functional}) with respect to $v_L$:
    \begin{equation}
    \left.
    \frac{\delta\mathcal{L}}{\delta v_L}\right|_{v_L=v_L^*}=0,
    \label{stationary}
    \end{equation}
yielding the OZ equation (\ref{oz}) within the RPA \cite{rosen_oz}. When we consider higher order terms beyond the RPA, we can evaluate from eq. (\ref{stationary}) correction potential to minus the direct correlation function $\gamma v_L^*=-c$ of long-ranged part optimized within the RPA. To be noted also, the second functional derivative of $\mathcal{L}$, arising from the logarithmic term on the right hand side of eq. (\ref{lower_functional}), has a negative sign, which proves that the maximum lower bound is located at the stationary point satisfying eq. (\ref{stationary}).

A set of our self-consistent equations is now complete by combining the OZ equation (\ref{oz}) (or eq. (\ref{stationary}) in the RPA), closure relation (\ref{closure}) and the saddle-point equation (\ref{mf_uniform}), which are the three simultaneous equations with three parameters: $\phi^*({\bf r})$, $v_L(r)$ and $h(r)$.

\section{An alternative to the lower bound of internal correlation energy}

Let us relate the best lower bound of internal correlation energy $e_L$ per particle in the SC limit to the optimized lower bound functional $\mathcal{L}_{max}$ of the free energy via the inequality:
   \begin{equation}
   e_L\leq\lim_{\gamma\rightarrow\infty}\frac{\gamma}{N}\left(
   \frac{\partial\mathcal{L}_{max}}{\partial\gamma}
   \right).
   \label{to_energy}
   \end{equation}
We demonstrate below that eq. (\ref{to_energy}) provides an alternative approach to the lower bound obtained so far \cite{review, totsuji, onsager, rosenfeld_lb, brilliantov, frusawa_lb, lieb}. Since the last term on the right hand side of eq. (\ref{lower_functional}) yields a negligible term in the SC limit, we obtain
   \begin{equation}
   \fl\qquad\quad
   \lim_{\gamma\rightarrow\infty}\frac{\gamma}{N}\left(
   \frac{\partial\mathcal{L}_{max}}{\partial\gamma}\right)
   =\frac{c(0)}{2}-\frac{\rho}{2}\int_{{\bf r}}\left[\,
   \gamma v(r)+c(r)\,\right]+\frac{\rho}{2}\int_{{\bf r}}g(r)\left[\,
   \gamma v(r)+c(r)\,\right]
   \label{limit_functional}
   \end{equation}
where use has been made of the relation $\gamma(\partial c(r)/\partial \gamma)=c(r)$ following the approximate solutions known in the liquid state theory \cite{onsager, rosenfeld_lb, evans}. The relations (\ref{to_energy}) and (\ref{limit_functional}) with the inequality $g(r)\geq 0$ lead to
   \begin{equation}
   e_L=\frac{c(0)}{2}-\frac{\rho}{2}\int_{{\bf r}}\left[\,
   \gamma v(r)+c(r)\,\right],
   \label{lower_energy}
   \end{equation}
which is in agreement with that derived in terms of the liquid state theory \cite{onsager, rosenfeld_lb, evans}. In either the soft mean spherical approximation (SMSA) or the hypernetted--chain (HNC) approximation of the closure relation (\ref{closure}), eq. (\ref{lower_energy}) has been found to give the lower bound \cite{onsager, rosenfeld_lb, evans} which is identical or quite similar to the Lieb-Narnhofer bound \cite{review, onsager, frusawa_lb, lieb} obtained from the ionic sphere model, or the Onsager ball model.

We would like to also note the connection between the lower bound functional and the correlation functional of free energy derived in the liquid state theory \cite{morita}. It is easy to check that the lower bound functional in the RPA is identified with the correlation functional in the SMSA. Since we have that $\int_{{\bf r}}g(r)[\gamma v(r)+c(r)]=0$ in the SMSA, it follows from eq. (\ref{lower_functional}) that
   \begin{equation}
   \frac{\mathcal{L}_{max}}{N}=\frac{c(0)}{2}-\frac{\rho}{2}\int_{{\bf r}}
   \left[\gamma v(r)+c(r)\right]
   +\frac{1}{2\rho}\int_{{\bf k}}\ln\left[1-\rho\tilde{c}(k)\right]
   \end{equation}
which is nothing but the SMSA functional \cite{onsager, rosenfeld_lb}. In the HNC approximation, on the other hand, the bridge function $b(r)$ in eq. (\ref{closure}) is ignored, reducing to the closure $\gamma v+c=c_{sr}=h-\ln g$. In the quadratic expansion of $\ln g\approx h-(h^2/2)$ valid for $|h|<<1$, the approximate HNC equation reads $\gamma v+c=c_{sr}\approx h^2/2$. We plug the approximate equation only into the integral $\int_{{\bf r}}g(r)[\gamma v(r)+c(r)]$ while leaving the integral $\int_{{\bf r}}\gamma v(r)+c(r)=\int_{{\bf r}}h(r)-\ln g(r)$, because the effective exclusion zone satisfying that $g(r)=0$ (or $h(r)=-1$), the main contribution to the latter integration, is irrelevant to the former. We thus have that $\int_{{\bf r}}g(r)[\gamma v(r)+c(r)]\approx(1/2)\int_{{\bf r}}h^2(r)+\mathcal{O}[h^3]$, arriving at the HNC functional form \cite{rosenfeld_lb}:
   \begin{equation}
   \fl\qquad\quad
   \frac{\mathcal{L}_{max}}{N}\approx\frac{c(0)}{2}-\frac{\rho}{2}\int_{{\bf r}}
   \left[\gamma v(r)+c(r)\right]
   +\frac{\rho}{4}\int_{{\bf r}}h^2(r)
   +\frac{1}{2\rho}\int_{{\bf k}}\ln\left[1-\rho\tilde{c}(k)\right].
   \end{equation}
Thus, we have seen that the present formulations based on the lower bound variational principle are consistent with previous forms of the conventional liquid state theory in the whole coupling range.

\section{Comparison with the LMF theory}

The LMF theory constitutes the potential separation, $v=v_S+v_L$, and the self-consistent LMF equation for the effective external field incorporating the long-ranged part \cite{weeks_ocp}.
The LMF simulations
\cite{weeks_ocp}
solve the LMF equation combined with Monte Carlo simulations of the short-ranged interaction system in the external field obtained from the LMF equation.
The mean-field equation (\ref{mf_uniform}) obtained here coincide with the LMF equation in the low density approximation named mimic Poisson-Boltzmann approximation \cite{weeks_ocp} when we change the variable as $\phi^*\rightarrow\psi/\gamma$.

        \begin{figure}[hbtp]
        \begin{center}
	\includegraphics[bb=50 0 612 430,clip,width=8cm]{separation.eps}
	\end{center}
	\caption{Separation of the full Coulomb potential $v(x)=1/x=a/r$ at $\gamma=140$ in three ways. While the long-raged potentials converge to the full potential, the short-ranged remainders go to zero within the present x-range. Our separations in two approximations, HNC approximation and SMSA, are close to each other but deviated from the LMF division.}
       \end{figure}

Figure 1 compares the potential separations of the OCP at $\gamma=140$: the LMF division that $v_L^*(r)=\mathrm{erf}(x/1.4)/x$  with $x=r/a$
\cite{weeks_ocp}
and ours taking two typical approximate solutions of $c(r)$ and $c_{sr}(r)$; while the explicit form of the solution in the HNC approximation has been found to be $-c(r)/\gamma=v_L^*(r)=\mathrm{erf}(1.08x)/x$
\cite{ng},
the other solution $-c(r)$ in the SMSA has a complicated expression of the MSA type for $x<1.33$ and is simply equal to $\gamma v(r)$ for $x\geq 1.33$ where we evaluated the crossover separation $x=1.33$ from imposing the continuity of the pair correlation function
\cite{rosenfeld_lb, evans}.
All curves of short-ranged and long-ranged potentials are cut off at longer and shorter distances, respectively; however, there is a quantitative difference between those of the LMF theory and ours though the LMF separation has been found to give better results than ours \cite{original, weeks_ocp, ng}. The deviation from the LMF division can be reduced by considering higher order terms of $\mathcal{A}\{v_L\}$ beyond the RPA, which will be presented elsewhere.

\section{Concluding remarks}

In conclusion, we have verified the applicability of the van der Waals picture to strongly coupled OCP by using the variational principle of the lower bound free energy, a first principle for the Coulomb potential separation which has been done in {\it ad hoc} ways: searching for the maximum lower bound of the free energy within the RPA valid at strong coupling, we found minus the direct correlation function as the optimal long ranged part. Since the direct correlation function has a finite value even at zero separation, the particles can overlap in the long-ranged interaction systems, one of which we have treated here field theoretically. Namely coarse-graining of particle density fields, necessary for constructing statistical field theory
\cite{brilliantov, frusawa_lb, samuel, brown},
is accomplished by introducing direct correlation function as a smeared long-ranged interaction potential \cite{frusawa_lb}, about which systematic discussions such as the non-perturbative renormalization theory
\cite{caillol}
are to be explored. It has also been demonstrated in section 4 that the present variational theory is consistent with the conventional liquid state theory, implying that our lower bound approach applies not only to the OCP but also to any multi-scale systems including inhomogeneous counterion systems in the SC regime \cite{netz_strong, grosberg, netz, weeks_prl}.

\vspace{10pt}
\hspace{-23pt}We are grateful to K. Miyazaki for the critical reading of our manuscript. Supported by the Yamada Science Foundation and KAKENHI no. 19031027.

\section*{References}

redpajama_set_name: RedPajamaArXiv


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